ÉTUDE D’UN HALL METALLIQUE AVEC PONT ROULANT ET …

Reacutepublique Algeacuterienne Deacutemocratique et Populaire

Ministegravere de lrsquoEnseignement Supeacuterieur et de la Recherche Scientifique

Universiteacute Aboubakr Belkaid Tlemcen

Faculteacute de Technologie

Deacutepartement de Geacutenie Civil

Meacutemoire pour lrsquoObtention du Diplocircme de Master en Geacutenie Civil

Speacutecialiteacute Construction Meacutetallique et Mixte

Thegraveme

EacuteTUDE DrsquoUN HALL METALLIQUE AVEC PONT ROULANT

ET POTENCE

Preacutesenteacute par

Achouri Abdelhamid Nazih

Moussi Mohammed El Hedi

Devant le jury composeacute de

Preacutesident Pr BOUMECHRA Nadir

Examinateur Dr MISSOUM Abdelghani

Encadreur Dr KAZI TANI Nabil

Anneacutee universitaire 2019-2020

Remerciements

Tout drsquoabord merci au bon dieu de nous avoir accordeacute cette vie

de nous permettre de nous instruire de grandir dlsquoeacutevoluer et de prendre soin des nocirctres

Merci agrave nos parents pour tout tout simplement

Merci agrave notre encadreur Dr KAZI TANI

Nabil il a eacuteteacute pour nous ces derniers mois comme un grand fregravere il nous a assister dans notre travail appris beaucoup de chose et nous a donneacute sans

compter de son temps et de son savoir

Merci agrave Djelti Abdessamad et Merad Sofiane pour leur aide sur diffeacuterents

points de ce modeste travail

AACHOURI et EMOUSSI

Deacutedicace

Je deacutedie ce Modeste travaille

A ma megravere ma raison drsquoecirctre ma raison de vivre la lanterne qui eacuteclaire mon chemin et mrsquoillumine de douceur et drsquoamour

A mon pegravere en signe drsquoamour de reconnaissance et de gratitude pour tous les soutiens et les sacrifices dont il a fait preuve agrave mon eacutegard

Agrave mon cousin ami et fregravere Djelti Abdesamad pour son aide inestimable

Agrave Mr KAZI TANI Nabil qui nous a encadreacute nous a guideacute et nous a tellement appris durant ces derniers mois en partageant avec nous ses astuces ses

retours drsquoexpeacuteriences et son savoir Aucun mot ne pourra deacutecrire son deacutevouement et ses sacrifices encore merci

Agrave tous mes amis en teacutemoignage de lrsquoamitieacute sincegravere qui nous a lieacutees et des

bons moments passeacutes ensemble en particulier mon binocircme Achouri Abdelhamid

Et enfin agrave tous les enseignants qui mrsquoont instruit durant ces cinq derniegraveres anneacutees speacutecialement monsieur Boumechra Nadir le plus deacutevoueacute de tous

Mr Moussi Mohammed El Hadi

Deacutedicace

Je deacutedie ce modeste travail

A mes chers parents pour tous leurs sacrifices leur amour leur tendresse leur soutien et leurs priegraveres tout au long de mes eacutetudes

A toute ma famille qui vit loin de moi pour leur soutien moral tout au long de

mon parcours universitaire

A Mr Kazi Tani Nabil notre encadreur qui agrave toujours eacuteteacute preacutesent pour le suivi pas agrave pas de notre travail ses conseils et sa compeacutetence nous ont beaucoup

appris dans la reacutealisation de ce manuscrit ainsi que dans le monde pratique du geacutenie civil

A tous les enseignants qui mrsquoont tant appris durant mon cursus universitaire

A tous mes amis pour leur appui et leur encouragement speacutecialement agrave mon

binocircme Moussi El Hedi avec qui jrsquoai partageacute des moments inestimables

A tous ceux qui ont contribueacute de preacutes ou de loin pour que ce projet soit possible je vous dis merci

Que ce travail soit lrsquoaccomplissement de vos vœux tant alleacutegueacutes et le fruit de

votre soutien infaillible

MrAchouri Abdelhamid Nazih

Reacutesumeacute

Notre projet de fin drsquoeacutetudes consiste en lrsquoeacutetude et dimensionnement drsquoune halle industrielle avec pont roulant Cet ouvrage destineacute agrave la maintenance drsquoengins meacutecaniques est composeacute de deux halles Il est situeacute dans la commune de Hassi Messaoud Wilaya de laquo Ouargla raquo elle est constitueacute de plusieurs portiques stabiliseacutes par des contreventements et couvert par une toiture agrave quatre versants symeacutetriques Ce projet fut eacutelaboreacute en plusieurs eacutetapes regroupant lrsquoeacutevaluation des charges surcharges et effets des actions climatiques lsquosable et ventrsquo selon le regraveglement Algeacuterien laquo RNV 99 V2013 raquo Le dimensionnement des diffeacuterents eacuteleacutements (principaux et secondaires) ainsi que leurs assemblages en se basant sur les regraveglements Algeacuteriens laquo RPA 99 V 2003 raquolaquo CCM 97 raquo et laquo BAEL 91 raquo Enfin pour notre simulation numeacuterique nous avons eu recours au logiciel laquoROBOT ANALYSIS STRUCTURALraquo Mots cleacutes Charpente meacutetallique - Halle industrielle ndash Assemblage ndash Preacutedimensionnement ndash Pont roulant

ملخص

ن ي يتكون من دراسة وتحجيم قاعة صناعية مع رافعة يتكون هذا العمل لصيانة الأجهزة الميكانيكية من قاعتي وعنا النهائ مشر

ي بلدية حسي مسعود ولاية ورقلة وهو يتألف من عدة أربعة بسقف متناظر من استقرت بواسطة الأقواس ومغطاة أروقةويقع فن

جوانب و ن تقييم الأحمال والحمولات الزائدة وآثار الإجراءات المناخيةوقد تم تطوير هذا المشر ع على عدة مراحل يجمع بي

laquoRNV 99 V2003raquo الرملية و الريحية وفقا للائحة الجزائرية تحجيم مختلف العناصر )الرئيسية والثانوية( فضلا عن تجمعاتها استنادا إلى اللوائح الجزائرية

RPA 99 V 2003 CCM 97 و BAEL 91 laquoROBOT ANALYSIS STRUCTURALraquo ا لمحاكاة الرقمية لدينا استخدمنا وأخي

ي رافعة علوية ndashالتحجيم المسبق ndashتجميع ال ndashالقاعة الصناعية -الكلمات الرئيسية الإطار المعدئن

Abstract

Our project of end of studies is about study and design a building industrial having a travelling crane he consists of two halls located in the commune of Hassi Messaoud Wilaya of laquoOuarglaraquo it is composed of several frames stabilized by bracing and covered by a roof with four symmetrical slopes The work is developed through several stages first of all the assessment of loadings as climate effects under the Algerian climatic rules laquoRNV 99 V2013 raquo and the evaluation of the structural steelrsquos secondary and principal elements according to their resistances then the dynamic analysis study according to the Algerian earthquake codes laquo RPA99 V2003 raquo to choose the bracing system those ensure the stability of the structure then the assemblies are studied by the laquo CCM 97 raquo Finally the foundations are dimensioned according to the code laquo BAEL 91 raquo For the structural analysis laquoROBOT ANALYSIS STRUCTURALraquo Keywords Steel structure ndashAssembly ndash Pre-sizing ndash Industrial hall ndash Overhead crane

Tables des matiegraveres

Chapitre-1 Geacuteneacuteraliteacute et preacutesentation de lrsquoouvragehelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip16

11 Introductionhelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip16

12 Lrsquoeacutetat limite ultime ELUhelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip18

13 Lrsquoeacutetat limite de service ELShelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip18

14 Etude parasismiquehelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip18

15 Lrsquoeffet du venthelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip19

16 Preacutesentation de lrsquoouvragehelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip20

17 Caracteacuteristiques geacuteomeacutetriqueshelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip20

18 Mateacuteriauxhelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip21

181 Acierhelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip21

182 Beacuteton armeacutehelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip22

183 Ferraillages et armatureshelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip22

Chapitre-2 Deacutetermination des charges climatiqueshelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip23


22 Deacutetermination de lrsquoaction du venthelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip23

221 Deacutetermination de la pression aeacuterodynamiquehelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip24

222 Calcul de la pression dynamique de pointe qphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip24

223 Coefficient de pression exteacuterieurehelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip26

224 Coefficient de pression inteacuterieurehelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip31

225 Deacutetermination de la pression statique du venthelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip33

23 Deacutetermination de lrsquoaction de la neigehelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip35

24 Deacutetermination de lrsquoaction du sablehelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip35

25 Charge permanentehelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip36

26 Charge drsquoexploitationhelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip36

Chapitre-3 Dimensionnement des eacuteleacutements secondaireshelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip38

31 Dimensionnement des pannes pour la toiture agrave plusieurs versantshelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip38

311 Fonctionnement de basehelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip38

312 Choix du bardage de couverturehelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip38

313 Redimensionnement des pannes avec IPE200helliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip43

3131 Eacutevaluation des charges et surchargeshelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip43

32 Dimensionnement de lrsquoeacutechantignolehelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip49

33 Dimensionnement des lisses de bardageshelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip51

331 Choix du bardagehelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip51

332 Deacutetermination de lrsquoespacement entre lissehelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip51

333 Le dimensionnement se fait par la condition de limitation de la flegravechehelliphelliphelliphelliphelliphelliphelliphellip53

334 Veacuterification des diffeacuterentes conditions de reacutesistanceshelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip54

34 Dimensionnement des liernes helliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip56

35 Calcul des cheacuteneauxhelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip57

36 Preacutedimensionnement des poteletshelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip59

Chapitre-4 Etude du pont roulanthelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip64


411 Caracteacuteristiques des ponts roulantshelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip65

42 Classification des ponts roulantshelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip66

421 Coefficient et classements des ponts roulants selon CTICMhelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip66

422 Description geacuteneacuterale du calculhelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip66

423 Deacutefinition des chargeshelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip67

424 Calcul des reacuteactions des galets du pont roulanthelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip67

425 Le choix du rail de roulement helliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip69

43 Preacutedimensionnement de la poutre de roulementhelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip70

431 Condition de la flegravechehelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip70

432 Classe du profileacute HEB 300helliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip72

433 Veacuterification de la reacutesistance de la poutre de roulementhelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip74

434 Reacutesistance de lrsquoacircme agrave la charge transversalehelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip75

435 Calcul du support du chemin de roulementhelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip77

Chapitre-5 Etude sismiquehelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip82


52 Analyse de la structurehelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip82

521 Meacutethode de calculhelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip83

522 Calcul de la force sismique totalehelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip83

523 Estimation de la peacuteriode fondamentalehelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip84

524 Meacutethode modale spectralehelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip85

525 Reacutesultat de calcul dynamiquehelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip86

526 Veacuterification de la reacutesultante des forces sismiqueshelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip87

527 Veacuterification de la peacuteriodehelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip87

528 Veacuterification des deacuteplacementshelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip87

Chapitre-6 Veacuterification des eacuteleacutements structurauxhelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip90


62 Veacuterification de la traverse IPE400helliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip90

63 Veacuterification des poteaux (HEA320)helliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip95

64 Veacuterification des eacuteleacutements de stabiliteacutes CAE (120x12)helliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip99

65 Veacuterification des potelets (IPE300)helliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip102

Chapitre-7 Calcul des assemblageshelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip107

71 Introductionhelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip107

72 Assemblage poteau-traverse (HEA320-IPE400)helliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip107

721 Veacuterification de la soudure de la semelle agrave la tractionhelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip109

722 Veacuterification de la soudure de lrsquoacircme au cisaillementhelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip109

723 Deacutetermination des efforts dans les boulonshelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip109

724 Deacutetermination de diamegravetre requis des boulonshelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip110

725 Veacuterification agrave la reacutesistance de lrsquoassemblagehelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip110

726 Veacuterification des boulons agrave lrsquointeraction cisaillement-tractionhelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip110

727 Veacuterification au poinccedilonnement de la semelle du poteauhelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip111

728 Veacuterification de la pression diameacutetralehelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip111

729 Veacuterification de la reacutesistance de lrsquoacircme du poteau dans la zone tenduehelliphelliphelliphelliphelliphelliphelliphellip111

7210 Veacuterification de la reacutesistance de lrsquoacircme du poteau dans la zone comprimeacuteehelliphelliphelliphelliphellip112

7211 Veacuterification de la reacutesistance de lrsquoacircme du poteau dans la zone cisailleacuteehelliphelliphelliphelliphelliphelliphellip113

73 Assemblage Traverse-Traverse (IPE400)helliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip113

731 Veacuterification de la soudure de la semelle agrave la tractionhelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip115



734 Deacutetermination du diamegravetre requis pour les boulonshelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip116





74 Assemblage des paleacutes de stabiliteacute (2L 120x120 X12)helliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip118

741 Veacuterification de la soudure gousset-semelle du poteau agrave la tractionhelliphelliphelliphelliphelliphelliphelliphelliphelliphellip119

742 Veacuterification au cisaillement des boulonshelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip119


744 Veacuterification agrave la reacutesistance du blochelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip120

75 Assemblage Panne-Traverse (Echantignole)helliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip120

751 Reacutesistance des boulons au cisaillementhelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip121

752 Reacutesistance des boulons agrave lrsquoeffort combineacutee traction-cisaillementhelliphelliphelliphelliphelliphelliphelliphelliphelliphellip121

Chapitre-8 Veacuterification des ancrages et calcul de fondationshelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip122

81 Veacuterification drsquoancrage des pieds de poteaux HEA320helliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip122

811 Introductionhelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip122

812 Dimensionnement de la plaque drsquoassisehelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip123

813 Resistance du beacuteton agrave la compressionhelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip123

814 Resistance de calcul agrave lrsquoeacutecrasement du mateacuteriau de scellementhelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip123

815 Calcul de lrsquoaire de la plaquehelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip123

816 Cordon de soudurehelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip124

817 Calcul de la reacutesistance agrave la flexion en preacutesence de lrsquoeffort axialhelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip124

818 Veacuterification de la reacutesistance de tiges drsquoancragehelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip127

819 Reacutesistance de la partie tendue de lrsquoassemblagehelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip128

8110 Resistance agrave la flexion de la plaque drsquoassise (par uniteacute de longueur)helliphelliphelliphelliphelliphelliphelliphellip128

8111 Veacuterification de la reacutesistance en flexionhelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip129

82 Etude des fondationshelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip129

821 Introductionhelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip129

822 Deacutetermination des sollicitationshelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip130

823 Dimensionnement de la semellehelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip130

824 Veacuterification des contrainteshelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip131

825 Veacuterification de la stabiliteacute au renversementhelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip131 826 Deacutetermination des armatures de la semellehelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip131

827 Calcul des longrineshelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip134

828 Veacuterification de la condition de non-fragiliteacutehelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip134 829 Ferraillage transversalhelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip135

8210 Calcul drsquoespacement des cadreshelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip135

Liste des tableaux

Tableau 11 Valeur des coefficients partiels de seacutecuriteacutehelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip18 Tableau 12 Classification des zones sismiqueshelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip19

Tableau 21 Donneacutees relatives au site dimplantationhelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip24 Tableau 22 Leacutegende relative pour les parois verticales (direction V1)helliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip27 Tableau 23 Coefficient de pression exteacuterieur Cpe pour le versant 1 face au vent de toiturehelliphellip28 Tableau 24 Coefficient de pression exteacuterieur Cpe10 pour les parois verticales direction V2helliphelliphellip30 Tableau 25 Coefficient de pression exteacuterieur pour la toiture (direction V2)helliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip 31 Tableau 26 Pressions du vent sur parois verticalhelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip33 Tableau 27 Pressions du vent sur toiturehelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip34 Tableau 28 Pressions du vent sur parois verticalhelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip34 Tableau 29 Pressions du vent sur toiturehelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip35 Tableau 31 Caracteacuteristiques de la section IPE180helliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip41 Tableau 32 Porteacutee maximale de la nervure TL75 en fonction des charges appliqueacuteeshelliphelliphelliphelliphelliphellip44 Tableau 33 Caracteacuteristiques de la section IPE200helliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip46 Tableau 34 Caracteacuteristiques geacuteomeacutetriques du profileacute UPN140helliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip53 Tableau 35 Caracteacuteristiques geacuteomeacutetriques drsquoIPE 300helliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip60

Tableau 41 Caracteacuteristiques du pont roulant (Annexe5)helliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip65 Tableau 42 Caracteacuteristiques geacuteomeacutetriques du pont roulanthelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip66 Tableau 43 Coefficient et classement des ponts roulantshelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip66 Tableau 44 Caracteacuteristiques geacuteomeacutetriques du railhelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip69 Tableau 45 Caracteacuteristiques du profileacute HEB360helliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip71 Tableau 46 Caracteacuteristiques du profileacute HEB400helliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip72 Tableau 47 Caracteacuteristiques du profileacute IPE300helliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip79 Tableau 48 Caracteacuteristiques du profileacute IPE360helliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip80 Tableau 51 Peacutenaliteacutes de veacuterificationhelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip84 Tableau 52 Veacuterification de lrsquoeffort tranchant agrave la basehelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip87 Tableau 53 Tableau des peacuteriodeshelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip87 Tableau 54 Deacuteplacement ultime en situation durablehelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip88 Tableau 55 Deacuteplacement relatif en situation accidentellehelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip89

Tableau 61 Caracteacuteristiques du profileacute IPE400helliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip91 Tableau 62 Caracteacuteristiques du profileacute HEA320helliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip96 Tableau 63 Caracteacuteristiques du profileacute 2CAE (120x12)helliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip100 Tableau 64 Caracteacuteristiques du profileacute IPE 300helliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip103

Tableau 71 Caracteacuteristiques geacuteomeacutetriques du boulon M18helliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip110 Tableau 72 Caracteacuteristiques geacuteomeacutetrique des boulonshelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip116 Tableau 73 Caracteacuteristiques geacuteomeacutetrique des boulonshelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip118

Tableau 81 Caracteacuteristique de boulon M30helliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip125 Tableau 82 Ferraillage choisis pour la semelle au-dessous de poteauhelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip133

Listes des figures Figure 11 Notre structure est preacutesente agrave Hassi Messaoud dans la wilaya de Ouarglahelliphelliphelliphelliphelliphelliphellip19 Figure 12 Zone de Ouargla (RPA)helliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip20 Figure 13 Vue sur pignon de lrsquoouvragehelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip21 Figure 14 Vue en perspective de la structurehelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip21

Figure 21 Repreacutesentation et deacutenominations des directions du venthelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip23 Figure 22 Leacutegende relative pour les parois verticale (direction V1)helliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip26 Figure 23 Leacutegende relative pour les parois verticale (direction V1)helliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip27 Figure 24 Leacutegende pour les toitures agrave versant multiple (directionV1-V3)helliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip28 Figure 25 Leacutegende pour les toitures agrave versant multiple (directionV1-V3)helliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip28 Figure 26 Zone de vent pour les parois verticales (V2) (V4)helliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip29 Figure 27 Zone de vent pour les parois verticales (V2) (V4)helliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip29 Figure 28 Leacutegende pour les toitures agrave versant multiple (V2)helliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip30 Figure 29 Leacutegende pour les toitures agrave versant multiple (V2)helliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip30 Figure 210 Coefficient de pression inteacuterieure Cpi pour la direction V1V3helliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip32 Figure 211 Coefficient de pression inteacuterieure Cpi pour la direction V2V4helliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip33

Figure 31 La position des deux pannes par rapport aux zones H et Fhelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip39 Figure 32 Reacutepartition de la charge drsquoentretien sur la pannehelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip43 Figure 33 Reacutepartition des pannes sur un versanthelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip44 Figure 34 Assemblage poutre-traverse avec eacutechantignolehelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip49 Figure 35 choix de lrsquoepaisseur du bardage helliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip51 Figure 36 Reacutepartition des lisseshelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip52 Figure 37 Disposition des liernes sur le bardagehelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip56 Figure 38 Coupe vertical sur le cheacuteneauhelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip58 Figure 39 Disposition des poteletshelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip59

Figure 41 Scheacutema 3D du pont roulanthelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip65 Figure 42 Scheacutema 2D du pont roulanthelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip65 Figure 43 Moment max pour deux charges eacutegales (Theacuteoregraveme de Barreacute)helliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip67 Figure 44 Coupe transversale du railhelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip68 Figure 45 Scheacutema de la poutre de roulement avec le railhelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip69 Figure 46 Scheacutema statique de la poutre de roulementhelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip70 Figure 47 Illustrations des efforts appliqueacutes sur la poutre de roulement par le galet et P la reacuteaction verticale maxhelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip70 Figure 48 Scheacutema statique de la poutre de roulement sur deux appuishelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip71 Figure 49 Illustration des galets sur la poutre de roulementhelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip76 Figure 410 Coupe verticale sur le support du chemin de roulementhelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip78 Figure 411 Scheacutema statique du support de chemin de roulementhelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip78 Figure 412 Diagramme du moment fleacutechissant du support de chemin de roulementhelliphelliphelliphelliphelliphellip80 Figure 413 Coupe verticale sur la reacutepartition des charges sur le support du chemin de

roulementhelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip81

Figure 51 Spectre de reacuteponse suivant la direction Xhelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip86 Figure 52 Spectre de reacuteponse suivant la direction Yhelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip86

Figure 53 Valeur limite des flegraveches horizontales des bacirctiments industrielshelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip88

Figure 61 Illustration de la traverse la plus solliciteacuteehelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip90 Figure 62 Vue en 3D de la structure illustration des poteauxhelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip95 Figure 63 Vue en 3D illustrant la position des contreventements et stabiliteacuteshelliphelliphelliphelliphelliphelliphelliphelliphelliphellip100 Figure 64 Ratio des eacuteleacutements structuraux (agrave partir du logiciel ROBOT)helliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip102 Figure 65 Vue en 3D de la structure illustration des poteletshelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip102

Figure 71 vue en plan de lrsquoassemblage poteau-traversehelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip107 Figure 72 Deacutesignation des entraxes et des pinceshelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip108 Figure 73 Vu en plan de lrsquoassemblage traverse-traversehelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip114 Figure 74 Deacutesignation des entraxes et des pinceshelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip114 Figure 75 Assemblage des diagonales doubles corniegraveres avec goussethelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip118 Figure 76 Assemblage panne-eacutechantignole eacutechantignole-traversehelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip120

Figure 81 Assemblage au pied de poteau rigidehelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip122 Figure 82 Illustration moment + effort normalhelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip124 Figure 83 Illustration de la partie comprimeacutee du pied de poteauhelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip125 Figure 84 Dispositions constructiveshelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip126 Figure 85 Longueur drsquoallongement des boulons drsquoancrageshelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip128 Figure 86 Les dimensions de la semelle sous poteauhelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip130 Figure 87 Ferraillage des semelleshelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip133 Figure 88 le ratio reacutealiseacute par cet assemblage de pied de poteau selon ROBOThelliphelliphelliphelliphelliphelliphelliphelliphelliphellip135

LISTE DES NOTATIONS

Majuscules latines

A Section brute drsquoune piegravece Anet Section nette drsquoune piegravece Aw Section de lrsquoacircme 119860119907 Aire de cisaillement Ct Coefficient de topographie Cr Coefficient de rugositeacute Cpnet Coefficient de pression nette Ce Coefficient drsquoexposition Cd Coefficient dynamique E Module drsquoeacutelasticiteacute longitudinale de lrsquoacier (E=21 105 MPa) F Force en geacuteneacuterale G Module drsquoeacutelasticiteacute transversale de lrsquoacier (G=81000 MPa) G Charge permanente I Moment drsquoinertie K0 Coefficient de flambement Kt Facteur de terrain L Longueur M Moment de flexion MSd Moment fleacutechissant sollicitant MRd Moment reacutesistant par uniteacute de longueur dans la plaque drsquoassise MPl Moment plastique MbRd Moment de la reacutesistance au deacuteversement Npl Rd Effort normal de la reacutesistance plastique de la section transversale brute NbRd Effort normal dun eacuteleacutement comprimeacute au flambement NSd Effort normal sollicitant Ntsd Effort normale de traction Ncsd Effort normal de compression NcRd Valeur de calcul de la reacutesistance de la section transversale agrave la compression Q Charge drsquoexploitation R Coefficient de comportement de la structure 119878 La charge de la neige 119881119904119889 Valeur de calcul de leffort tranchant Vreacutef Vitesse de reacutefeacuterence du vent Wpl Module de reacutesistance plastique W Poids de la structure

Minuscules latines f La flegraveche fy Limite deacutelasticiteacute

h Hauteur drsquoune piegravece L Longueur drsquoune piegravece (Poutre Poteau) Lf Longueur de flambement t Eacutepaisseur drsquoune piegravece tf Eacutepaisseur drsquoune semelle de poutre tw Eacutepaisseur de lrsquoacircme de poutre

Z Hauteur au-dessus du sol Z0 Paramegravetre de rugositeacute Zeq Hauteur eacutequivalente

Minuscules grecques 120582119871119879 Eacutelancement de deacuteversement empty119871119879 Rotation de deacuteversement 120591 Contrainte limite de cisaillement en eacutelasticiteacute

휀 Coefficient de reacuteduction eacutelastique de lrsquoacier 120590119886 Contrainte de lrsquoacier 120590119887 Contrainte du beacuteton ξ Pourcentage drsquoamortissement critique η Facteur de correction drsquoamortissement δek Deacuteplacement ducirc aux forces sismiques μ coefficient de forme de la charge de neige

Introduction Geacuteneacuterale Ce projet de fin drsquoeacutetudes est lrsquooccasion pour nous de mettre en pratique lrsquoensemble des connaissances theacuteoriques acquises durant notre cursus universitaire tout en nous familiarisant avec les regraveglements nationaux et internationaux reacutegissant les principes de conception et de calcul drsquoouvrages meacutetalliques ou autres comme le laquo RNV 2013 RPA 99v2003 BAEL91 et lrsquoEUROCODE 3raquo ainsi qursquoagrave utiliser des outils de calcul et de simulation numeacuterique Lrsquoeacutetude drsquoune structure meacutetallique comme toutes les autres structures est reacutealiseacutee par un dimensionnement aux eacutetats limites ultimes et une veacuterification des deacuteplacements aux eacutetats limites de services en tenant compte des actions qui srsquoappliquent sur elle qursquoelles soient de nature permanentes variables ou accidentelles Notre projet plus preacuteciseacutement consiste au dimensionnement drsquoune halle industrielle en charpente meacutetallique dans la wilaya de Ouargla agrave des fins de maintenances industrielles avec la veacuterification de chaque piegravece profileacute ou assemblage conformeacutement aux regraveglements en vigueur Notre travail est composeacute de la faccedilon suivante Drsquoabord une introduction sur lrsquoeacutetat des lieux la superficie de lrsquoouvrage sa position son environnement puis on deacuteterminera gracircce agrave la regraveglementation citeacutee ci-dessus les diffeacuterentes charges qui peuvent srsquoappliquer agrave notre ouvrage En fonction de ces charges on fera un preacutedimensionnement des diffeacuterents eacuteleacutements secondaires existants dans lrsquoouvrage ensuite on introduira toutes ces donneacutees dans le logiciel et on exeacutecutera la simulation numeacuterique Cette simulation va nous donner les sections des diffeacuterents eacuteleacutements principaux de la halle ces sections vont soit ecirctre gardeacutees soit ecirctre remplaceacutees par drsquoautre sections plus disponibles sur le marcheacute puis on les reveacuterifiera manuellement avec les diffeacuterentes exigences du CCM97 on dimensionnera les assemblages adeacutequats agrave chaque reacuteunion drsquoeacuteleacutements ainsi que les fondations Enfin nous verifirons tout nos eacutelements et tout nos assemblages a lrsquoaide du robot on peut prevoir drsquoautres veacuterifications de la structure tel que la torsion global de la structure ou bien simuler une explosion ou un accident dans notre ouvrage

16

Chapitre-1

Geacuteneacuteraliteacute et preacutesentation de lrsquoouvrage

11 Introduction

Le domaine de la construction meacutetallique est un domaine vaste qui a connu dans son histoire plusieurs eacutevolutions non seulement dans les proceacutedeacutes de conception et de reacutealisation mais eacutegalement dans les techniques et les mateacuteriaux utiliseacutes dans les structures Ainsi on a deacutesormais une varieacuteteacute de choix allant du beacuteton a lrsquoacier en passant par lrsquoaluminium la maccedilonnerie ou encore le bois En Europe le fer a commenceacute agrave faire son apparition comme eacuteleacutement de construction au 18iegraveme siegravecle alors que les mateacuteriaux usuels agrave cette eacutepoque eacutetaient le bois et la pierre au 14iegraveme siegravecle Avec lrsquointroduction du fer comme eacuteleacutement de construction les meacutethodes de conception furent bouleverseacutees le concepteur ne travaillait plus en effet avec des eacuteleacutements singuliers mais avec des profileacutes standards en I T L etchellip Un peu plus tard les progregraves techniques dans le domaine sideacuterurgique contribuegraverent agrave lrsquoapparition drsquoun nouveau mateacuteriau lrsquoacier Agrave la Premiegravere moitieacute du 20iegraveme siegravecle lrsquoacier a subi principalement en Europe une forte concurrence du beacuteton armeacute Lrsquoengouement pour ce nouveau mateacuteriau entraicircna une baisse significative du nombre drsquoouvrages en meacutetal construit durant cette peacuteriode cependant de lrsquoautre cocircteacute de lrsquoatlantique la situation eacutetait toute autre aux Eacutetats-Unis ougrave lrsquoacier reacutepondait preacuteciseacutement au besoin de la creacuteation drsquoimmeubles de grande hauteur il fut massivement utiliseacute (tireacute de notechfranceservcom) Actuellement en Algeacuterie lrsquoutilisation de la charpente meacutetallique est principalement employeacutee dans le secteur industriel pour ses avantages de rapiditeacute drsquoexeacutecution pour les longues porteacutees qursquoelle offre et pour son amovibiliteacute Notre projet traiteacute ici ne fait pas exception il a fallu pour le reacutealiser devoir calculer les charges qui lui sont appliqueacutees dimensionner ses eacuteleacutements le modeacuteliser numeacuteriquement et reveacuterifier toutes ces sections par rapport aux normes et regraveglements actuels en vigueur Les diffeacuterents regraveglements et documents utiliseacutes pour nos calculs - Regraveglement Neige et Vent 2013 DTR C 2-47 laquo RNV 2013 raquo - Regraveglement parasismique algeacuterien DTR BC 248 laquo RPA99v2003 raquo

17

- Regravegles de conception et de calcul des structures en acier DTR BC 244 laquo CCM97 raquo - Charges permanentes et charges drsquoexploitations DTR BC 22 - Regravegles de conception et de calcul des structures en beacuteton armeacute DTR BC 241 laquo CBA93 raquo - Calcul des structures en acier ENV 1993-1-1laquo Eurocode3 raquo - Conception et dimensionnement des structures mixtes acier-beacuteton ENV1994-1-1 laquoEurocode4raquo - Rapport geacuteotechnique du site drsquoimplantation de la structure Le principal document utiliseacute est Le CCM97 document technique reacuteglementaire qui a pour objectif de fournir une codification du dimensionnement pour calcul et des veacuterifications des structures de bacirctiments agrave ossatures meacutetalliques Les combinaisons qursquoil propose deacutependent des actions suivantes Actions permanentes Gi

Comprenant - Le poids propre des eacuteleacutements structuraux - Le poids propre des eacuteleacutements fixes - Les pousseacutes et pression des terres et hydrostatiques - Les deacuteformations permanentes imposeacutees agrave la construction tels que les deacuteplacements diffeacuterentiels des appuis Actions variable Qi Comprenant - Les charges drsquoexploitations - Les charges appliqueacutees en cours drsquoexeacutecution - Les actions climatiques Actions accidentelles Ai Comprenant Les actions sismiques les explosions le calcul au feu les chocs etc En ce qui concerne les eacutetats limites le CCM97 explique que les eacutetats limites permettent de combiner les charges G Q S W E afin de simuler au mieux un pheacutenomegravene qui peut se produire en prenant en compte ce qui repreacutesente la limite maximale consideacutereacutee pour les charges Grace agrave ces combinaisons nous pourront deacuteterminer les efforts maximaux et les deacuteplacements ultimes afin de les comparer agrave lrsquoeffort ou au deacuteplacement toleacutereacute Les valeurs des coefficients partiels de seacutecuriteacute agrave prendre en consideacuteration sont repreacutesenteacutees dans le tableau suivant

18

Action

permanente (γG)

Action variable (γQ)

Action variable de base Action variable

drsquoaccompagnement

Effet favorable

γGinf

10 1 0

Effet deacutefavorable

γGsup

135 15 15

Tableau 11 Valeur des coefficients partiels de seacutecuriteacute

12 Pour lrsquoeacutetat limite ultime ELU - Prise en compte drsquoune seule action variable la plus deacutefavorable la combinaison sera

repreacutesenteacutee comme suit 120574119866119894119904119906119901 119866119896119895 + 150 119876119896119898119886119909

135119866119896119895 + 15119876119896119898119886119909

- Prise en compte de plusieurs actions variables deacutefavorables la combinaison sera

repreacutesenteacutee comme suit sum119895120574119866119894119904119906119901 119866119896119895 + 135sum119894gt1119876119896119894 135119866119896119895 + 135119876119896119898119886119909 + 135119882 135119866119896119895 + 135119876119896119898119886119909 + 135119878

- Prise en compte drsquoune seule action variable dirigeacutee vers le haut exemple vent en

deacutepression 120574119866119894119894119899119891 119866119896119895 + 150119882minus

1 119866119896119895 + 150119882minus

13 Pour lrsquoeacutetat limite de service ELS - Prise en compte uniquement de lrsquoaction variable la plus deacutefavorable

sum119866119896119895119895

+ 119876119896119898119886119909

119866119896119895 + 119876119896119898119886119909

- Prise en compte de toutes les actions variables deacutefavorables

sum119866119896119895119895

+ 09sum119876119896119894119894gt1

119866119896119895 + 09119876119896119898119886119909 + 09119878 119866119896119895 + 09119876119896119898119886119909 + 09119882

14 Etude parasismique La reacuteglementation relative agrave la construction parasismique se compose de texte drsquoorigine leacutegislative et de texte technique les preacutesentes regravegles viennent garantir une protection satisfaisante des vies humaines et des constructions vis-agrave-vis des effets des actions sismiques par des conceptions et dimensionnements approprieacutes Ainsi pour les ouvrages courants le but viseacute crsquoest de limiter les

19

dommages non structuraux et drsquoeacuteviter les dommages structuraux en dotant la structure drsquoune ductiliteacute et drsquoune capaciteacute de dissipation drsquoeacutenergie produite par le seacuteisme

Zones de sismiciteacutes

Zone 0 Sismiciteacute neacutegligeable

Zone I Sismiciteacute faible

Zone IIa et IIb Sismiciteacute moyenne

Zone III Sismiciteacute eacuteleveacutee

Tableau 12 Classification des zones sismiques

15 Lrsquoeffet du vent Le vent est consideacutereacute comme une force toujours perpendiculaire a la surface sur laquelle il est appliqueacute il peut engendrer des pressions sur les surfaces en soufflant de lrsquoexteacuterieur mais aussi des deacutepressions par pheacutenomegravene de succion ou juste en soufflant de lrsquointeacuterieur de la structure Le vent a une vitesse de reacutefeacuterence calculeacutee et reacutepertorieacutee par le RNV sur la base de relations empiriques cette vitesse diffegravere drsquoune reacutegion agrave une autre la carte ci-dessous montre les diffeacuterentes valeurs de cette vitesse dans le territoire nationale

Figure 11 Notre structure est preacutesente agrave Hassi Messaoud dans la wilaya de Ouargla

20

Figure 12 Zone de Ouargla (RPA)

16 Preacutesentation de lrsquoouvrage Notre projet traite le dimensionnement drsquoune halle en charpente meacutetallique avec ponts roulants et potences implanteacute dans la wilaya de Ouargla un site ou la sismiciteacute ainsi que les charges dues agrave la neige sont neacutegligeables mais par contre le vent souffle tregraves fort et le sable peut se deacuteposer sur certaine partie de la toiture La surface totale de notre ouvrage fait 1080 1198982 la hauteur du halle est de 89m alors que celle de la faicirctiegravere est de 1025m Lrsquoouvrage dispose de six portails de dimension (5x4) 8 ouvertures pour lrsquoeacuteclairage ainsi que pour le renouvegravelement drsquoair de la structure ou de fumeacutee en cas drsquoincendie

17 Caracteacuteristiques geacuteomeacutetriques Suivant les plans architecturaux les dimensions de la structure se preacutesentent comme suit - Longueur de lrsquoouvrage (Long-pan) L= 30m - Largeur (Pignon) l= 36m - Hauteur totale H=89 m - Hauteur de lanterneau a=135m - Pente du versant est 15

21

Figure 13 Vue sur pignon de lrsquoouvrage

Figure 14 Vue en perspective de la structure

18 Mateacuteriaux Les diffeacuterents mateacuteriaux de constructions utiliseacutes dans notre construction sont

181 Acier En construction meacutetallique lrsquoacier fait lrsquoobjet drsquoune normalisation rigoureuse dans laquelle on

speacutecifie la limite drsquoeacutelasticiteacute fy la reacutesistance agrave la rupture fu et lrsquoallongement agrave la rupture 휀 Le choix de la nuance drsquoaciers deacutepend des facteurs techniques et eacuteconomiques Limite drsquoeacutelasticiteacute fy=235MPa La contrainte de rupture fu=360 MPa Le module de Young E = 210 000 MPa

22

Le coefficient de poisson ν=03 Le module de cisaillement 119866 = 80769 MPa La masse volumique de lrsquoacier ρ=7850 Kgm3

182 Beacuteton armeacute Caracteacuteristiques meacutecaniques Reacutesistance agrave la compression fc28=25 MPa Reacutesistance agrave la traction ft28=06+006fc28= 21 MPa Le poids volumique ρ=2500 Kgm3

183 Ferraillages et armatures - La limite drsquoeacutelasticiteacute fe=400 MPa - Le coefficient de seacutecuriteacute pour les situations courantes γs = 115 - La contrainte admissible agrave lrsquoELU fsc =feγs = 348 MPa - Le module de Young Es=210 000 MPa

23

Chapitre-2

Eacutevaluation des surcharges climatiques

21 Introduction

Les effets climatiques sur une structure meacutetallique sont souvent preacutepondeacuterants Une

eacutetude approfondie et deacutetailleacutee doit ecirctre meneacutee minutieusement afin de deacuteterminer les

diffeacuterentes actions et sollicitations

La reacuteglementation nationale Neige et Vent (RNV 2013) met agrave notre disposition les principes geacuteneacuteraux et proceacutedures agrave suivre afin de mieux preacutevoir ces surcharges et de mener agrave bien des calculs Les pressions du vent appliqueacutees sur les structures meacutetalliques deacutependent des facteurs suivants

- La reacutegion (Zone 0) - Les reliefs du site drsquoimplantation - La hauteur de la construction - La configuration geacuteomeacutetrique de la structure - La forme de la toiture

22 Deacutetermination de lrsquoaction du vent

- Effet de la reacutegion

Notre halle industrielle se situe agrave la wilaya drsquoOuargla dans la commune de Hassi Messaoud selon le regraveglement RNV 2013 la reacutegion est classeacutee comme zone 4 la pression dynamique de reacutefeacuterence est de 575 Nm

Figure 21 Repreacutesentation et deacutenominations des directions du vent

24

- Effet du site

Le regraveglement RNV2013 preacutevoit eacutegalement lrsquoeffet de la nature du terrain Notre

ouvrage se trouve dans une zone laquo agrave couverture veacutegeacutetale neacutegligeable raquo donc

nous nous situons dans une cateacutegorie de terrain 1 avec un facteur de terrain

Kt = 0170 paramegravetre de rugositeacute Z0= 001 m Zmin= 1 m et le coefficient ξ= 044

Les donneacutees relatives au site telle que la pression de reacutefeacuterence ainsi que la

vitesse de reacutefeacuterence sont repreacutesenteacutees dans le tableau suivant

Site plat Ct(Z)=1 RNV2013 chapitre245 sect2451

Ouargla (Zone 4)

qreacutef =575 Nmsup2 Vreacutef =31ms

RNV2013 chapitre23 sect231

Terrain de cateacutegorie 1

Kt=017 Z0=001m Zmin=1m ξ=044

RNV2013 chapitre244 sectTableau 24

Tableau 21 Donneacutees relatives au site dimplantation

221 Deacutetermination de la pression aeacuterodynamique

La pression aeacuterodynamique W(Zj) agissant sur une paroi est obtenue comme suit

119882(119911119895) = 119902119901(119885119890) times [119862119901119890 minus 119862119901119894] (daNm) 119825119821119829120784120782120783120785 119836119841119834119849119842119853119851119838120784 120787 120784 sect120784 120788

Avec

- CPe est le coefficient de pression exteacuterieure

- CPi est le coefficient de pression inteacuterieure

222 Calcul de la pression dynamique de pointe qp La pression dynamique de pointe qp(z) est la pression dynamique utiliseacutee dans les calculs elle deacutepend du climat du lieu de la hauteur de reacutefeacuterence de la rugositeacute du terrain et du coefficient de topographie

119902119901(119885) = 119902119903119890119891 times 119862119890

Avec

- 119902ref = 575 119889119886119873119898sup2

Coefficient drsquoexposition 119862119890 = 119862119903

2(119885) times [1 + 7119868119907] 119825119821119829120784120782120783120785 119836119841119834119849119842119853119851119838 120784 120786 sect120784 120786 120784 119834

Coefficient de rugositeacute 119825119821119829120784120782120783120785 119836119841119834119849119842119853119851119838 120784 120786 120786

25

Terrain de cateacutegorie 1 Kt=017 z0=001m zmin=1m ξ=044 ( g

119862119903(119911)

119870119905 119871119899 (1199111198981198941198991199110

) 119901119900119906119903 119911 lt 119911119898119894119899

119870119905 119871119899 (119911

1199110) 119901119900119906119903 119911119898119894119899 le 119911 le 200119898

Parois vertical (z le zmin ) 119862119903(z)=Kt Ln(119911119898119894119899 1199110

)=0783

Parois et toiture (zminltzlt200m) 119862119903(z)=KtLn(Z

Zo)=1178

On retient 119862119903= 1178

- Intensiteacute de turbulence RNV2013 chapitre246

119868119907(119911)

1

119862119905(119911) 119871119899 (119911

1199110) 119901119900119906119903 119911 gt 119911119898119894119899

1

119862119905(119911) 119871119899 (1199111198981198941198991199110) 119901119900119906119903 119911 le 119911119898119894119899

Pour z gt zmin 119868119907(119911) =1

1Ln(1

001)= 0217

Pour z lt zmin 119868119907(119911) =1

1Ln(1025

001)= 0144

On retient 119868119907 = 0144 pour lrsquoensemble de la structure

- Coefficient drsquoexposition

119862119890(119911119895) = 119862119903(119911119895)2[1 + 7 119868119881]

Pour z gt zmin

119862119890(119911) = 11782 times 12 times [1 + 7(0144)] = 2786

Pour z lt zmin

119862119890(119911) = 07832 times 12 times [1 + 7(0217)] = 154

- Pression dynamique de pointe qp

Avec

26

- 119902119903119890119891 = 575 119889119886119873119898sup2

Pour z lt zmin qp= 575times1544=8878 Nm2

Pour z gt zmin qp= 575times2786=160195 Nm2

qp = 160195Nm2 = 16 kNm2

223 Coefficient de pression exteacuterieure Les valeurs des coefficients de pression exteacuterieure donneacutees dans les tableaux du RNV2013 sont relatives agrave des zones bien deacutefinies Ces coefficients deacutependent de la dimension de la surface chargeacutee produisant laction du vent dans la section agrave calculer

Pour un vent perpendiculaire au long-pan (V1)

-Parois verticale RNV2013 chapitre521

Pour cette direction du vent les dimensions sont les suivantes

- b=30 m

- d=36 m

- h=89 m

Cp =Cpe10 car Slt10119950120784 avec S la surface chargeacute (chapitre2013 chapitre5 sect5112)

e = min (d 2h)

d=32 ou 36 m selon la direction du vent mais toujours gt e =2h

Donc e = 2x1025 = 205m

Toiture a versant multiple Cas ougrave d gt e se preacutesente ainsi

Figure 22 Leacutegende relative pour les parois verticale (direction V1)

27


Le calcul des coefficients de pressions exteacuterieures est obtenu agrave partir des formules suivantes

119862119901119890 = 1198621199011198901 119878119894 119878 le 11198982

119862119901119890 = 1198621199011198901 + (11986211990111989010 minus 1198621199011198901) times 11989711990011989210(119878) 119878119894 11198982 lt 119878 lt 101198982

119862119901119890 = 11986211990111989010 119878119894 119878 ge 101198982

RNV2013 Chapitre 5 sect 5111

Les coefficients de pression exteacuterieures pour les parois verticales sont preacutesenteacutes dans le tableau suivant

Zone

Parois lateacuterale Parois au vent

Parois sous le vent

AArsquo BBrsquo CCrsquo D E

Cpe10 -10 -08 -05 +08 -03

Tableau 22 Leacutegende relative pour les parois verticales (direction V1)

Versant de Toiture

Les zones pour les toitures et les coefficients de pression exteacuterieure cpe10 qui y sont

attacheacutees sont deacutefinies dans le RNV2013 Chapitre 5 sect518 le cas drsquoune toiture agrave

versant multiple est celui de notre projet

28

Figure 24 Leacutegende pour les toitures agrave versant multiple (directionV1-V3)


Le regraveglement RNV2013 cite dans son paragraphe 5182 que laquo pour un vent perpendiculaire aux

geacuteneacuteratrices on prendra les valeurs de Cpe des toitures agrave double versant pour 120572 lt 0deg raquo

Les coefficients de pression exteacuterieure Cpe pour le versant face au vent sont deacutetermineacutes agrave partir

drsquoune interpolation lineacuteaire entre lrsquoangle -15 et -5 les valeurs des coefficients sont preacutesenteacutees dans

le tableau suivant

Angle de pente α Cpe pour vent de direction θ=0deg

853deg F G H

-237 -123 -083

Tableau 23 Coefficient de pression exteacuterieur Cpe pour le versant 1 face au vent de toiture

- Pour un vent perpendiculaire au pignon (V2) (V4)

- Parois verticales


-b=36 m

29

-d=30 m

-h=1025

119862119901119890 = 11986211990111989010 RNV2013 chapitre5 sect5112

e=Min (b 2h) = Min (36 205) = 205 m

Le cas ougrave d gt e se preacutesente ici

Figure 26 Zone de vent pour les parois verticales (V2) (V4)


Les coefficients de pression exteacuterieurs pour les parois verticales sont preacutesenteacutes dans le tableau suivant

30

Zone


Parois sous le vent

AArsquo BBrsquo CCrsquo D E Cpe10 -10 -08 -05 +08 -03

Tableau 24 Coefficient de pression exteacuterieur laquo Cpe10 raquo pour les parois verticales direction V2

- Versant de toiture

Les zones pour les toitures et les coefficients de pression exteacuterieure Cpe10 qui y sont attacheacutees sont deacutefinies dans le RNV2013 Chapitre 5 sect518

Figure 28 Leacutegende pour les toitures agrave versant multiple (V2)


Le regraveglement RNV2013 cite dans son paragraphe 5181 que pour laquo un vent dont la direction est parallegravele aux geacuteneacuteratrices les coefficients de pression pour chaque versant

31

srsquoobtiennent en utilisant les valeurs de toiture agrave un versant pour θ=90deg raquo

Les coefficients de pression exteacuterieure CPe10 pour un angle de 853deg sont deacutetermineacutes agrave partir de lrsquointerpolation lineacuteaire entre lrsquoangle de 5deg et 15deg

Angle α Fsup Finf G H I

853deg -22 -192 -183 -067 -057

Tableau 25 Coefficient de pression exteacuterieur pour la toiture (direction V2)

224 Coefficient de pression inteacuterieure Le coefficient de pression inteacuterieure Cpi deacutepend de la dimension et de la reacutepartition

des ouvertures dans lrsquoenveloppe du bacirctiment

- Pour les 2 cas de direction du vent (V1 et V3)

- Pour cette direction le taux drsquoouverture est de

2(5 times 4)

30 times 89= 014 = 14

On commence tout drsquoabord agrave deacuteterminer lrsquoindice de permeacuteabiliteacute microp

μ119901 =120

160= 075

Le coefficient de pression inteacuterieure Cpi est donneacute en fonction de lrsquoindice de permeacuteabiliteacute Figure 514 du Regraveglement RNV2013 en fonction du rapport

ℎ119889 = 102536 = 028gt025 =gt Interpolation neacutecessaire

Pour μ119901=075 on lit 119862119901119894 =-016

32

Figure 210 Coefficient de pression inteacuterieure Cpi pour la direction V1 V3

Pour les 2 cas de direction du vent (V2 et V4)

Pour cette direction le taux drsquoouverture est de

2 times (5 times 4)

36 times 9575= 0116 = 116

ℎ119889 = 102530 = 034 gt 025 =gt Interpolation neacutecessaire

Pour μ119901=075 rarr 119862119901119894 =-02

33

Figure 211 Coefficient de pression inteacuterieure Cpi pour la direction V2V4

225 Deacutetermination de la pression statique du vent

Apregraves avoir deacutefini tous les coefficients tels que la pression dynamique coefficient

de pression inteacuterieure et exteacuterieure on peut calculer la pression due au vent pour

Direction V1 V3

Parois verticales Zone qdyn(daNm2) Cpe Cpi Cpe - Cpi qfin(daNm2)

A 1602 -10 -0154 -0846 -135529

B 1602 -08 -0154 -0646 -103489

C 1602 -05 -0154 -0346 -55429

D 1602 +08 -0154 +0954 +152831

E 1602 -03 -0154 -0146 -23389

Tableau 26 Pressions du vent sur parois vertical

34

Toiture

Zone qdyn(daNm2) Cpe Cpi Cpe - Cpi qfin(daNm2)

F 1602 -237 -0154 -2276 -355003

G 1602 -123 -0154 -1076 -172375

H 1602 -084 -0154 -0676 -108295

Z1 1602 -1 -0154 -0846 -135529

Z2 1602 -06 -0154 -0446 -71449

Tableau 27 Pressions du vent sur toiture

Direction V2 et V4

Parois verticales


A 1602 -10 -0162 -0838 -134247

B 1602 -08 -0162 -0638 -102207

C 1602 -05 -0162 -0338 -54147

D 1602 +08 -0162 +0962 +154112

E 1602 -03 -0162 -0138 -22107


35

Toiture


Finf 1602 -12 -0162 -1038 -1662876

Fsup 1602 -22 -0162 -2038 -3264876

G 1602 -183 -0162 -1668 -2672136

H 1602 -067 -0162 -0508 -813816

I 1602 -057 -0162 -0408 -653616


23 Deacutetermination de lrsquoaction de la neige

Le calcul de la surcharge climatique de la neige est en fonction de la localisation geacuteographique

et de lrsquoaltitude du lieu

Notre projet se situe dans la Wilaya de Ouargla (Hassi Messaoud) lrsquoaltitude est de 171 m

La wilaya de Ouargla est consideacutereacutee comme une zone D =gt Pas de neige dans cette reacutegion

24 Deacutetermination de lrsquoaction du sable

La Pente du toit = 135

9= 015

La pente est de 15 soit gt a 5 =gtLe toit ne peut ecirctre consideacutereacute comme plat

=gtLa charge due au sable ne peut ecirctre consideacutereacutee uniformeacutement reacutepartie

Deux charges lineacuteaire q1 et q2 seront pris en compte

q1= 300 Nml

q2= 500 Nml

25 Charge permanente

- Couverture et bardage Choix du systegraveme de couverture

36

Notre choix pour la toiture et le bardage de notre halle sera axeacute sur les panneaux sandwich car ils assurent le minimum requis pour notre halle cagraved

- Une bonne isolation thermique

- Une bonne reacutesistance au feu

Le systegraveme panneaux sandwich de type TL-75 qui est constitueacute drsquoun parement exteacuterieur et un parement inteacuterieur qui sont colleacutes agrave une mousse rigide en polyureacutethane sera retenu

Ces caracteacuteristiques se preacutesentent comme suit

- Epaisseur totale 75mm

- Largeur de panneau 1000mm

- Poids du panneau 142 daNmsup2

Choix du systegraveme de bardage

Le bardage reacutepondant agrave lrsquoexigence drsquoune isolation thermique est le systegraveme panneaux sandwich de type LL50 les caracteacuteristiques sont les suivantes

- Epaisseur 50 mm

- Largeur 1000 mm

- Poids volumique du panneau G= 129 kgmsup2

26 Charge drsquoexploitation

Notre toiture est inaccessible donc la seule charge drsquoexploitation que peut avoir notre toiture crsquoest

la charge drsquoentretien

Selon le DTR BC22

La porteacute L=6m (distance entre portique) =gt les charges drsquoentretien seront deux charges ponctuelles

de 1kN appliqueacute a 13 de chaque appuis

On peut les convertir en une charge uniformeacutement reacutepartie eacutequivalente ainsi

37

119902 =8119875

3119871= 044 119896119873119898

119902 = 444 119889119886119873119898

Ceci juste pour avoir une charge lineaire et pouvoir faire un predimensionnement de la panne

Sur la modeacutelisation avec ROBOT les deux charges serons introduitents comme charges ponctuels

- Effet du frottement

Pour les cas V1 et V3

Lrsquoeffet du frottement du vent sur la surface peut ecirctre neacutegligeacute car mecircme en prenant la toiture

comme faiblement inclineacutee ce qui nrsquoest pas le cas on veacuterifie la condition de neacutegligence du

frottement du vent qui dit

sum surfaces parallegraveles au vent le 4 times sum surfaces perpendiculaires au vent

Cas de vent sur long pan

[(36+36)times9575]+4[91times30]=17814 m2 le4times(30+30)times89= 2136m2 CV

Cas de vent sur pignon

[(30+30)times89]+ 4[91times30]=1626m2 le 4times(36+36)times9575= 27576 m2 CV

38

Chapitre-3

Dimensionnement des eacuteleacutements secondaires 31 Dimensionnement des pannes pour la toiture agrave plusieurs versants

311 Fonctionnement de base

La fonction des pannes de toiture est drsquoassurer le transfert des actions appliqueacutees agrave la couverture drsquoun bacirctiment et agrave sa structure principale les lisses jouent le mecircme rocircle en faccedilades Les pannes et les lisses sont des constituants importants de la structure secondaire du bacirctiment Un empannage comprend non seulement les pannes elles-mecircmes mais eacutegalement les eacuteventuelles eacuteclisses qui reacutealisent la continuiteacute des pannes les eacutechantignoles qui assurent la liaison entre pannes et structure principale ainsi que les liernes et brettelles qui maintiennent les pannes lateacuteralement

312 Choix du bardage de couverture Pour le choix de notre systegraveme de couverture il srsquoest aveacutereacute qursquoune couverture de type TL 75 remplie correctement les critegraveres de conception agrave savoir - Assurer la fonction eacuteleacutementaire de protection face aux intempeacuteries - Satisfaire les exigences acoustiques - Satisfaire agrave lrsquoexigence nationale imposeacutee par les documents reacuteglementaires relatifs aux charges de neige de vent et aux autres charges dexploitation Les charges supporteacutees par la toiture - Charge drsquoentretien Q=4444 daNml - Action du sable q1=30 daNml q2=50 daNml - Action du vent W= -355 daNmsup2 et W=-1723 daNm2 - Poids propre de la couverture 119866 =142 daNmsup2 Charge eacutequivalente du vent sur une panne de 6m dans la partie du toit ougrave lrsquoeffet du vent est le plus

deacutefavorable

39

(minus354 times5125

6) + (minus1723 times

0875

6) = minus32754 1198891198861198731198982

Qeq (vent) = 3276 daN1198982

-la charge de deacutepression du vent sur la panne est largement supeacuterieure aux autres charges

Crsquoest donc la combinaison G-15W qursquoil faut prendre en compte (pour le plan z-z seulement)

Figure 31 La position des deux pannes par rapport aux zones H et F

En essayant plusieurs valeurs drsquoespacement entre pannes et en faisant toutes les veacuterifications

neacutecessaires agrave chaque fois on arrive aux reacutesultats suivants

Pour e=12m -gt panne 2 la plus chargeacutee -gt section minimum neacutecessaire (IPE180)

-gt nbr de panne neacutecessaires 8 par versant

Pour e=14m 16m 18m 2m -gt panne 1 la plus chargeacutee -gt section minimum neacutecessaire (IPE200)

-gt nbr de panne neacutecessaires 5 par versant (pour e=2m)

Crsquoest donc par souci drsquoeacuteconomie et de poids total qursquoon prend un espacement entre panne de 2m

et un choix de section IPE200 pour les pannes mais seuls les deux derniers choix faits seront

deacuteveloppeacutes ci-dessus cad

-IPE180 + liernes avec e =2m (ce qui ne veacuterifie pas toutes les conditions de seacutecuriteacute)

-IPE200 avec e =2m (le choix final retenu celui qui veacuterifie toutes les conditions)

40

Actions par megravetre lineacuteaire sur cette panne (G IPE180 = 188 danml) G = (142+188)x14 =462 daNml W= -3276x14=-45864 daNml E=444 daNml Angle drsquoinclinaison de la panne 853deg Les combinaisons possibles dans les deux plans et pour les deux eacutetats limites

Pour lrsquoeacutetat limite de service Remarque Dans notre projet il n yrsquoa de charge de neige possible et aussi la charge de sable ne srsquoapplique pas sur les pannes donc pas de combinaison avec trois charges possible Plan z-z G+E (462+444)cos853=8959 daNml G+W 462cos853 -45864=-413 daNml Qsz=413kN Plan y-y G+E (462+444)sin853=1328 daNml Qsy=0135 kN Pour lrsquoeacutetat limite ultime Plan z-z G+E 135(462+444)cos853=12095 daNml G+W (1x462cos853)-(15x45864)=-642 daNml

41

Quz=642 kN Plan y-y G+E 135(462+444)sin853 =18 daNml Quy=018 kN Calcul des diffeacuterentes sollicitations sur la panne L=6m

Vzsd =119902119906119911 times 119897

2=1878 kN

Mysd=119902119906119911 times 119897

2

8=2817 kNm

Mzsd=119902119906119910 times 119897

2

8=081 kNm

Apres ajout de liernes Lz=3m Mzsd=020 kNm Caracteacuteristiques du profileacute

Profileacute PARAMETRES DE LA SECTION

IPE 180 A Cm2

h mm

b mm

119905f

mm 119905w

mm 119868y

Cm4

119868z

Cm4

119908ply cm3

119908plz cm3

MATERIAU ACIER S235

239 180 91 8 53 1317 101 146 346

Tableau 31 Caracteacuteristiques de la section IPE180 Classe de la section Tableau 531 CCM97 Classe de lrsquoacircme dtw = 14653=2754 lt 72Ɛ=72 rarr acircme de classe 1 Classe de la semelle ctf= 4558=568 lt 10Ɛ=10 rarr semelle de classe 1 La section de la panne est de classe 1

Veacuterifications de la flegraveche a lrsquoELS 119827119834119835119845119838119834119854 120786 120783 119810119810119820 120791120789

Plan y-y 5 times 119902119904119911 times 119897

4

384 times 119864 119868119910lt

119897

200=

5 times 413 times 3004

384 times 21 times 105 times 1317= 015 lt

119897

200= 3 119862119900119899119889119894119905119894119900119899 119907eacute119903119894119891119894eacute119890

Plan z-z

5 times 119902119904119910 times 1198974

384 times 119864 119868119911lt

119897

200=



119897

200= 3 119862119900119899119889119894119905119894119900119899 119907eacute119903119894119891119894eacute119890

42

Veacuterification de la panne au deacuteversement 119912119955119957 120787 120787 120784 (120787 120786120790)119914119914119924120791120789

Relation agrave veacuterifier

119872119887119903119889 =ꭕ119871119879times 120573119908 times119882119901119897119910 times 119891119910

1205741198721 gt 119872119910119904119889 = 2817 119896119873119898

Calcul de 119872119887119903119889

Pour les profileacutes lamineacutes

Pour des sections transversales constantes et doublement symeacutetriques lrsquoexpression de

srsquoeacutecrit sous la forme suivante

λ119871119879 =

119871119894119911

119888105

[

1 +120(

119871119894119911ℎ119905119891

)

2

] 025

Avec

C1 Facteur deacutependant de condition de charge et drsquoencastrement C1= 1132

(Tableau B12 CCM97)

iz =224mm tf =85mm

L=Lz=3000mm h=200mm

λ119871119879 =

119871119894119911

119888105

[

1 +120(

119871119894119911ℎ119905119891

)

2

] 025 = 9457 rarr λ119871119879 =

989

939= 1007

rarr =1092

43

Avec 120572LT = 021 car profile laminer

rarr ꭕ119871119879=

1

(empty119897119905 + radicempty1198971199052 minus λ119897119905

2)= 066 le 1

rarr 119872119887119903119889 =ꭕ119871119879times 120573

119908times 119882119901119897119910 times 119891119910

1205741198721

=066 1 166 235

11= 234 119896119873 119898

234 lt Mysd =2817 condition non veacuterifieacutee on augmente la section ou changer de

nuance drsquoacier crsquoest la premieacutere option qursquoon vas choisir par souci de

disponibiliteacute sur le marcheacute

313 Redimensionnement des pannes avec IPE200

- Chaque panne repose sur deux appuis drsquoune distance de L= 6 m - On dispose 5 fils de pannes sur chaque versant de la toiture - La pente de la toiture 15 - Espacement entre pannes adopteacute est de 2 m

3131 Eacutevaluation des charges et surcharges - Poids propre de la couverture (panneau sandwich) 142 daNmsup2 - La charge du vent deacutepression -3275 daNmsup2 Surcharge drsquoentretien (P) sect731 DTR BC 22 Dans le cas des toitures inaccessibles on considegravere uniquement une charge drsquoentretien qui est eacutegale agrave 100Kg chacune situeacutee agrave 13 et 23 de la porteacutee de la panne La charge uniformeacutement repartie P due aux surcharges drsquoentretien est obtenue en eacutegalisant les deux moments maximaux dus agrave P

Figure 32 Reacutepartition de la charge drsquoentretien sur la panne

119872119872119860119883 =119901prime 119897

3=119901 1198972

8⟹ 119901 =

8 119901prime

3119897=800

18= 4444 119889119886119873119898119897

44

Tableau 32 Porteacutee maximale de la nervure TL75 en fonction des charges appliqueacutees

(ANNEXE ndash 1)

Soit

119876119890119902 =327 + 1082

2= 2176 1198891198861198731198982

Les valeurs 327 et 1082 daNm2 sont les valeurs de depressions des deux zones de vent FG et H repris par

la panne 2 (regarder Figure31)

Drsquoapregraves le tableau ci-dessus on peut aller jusqursquoagrave un espacement en appuis de 394m sans risquer

que la nervure cegravede sous les charges appliqueacutees

La charge supporteacutee par la panne

- Charge drsquoentretien Q=4444 daNml - Action du vent W= -3276 daNmsup2 - Poids propre de la couverture 119866 =142 daNmsup2 -Poids propre de la panne IPE200 (apregraves que IPE180 nrsquoa pas veacuterifier toutes les conditions) G=224 daNml La panne la plus deacutefavorable Bien que lrsquoespacement entre panne soit de 2m la panne la plus deacutefavorable crsquoest-agrave-dire celle de rive ne reprend qursquoune largeur de bardage de 14m seulement

Figure 33 Reacutepartition des pannes sur un versant

Actions par megravetre lineacuteaire sur cette panne G = (142+224)x14 =5124 daNml

45

W= -3276x14=-45864 daNml E=444 daNml Angle drsquoinclinaison de la panne 853deg Les combinaisons possibles dans les deux plans et pour les deux eacutetats limites

Pour lrsquoeacutetat limite de service Plan z-z G+E (5124+444)cos853=9458 daNml G+W 5124cos853 -45864=-40796 daNml Qsz=407kN Plan y-y G+E (5124+444)sin853=1418 daNml Qsy=014 kN Pour lrsquoeacutetat limite ultime Plan z-z G+E 135(5124+444)cos853=12768 daNml G+W (135x5124cos853)-(15x45864)=-61955 daNml Quz=62 kN Plan y-y G+E 135(5124+444)sin853 =1915 daNml Quy=019 kN Calcul des diffeacuterentes sollicitations sur la panne L=6m

Vzsd =119902119906119911 times 119897

2=186 kN

Mysd=119902119906119911 times 119897

2

8=279 kNm

Mzsd=119902119906119910 times 119897

2

8=0855 kNm

46

Caracteacuteristique du profileacute


IPE 200 A Cm2

h mm

b mm

119905f

mm 119905w

mm 119868y

Cm4

119868z

Cm4

119908ply cm3

119908plz cm3

MATERIAU ACIER S235

285 200 100 85 56 1943 142 221 446

Tableau 33 Caracteacuteristiques de la section IPE200 Classe de la section Tableau 531 CCM97 Classe de lrsquoacircme dtw = 15956=2839 lt 72Ɛ=72 rarr Acircme de classe 1 Classe de la semelle ctf= 3885=447 lt 10Ɛ=10 rarr Semelle de classe 1 La section de la panne est de classe 1

Veacuterification de la flegraveche a lrsquoELS 119827119834119835119845119838119834119854 120786 120783 119810119810119820 120791120789


4

384 times 119864 119868119910lt

119897

200=



119897

200= 3 119862119900119899119889119894119905119894119900119899 119907eacute119903119894119891119894eacute119890

Plan z-z

5 times 119902119904119910 times 1198974

384 times 119864 119868119911lt

119897

200=



119897

200= 3 119862119900119899119889119894119905119894119900119899 119907eacute119903119894119891119894eacute119890


Relation a veacuterifier


1205741198721 gt 119872119910119904119889 = 279 119896119873119898

Calcul de 119872119887119903119889

47




λ119871119879 =

119871119894119911

119888105

[

1 +120(

119871119894119911ℎ119905119891

)

2

] 025

Avec

-C1 Facteur deacutependant de condition de charge et drsquoencastrement C1= 1132

(Tableau B12 CCM97)

-iz =224mm -tf =85mm

-L=Lz=6000mm -h=200mm

λ119871119879 =

119871119894119911

119888105

[

1 +120(

119871119894119911ℎ119905119891

)

2

] 025 = 989 ⟶ λ119871119879 =

989

939= 105

rarr =114

Avec 120572LT = 021 car profileacute lamineacute

rarr ꭕ119897119905=

1


2)= 063 le 1

rarr 119872119887119903119889 =ꭕ119897119905times 120573

119908times 119882119901119897119910 times 119891119910

1205741198721

=063 times 1 times 221 times 235

11= 2974119896119873119898

2974 kNm gt Msd =279 kNm condition veacuterifieacutee

Veacuterification au cisaillement

48

Relation agrave veacuterifier Vzsd lt 05 Vplzrd 119912119955119957 120787 120786 120788(120784)119914119914119924120791120789

Avec

119881119901119897119911119903119889 =

119860119907119911 (119891119910

radic3)

11 119890119905 119860119907119911 = 1400 1198981198982

Donc

05119881119901119897119911119903119889 = 05

1400 (235

radic3)

11= 8634 119896119873

Vzsd =186kN lt 05 Vplzrd = 8634kN Condition veacuterifieacutee

Resistance au voilement par cisaillement

Si 119889

119905119908 lt 69휀 il nrsquoest pas neacutecessaire de veacuterifier le voilement par cisaillement

CCM97 art 561(1)

119889

119905119908 =

159

56 = 284 lt 69 휀 Condition veacuterifieacutee

Donc il nrsquoest pas neacutecessaire de veacuterifier le voilement par cisaillement

Veacuterification a la flexion deacutevieacutee composeacutee

On doit veacuterifier la relation suivante

(119872119910119904119889

119872119901119897119910119903119889)

120572

+ (119872119911119904119889119872119901119897119911119903119889

)

120573

le 1 119912119955119957 120787 120786 120790 (120783120783)119914119914119924 120791120789

Avec B= 1 a = 2 pour les sections en I et H

119872119901119897119910119903119889 =119882119901119897119910 times 119891119910

11=221 times 235

11= 4721 119896119873119898

119872119901119897119911119903119889 =119882119901119897119911 times 119891119910

11=446 times 235

11= 952 119896119873119898

119872119910119904119889 = 279 119896119873119898

119872119911119904119889 = 0855 119896119873119898

(279

4721)2

+ (0855

952) = 044 lt 1 119888119900119899119889119894119905119894119900119899 119907eacute119903119894119891119894eacute119890

49

Conclusion la panne IPE 200 veacuterifie les diffeacuterentes conditions de seacutecuriteacute par rapport aux

diffeacuterents cas drsquoinstabiliteacutes elle est donc largement convenable pour notre structure

32 Dimensionnement de lrsquoeacutechantignole

Figure 34 Assemblage poutre-traverse avec eacutechantignole

Calcul des charges revenant agrave une eacutechantignole

Effort de soulegravevement

quz=Gtimescos120572 -15W-- avec

G=39 daNml W--=ndash426 daNml E = 444 daNml

quz = 39timescos 853 ndash 15times426

quz= ndash60043 daNml = ndash6 kN

Effort rampant

quy=(135G+15E)sin120572 =(135times39+15times444)sin 853 = 1768 daNml =018 kN

Lrsquoexcentrement

Lrsquoexcentrement (t) est limiteacute par la condition suivante

2 (119887

2) le 119905 le 3(

119887

2)

Avec b=10 cm pour un profileacute IPE200

50

2 (10

2) = 10 le 119905 le 3(

10

2) = 15

On prend t=10 cm

Pour lrsquoeacutechantignole de rive

119877119911 = 119902119906119911 times119897

2= 6 times

6

2= 18 119896119873

119877119910 = 119902119906119910 times119897

2= 054 119896119873

Pour lrsquoeacutechantignole intermeacutediaire

119877119911 = 18 times 2 = 36 119896119873

119877119910 = 054 times 2 = 108 119896119873

Calcul du moment de renversement

119872119877 = 119877119911 times 119905 + 119877119910 timesℎ

2= 36 times 10 + 108 times 10 = 3708 119896119873 119888119898 = 37119896119873119898

Choix de la section brute

119872119890119897119877119889 =119908119890119897 times 119891119910

1205741198720 119912119955119957 120787 120786 120787 120783 (120784)119914119914119924120791120789

119872119890119897119877119889 =119908119890119897 times 1198911199101205741198720

=gt 119908119890119897 ge119872119890119897119877119889 times 1205741198720

119891119910=gt 119908119890119897 ge

00037 times 11

235

= 173 times 10minus51198983

119908119890119897 = 17321198881198983

Deacutetermination de la largeur et lrsquoeacutepaisseur de lrsquoeacutechantignole

b largeur de lrsquoeacutechantignole

e eacutepaisseur de lrsquoeacutechantignole

119908119890119897 =119887 1198902

6=gt 119890 ge radic

6 times 1732

119887= radic

6 times 1732

180

119890 ge 076

b est prise eacutegale agrave 180 mm soit la largeur de la traverse (Calculer dans le chapitre 6)

Donc on prend e=1cm

51

33 Dimensionnement des lisses de bardages

Les lisses de bardages sont constitueacutees de poutrelles (UPN UAP UPE) oude profils

minces plieacutes Eacutetant disposeacutees horizontalement elles sont porteacutees soit par les poteaux de

portiques soit par les potelets intermeacutediaires Lrsquoentre-axe des lisses est deacutetermineacute par la

porteacutee admissible des bacs de bardage pour notre structure un UPN agrave eacutetait adopteacute

331 Choix du bardage

Le choix du bardage se fait en fonction des charges du vent (pressiondeacutepression) qui

lui sont appliqueacutes Pour notre halle les valeurs maximums de pression et deacutepression

que subissent les parois sont

W+ = 1541 daNm2 W- = -1355 daNm2 (regarder chapitre 2)

Drsquoapregraves le tableau ci-dessous (ANNEXE 3) le bardage choisi doit ecirctre drsquoau moins de

50mm drsquoeacutepaisseur un LL50 pour un poids de 133 daNmsup2 sur 3 appuis avec pas plus

de 3m drsquoentre appuis est le meilleur choix

Figure 35 choix de lrsquoeacutepaisseur du bargade en fonction des pressions et depressions

332 Deacutetermination de lrsquoespacement entre lisse

Toujours drsquoapregraves le tableau ci-dessus on peut aller jusqursquoagrave 3m de distance drsquoentre axe pour le

bardage qursquoon a choisi

Apregraves plusieurs essais empiriques le nombre optimal de lisses neacutecessaire est de 4 ce qui donne un

espacement de longueur de paroi 89m ndash longueur mur maccedilonnerie 4m ( 89 - 4 = 5m )

5m4lisse rarr e =125m

52

Figure 36 Reacutepartition des lisses

Deacutetermination des charges et surcharges

Donneacutees de calcul

- Chaque lisse repose sur deux appuis

- Espacement entre lisse = 125 m

- On dispose 4 lignes de lisse entre portique

- Longueur des lisses 600 m

Les charges permanentes

- Poids propre de bardage (panneau sandwich) 133 daN msup2

- Poids propre des accessoires drsquoattache 5 daN msup2

G=g sy=(Pbardage+Paccessoire)timese

qsy =(133 + 5) times 125=2288daNml

qsy = 0228 kN

quy=135G=03kN

La surcharge climatique due au vent

On calcul les lisses de bardage avec la valeur max sur long- pan

W += 1541 daN m2

- Charges appliqueacutees agrave LrsquoELU

quz=15W

quz=288kN

53

- Charge appliqueacutee agrave LrsquoELS

qsz=Wtimese=1541times125

qsz=19262daN=192kN

333 Le dimensionnement se fait par la condition de limitation de la flegraveche

119891119911 =5 times 119902119904119911 times 119897

4

384 times 119864119910 times 119868le 119891119886119889119873 =

119897

200=600

200= 3 119888119898

119868119910 ge5 times 192 times 6004

384 times 21 times 105 times 3= 51428 1198881198984

On opte pour un UPN 140 avec les caracteacuteristiques suivantes

Profileacute

PARAMETRES DE LA SECTION

UPN 140 A Cm2

h mm

b mm

119905f mm

119905w mm

Iy

Cm4

Iz

Cm4

119908pSy

cm3

119908pSz

cm3

MATERIAU ACIER S235

20 140 60 10 7 605 627 103 283

Tableau 34 Caracteacuteristiques geacuteomeacutetriques du profileacute UPN140

Recalcul des charges avec le poids propre de la lisse ajouteacute

- Poids propre de la lisse UPN 140 1568 daN ml



G=qsy=(Pbardage+Paccessoire)timese

qsy =(133 + 5) times 125 +1568 = 3856daNml

qsy = 038 kN

quy=135G

quy =053kN

qsz=Wtimese=1541times125=19262daN

qsz=192kN

quz=15W

quz=288kN

54

334 Veacuterification des diffeacuterentes Conditions de reacutesistances

Deacutetermination de la Classe

- Classe de lrsquoacircme fleacutechie

119888

119905119891=60

10= 6 lt 10휀 =gt 119888119897119886119904119904119890 1

- Classe de la semelle (comprimeacutee)

119889

119905119908=98

7= 14 lt 72휀 =gt 119888119897119886119904119904119890 1

Condition de reacutesistance

(119872119910119904119889

119872119890119897119910119877119889)

1

+ (119872119911119904119889

119872119890119897119911119877119889)1

le 1

- En preacutesence de lrsquoaction du vent

119872119910 =119902119906119911 times 119897

2

8=288 times 62

8= 1296 119896119873119898

- Sous lrsquoeffet des charges verticales permanentes

119872119911 =119902119906119910 times 119897

2

8=058 times 62

8= 261119896119873119898

119872119890119897119910119877119889 =119908119890119897119910 times 119891119910

1205741198720=864 times 103 times 235

11= 1845 119896119873119898

119872119890119897119911119877119889 =119908119890119897119911 times 119891119910

1205741198720=148 times 103 times 235

11= 316 119896119873119898

Donc

(1296

1845)1+ (

261

316)1= 152 gt 1 Condition non veacuterifieacutee

On rajoute des liernes pour reacuteduire Lz (Lz=3m)

55

Nouveau 119872119911

119872119911 =119902119906119910 times 119897

2

8=058 times 32

8= 065119896119873119898

(1296

1845)1+ (

065

316)1 = 09 lt 1 Condition veacuterifieacutee


Condition agrave veacuterifier Vsd lt Vplrd

119881119911119904119889 =15119882119871

2= 1296 119896119873

119881119901119897119877119889 =119860119907119911 times 119891119910

radic3times 1205741198720= 12855 119896119873

119881119911119904119889 = 1296 119896119873 lt 119881119901119897119877119889 = 12855 119896119873 rarr condition veacuterifieacutee

Veacuterification au deacuteversement

On doit veacuterifier


1205741198721gt 119872119910119904119889 119912119955119957 120787 120787 120784 (120787 120786120790)119914119914119924120791120789

Avec

119872119888119903 = 11986211205872 119864 1198681199111198712

radic119868119908119868119911+1198712 119866 1198681199051205872 119864 119868119911

119912119925119925119916119935119916 119913 (119913 120783 120785) minus 119914119914119924120791120789

119872119888119903=311713762 Ncm

λ119897119905 = radic120573119908 times119882119901119897119910 times 119891119910

119872119888119903

120573119908= 1 car la section est de classe 1

119882119901119897119910 (upn140) =103 cm3

56

λ119897119905 = 0881

empty119897119905 = 05 times [1 + 120572119897119905(λ1198711198792 minus 02) + λ119871119879

2 ]

120572119897119905=021 Car profileacute lamineacute

empty119897119905 = 0959

ꭕ119897119905=

1

(empty119897119905 +radicempty1198971199052 minus λ119897119905

2 )

le 1

ꭕ119897119905= 075

119872119887119903119889 = 1652 119896119873119898

119872119887119903119889 = 1652 119896119873119898 gt 119872119910119904119889 = 1296 119896119873119898 119862119900119899119889119894119905119894119900119899 119907eacute119903119894119891119894eacute119890

Conclusion La section UPN140 assure une bonne reacutesistance vis agrave vis des diffeacuterents cas

drsquoinstabiliteacute elle est convenable pour les lisses de notre structure

34 Dimensionnement des liernes

Figure 37 Disposition des liernes sur le bardage

Calcul de lrsquoeffort de traction dans les liernes

La reacuteaction R au niveau du lierne

57

119877 = 125119902119910 times 119897

2

Avec 119902119910 = [135(119866119880119875119873140 + 119866119888119900119906119907119890119903119905119906119903119890)]

119902119910 = 0837119896119873

119897 = 6 119898

119877 = 125119902119910 times 119897

2= 125 times 0837 times 3 = 32119896119873

Effort de traction dans chaque lierne

1198791 =119877

2= 16119896119873

1198792 = 1198791 + 119877=48 kN

1198793 =1198792

2 sin 120579= 374 119896119873 119860119907119890119888 120579 = 119886119903119888 119905119892

25 119898

3 119898= 398deg

Crsquoest 1198792 = 48 119896119873 la tension la plus deacutefavorable donc on dimensionne par rapport agrave elle nos liernes

Dimensionnement de la lierne

119873119905119904119889 =119860 times 119891119910

1205741198720= 4800 119873 =gt 119860 ge

11 times 4800

235 =gt 119860 ge 22461198981198982

119860 =120587empty2

4=gt empty ge radic

4119860

120587= radic

4 times 2246

314= 534 119898119898

On prend empty = 12 119898119898 soit un T12 car crsquoest le diamegravetre le plus courant sur le marcheacute

35 Calcul des cheacuteneaux

Introduction

Le cheacuteneau a pour rocircle lrsquoeacutevacuation des eaux pluviales et drsquoeacuteviter leur stagnation afin drsquoassurer une

bonne eacutetancheacuteiteacute de la toiture et de la construction

58

Figure 38 Coupe vertical sur le cheacuteneau

La section du checircneau sera deacutetermineacutee comme suit 119904

119878ge

63

radic119904

119889times119875

Avec

- s Section transversale du cheacuteneau en cmsup2

- S Surface couverte du checircneau en msup2

- d Peacuterimegravetre de la section mouilleacutee du checircneau en cm

- p Pente du checircneau

Remarque on preacutevoit 4 points de descente drsquoeau sur le long pan au niveau du portique inteacuterieur

Dimensionnement du cheacuteneau de rive

S=91times30=273 m2 avec P= 5mmm (pour eacuteviter lrsquoaccumulation du sable aussi)

Srsquo=273

4=6825 m2

Suivant lrsquoabaque (Annexe 2) =gt S=100 cm2 =gt d=10 cm

On prend un tuyau de PVC de diamegravetre 100mm

Dimensionnement de cheacuteneau intermeacutediaire

Surface en plan des combles desservis en msup2

Srsquo=6825times2= 1365 et P= 5 mmm


On prend un tuyau de PVC de diamegravetre 90 mm ou 100 mm

59

36 Preacutedimensionnement des potelets

Les potelets sont des profileacutes lamineacutes qui ont pour rocircle de transmettre les

diffeacuterents efforts horizontaux agrave la poutre au vent et les efforts verticaux vers le sol

Ce sont des profileacutes disposeacutes verticalement sur le pignon comme indiqueacute sur la figure

ci-dessous et sont surtout sujet agrave la flexion composeacutee sous les efforts suivant

- Effort normal produit par le poids propre du potelet du bardage et des lisses

- Effort de flexion produit par lrsquoaction du vent sur le pignon

Figure 39 Disposition des potelets

Ils sont consideacutereacutes comme articuleacutes dans les deux extreacutemiteacutes

Eacutevaluations des charges et surcharges revenantes agrave un potelet

Charges permanentes G (verticale concentreacutee)

- Poids propre de bardage (panneau sandwich) 133 daNmsup2

- Poids propre des accessoires drsquoattaches 5 daNmsup2

- Poids propre de la lisse UPN 140 1568 daNml

Nous avons 4 lisses de 6m de long

119866 = (119866UPN times 119890 times 119899) + (119866bardage + 119901119901a) times 119878 119866 =(1568times6times4)+[(133+5)times(6times56)]= 991 kNml

Charge due au vent W

W=(1541times56) = qeqtimes96 =gt qeq=1541times56

96=8989 daNm2

Donc W = 8989 x 6 = 539 daNml = 539 kNml

Preacutedimensionnement de la section du potelet

Sous la condition de la limite de la flegraveche (ELS) tableau 41 CCM 97

Les potelets eacutetant articuleacutes en tecircte et en pied la flegraveche max est

60

119891119910 =5 times119882 times 1198974

384 times 119864 times 119868119910le 119891119886119889119898 =

119897

200

119868119910 gt1000 timesWtimes Iᶟ

384 times E= 59136 1198881198984

Ce qui correspond agrave un profileacute IPE300 avec 119868119910 = 83561198881198984

Profileacute


IPE300 A Cm2

h mm

b mm

tf mm

tw

mm 119868y

Cm4

119868z Cm4

Wply

cm3

Wplz

cm3

MATERIAU ACIER S235

538 300 150 107 71 8356 746 628 125

Tableau 35 Caracteacuteristiques geacuteomeacutetriques drsquoIPE 300

Veacuterification de la reacutesistance du profileacute

Classe de la section

Classe de la semelle

119888

119905119891=

75

107= 7 lt 10 = 10 119878119890119898119890119897119897119890 119889119890 119888119897119886119904119904119890 1

Classe de lrsquoacircme

119889

119905119908=2486

71= 35 lt 38 = 38 Acirc119898119890 119889119890 119888119897119886119904119904119890 1

Veacuterification a lrsquoeffort tranchant

Pour la veacuterification de lrsquoeffort tranchant on doit veacuterifier la condition suivante

Si 119881119904119889 le 05 119881119901119897119903119889 ⟹119872119904119889 le 119872119888119903119889 119912119955119957120787 120786 120789 119914119914119924 120791120789

61

119881119904119889 =15 times119882 times 119897

2=15 times 539 times 96

2= 388 119896119873 lt 05 119881119901119897119903119889 = 05 (

2570 times 235

radic3 times 11) = 1585 119896119873

Condition veacuterifieacutee

Donc pas drsquoincidence de lrsquoeffort tranchant sur le moment reacutesistant

Veacuterification a lrsquoeffort axial

On utilise la condition suivante

Si

119873119904119889 le 119872119894119899 (025119873119901119897119903119889 05119860119908 119891119910

1205741198980)

Pas drsquointeraction entre le moment reacutesistant et lrsquoeffort axial

025119873119901119897119903119889 = 025119860 times 119891119910

1205741198720= 025

5380 times 235

11= 28734 119896119873

05119860119908 times 119891119910

1205741198720= 05

2170 times 235

11= 2317 119896119873

119873119904119889 = 135119866 = 1337 119896119873 lt 119898119894119899 (025119873119901119897119903119889 05119860119908 times 119891119910

1205741198720)


Donc on doit veacuterifier la relation suivante

Lrsquoindice de lrsquoeffort axial sur le moment fleacutechissant est neacutegligeacute

Veacuterification a la flexion composeacutee

119872119910119904119889 =15119882 times 1198972

8= 9313119896119873119898 119872119911119904119889 = 0 119872119901119897119910119903119889 = 13416 119896119873119898

λ119897119905 =

119871119911119894119911

119888105

[

1 +120(

119871119911119894119911ℎ119905119891

)

2

] 025

C1=1132 Annexe B Tableau B12 CCM97

62

119871119911 = 1250 119898119898 119894119911 = 335 119898119898 ℎ = 300 119898119898 119905119891 = 107 119898119898

λ119897119905 = 3433 =gt λ119897119905 = 036 lt 04 Pas de risque de deacuteversement


Flexion composeacutee sans risque de deacuteversement Art 554 (551) CCM97

119873119904119889ꭕ119898119894119899

119873119901119897119903119889+119870119910 119872119910119904119889

119872119901119897119910119903119889+119870119911 119872119911119904119889119872119901119897119911119903119889

le 10 helliphellip (1)

Avec

λ119910 =119871119910

119894119910=960

125= 768 rarr λ119910 =

768

939= 081

=gt 120583119910 = λ119910(2119861119898119910 minus 4) +119882119901119897119910 minus119882119890119897119910

119882119890119897119910= minus1134 + 0127 = minus1007 lt 09

120572 = 021 λ119910 = 081

empty119910 = 05 [1 + 120572119910(λ119910 minus 02) + λ1199102]

empty119910 = 05[1 + 021(081 minus 02) + 0812] = 089

ꭕ119910=

1

(empty119910 +radicempty1199102 minus λ1199102 )

ꭕ119910= 0794 rarr 119870119910 = 1 minus

minus1 times 135 times 991

0794 times 538 times 2350= 101

120582119911 =125

335= 3731 =gt 120582119911 = 0397 rarr empty119911 = 0611 =gt ꭕ

119911= 092

ꭕ119898119894119899

= ꭕ119910= 0794

119873119901119897119903119889 =119860119891119910

1205741198980=5380 times 235

11= 114936 119896119873

119872119910119904119889 =151198821198712

8= 9313 119896119873119898

119872119901119897119910119903119889 = 13416 119896119873119898

119873119904119889 = 135119866 = 1337 119896119873

119896119910 = 101

119872119911119904119889 = 0

63

119873119904119889120594119898119894119899 119873119901119897119903119889

+119896119910 119872119910119904119889

119872119901119897119910119903119889+119896119911 119872119911119904119889119872119901119897119911119903119889

le 10

1337

0794 times 114836+101 times 9313

13416= 071 lt 1 119862119900119899119889119894119905119894119900119899 119907eacute119903119894119891119894eacute119890

Conclusion le profileacute IPE300 veacuterifie toutes les conditions de reacutesistances des diffeacuterentes instabiliteacutes

auxquels il peut ecirctre sujet

Donc il convient parfaitement comme potelet pour notre structure

64

Chapitre 4

Etude du pont roulant

41 Introduction

La vocation de notre halle neacutecessite deux ponts roulants drsquoune capaciteacute de 125t chacun il

est neacutecessaire donc de leur dimensionner des poutres porteuses ainsi que les rails sur

lesquelles il va glisser

- Le pont roulant

Est un engin de levage mobile circulant sur une voie de roulement Il est constitueacute drsquoun

palan de transfert eacutequipeacute drsquoun treuil pour le levage de la charge

- La voie de roulement

Est la structure porteuse de lrsquoengin de levage constitueacutee de deux poutres de roulement et

ses supports les deux poutres parallegraveles sont surmonteacutees drsquoun rail speacutecial sur lesquelles

circule le pont roulant

- La poutre de roulement

Est lrsquoeacuteleacutement porteur longitudinal de la voie les poutres de roulement sont des poutres

simples ou continues Leurs appuis sont constitueacutes par corbeaux (consols) fixeacutes sur les

poteaux de la halle

65

411 Caracteacuteristiques des ponts roulants

Figure 41 Scheacutema 3D du pont roulant


Soit le pont roulant avec la porteacutee de 18 m

Puissances

N (t)

Porteacutee

L(m)

Vitesse (mmin) Poids (t) Reacuteaction (t)

Levage Direction Translation Pont

B

Chariot

K

Total

B+K

Rmax Rmin

125 18 085 520 1040 6809 1151 796 814 194

Tableau 41 Caracteacuteristiques du pont roulant (Annexe5)

66

a min (m) b(m) c(m) d(m) e(m)

1 035 06 2 36

Tableau 42 Caracteacuteristiques geacuteomeacutetriques du pont roulant

Groupe c ψ1 ψ2 Classe

I 02 11 11 A-2

Tableau 43 Coefficient et classement des ponts roulants

42 Classification des ponts roulants

Les ponts roulants sont classeacutes selon deux critegraveres

- Intensiteacute de lrsquousage du pont

- La variation de la charge souleveacutee

421 Coefficient et Classements des ponts roulants selon le CTICM

- Les ponts roulants agrave usage intensif (les poutres de roulement roulants

doivent ecirctre conccedilues et calculeacutees avec soin)

- Les ponts roulants drsquousage peu freacutequent (le calcul de poutre de roulement

est similaire agrave celui drsquoune poutre quelconque sous charge statique)

- Utilisation reacuteguliegravere en service intensif suivant lrsquoeacutetat de charge

C Coefficient drsquoadheacuterence drsquoun galet sur son rail

Ψ Coefficient de majoration dynamique des reacuteactions verticales Dans

ce projet le pont roulant utiliseacute est de Type A classe 2

Groupes II

Remarque Les ponts roulant agrave crochet sont classeacute dans le groupe II

422 Description geacuteneacuterale du calcul En geacuteneacuteral les poutres de roulements sont conccedilues sur deux appuis particuliegraverement celles

destineacutees agrave recevoir les ponts de type A pour que lrsquoalternance de sollicitations M(+) M(-) conduit

agrave reacuteduire les contraintes admissibles en fatigue Le moment maximum est deacutetermineacute par le

theacuteoregraveme de BARRE il est deacutefini comme suit

67

Figure 43 Moment max pour deux charges eacutegales (Theacuteoregraveme de Barreacute)

423 Deacutefinition des charges Charges verticales (RVmax)

- Le poids des poutres de roulement

- Le poids du pont du chariot et de la charge souleveacutee

- Les surcharges sur passerelles si elles existent

Charges horizontales transversales (RHmax)

- Reacuteaction transversale provoqueacutee par le roulement

- Freinage de direction

- Vent sur la poutre dans le cas des poutres de roulement agrave lrsquoexteacuterieur du hangar

Charges horizontales longitudinales (RLmax)

- Freinage longitudinale (de translation)

- Effet de tamponnement

- Vent sur pont srsquoil est agrave lrsquoexteacuterieur du hangar

424 Calcul des reacuteactions des galets du pont roulant

Charges statiques (reacuteaction par galet)

119877119898119886119909 = 814 119870119873 119877119898119894119899 = 194 119870119873

Charges verticales

119877119881119898119886119909 = Ψ1 119877119898119886119909 = 115 times 814 = 8954 119870119873

119877119881119898119894119899 = Ψ2 119877119898119894119899 = 11 times 194 = 2134 119870119873

Charges horizontale longitudinale

68

119877119871119898119886119909 = 119862 119877119898119886119909 = 02 times 814 = 1628 119870119873

119877119871119898119894119899 = 119862 119877119898119894119899 = 02 times 194 = 388 119870119873

Charges horizontales transversales

Palan au milieu de la porteacutee du pont

1198771198671119898119886119909 = plusmn [0024(119870 + 119873 + 119861)119871

119890+ 0021(119873 + 119870)]

= plusmn [0024(1151 + 125 + 6809)18

36+ 0021(125 + 1151)]

1198771198671119898119886119909 = plusmn274 119905

1198771198671119898119894119899 = plusmn [0024(119870 + 119873 + 119861)119871

119890minus 0021(119873 + 119870)]

= plusmn [0024(1151 + 125 + 6809)18

36minus 0021(125 + 1151)]

1198771198671119898119894119899 = plusmn2168 119905

Palan agrave distance minimale du chemin de roulement

1198771198672119898119886119909 = plusmn [00052(119870 + 119873 + 5119861)119871

119890+ 0021(119873 + 119870)]

= plusmn [00052(1151 + 125 + 5 times 6809)18

36+ 0021(125 + 1151)]

1198771198672119898119886119909 = plusmn1526 119905

1198771198672119898119894119899 = plusmn [00052(119870 + 119873 + 5119861)119871

119890minus 0021(119873 + 119870)]

= plusmn [00052(1151 + 125 + 5 times 6809)18

36minus 0021(125 + 1151)]

1198771198672119898119894119899 = plusmn0953 119905

Les premiers membres de ces formules correspondent aux efforts induits par la marche

appeleacutee marche en crabe du pont roulant les deuxiegravemes membres de ces formules

correspondent aux efforts dus au freinage du palan charge

69

425 Le choix du rail de roulement

Pour notre cas on a un pont roulant de 125T on va utiliser des rails A55

maintenues avec des crapauds

Figure 44 Coupe transversale du rail

Rail

Poids

(Kgm)

B

(mm)

H

(mm)

P

(mm)

Section

A (cm2)

I x

(cm4)

I y

(cm4)

A55

318

55

65

150

407

178

337

Tableau 44 Caracteacuteristiques geacuteomeacutetriques du rail

Figure 45 Scheacutema de la poutre de roulement avec le rail

70

43 Preacutedimensionnement de la poutre de roulement Le dimensionnement de la poutre du chemin de roulement se fait selon le regraveglement laquo CCM97 raquo et le calcul se fait avec les charges les plus deacutefavorables

431 Condition de la flegraveche Drsquoapregraves le CTICM le dimensionnement de la poutre de roulement se fait avec la condition de flegraveche La flegraveche admissible est obtenue quand les deux charges sont en position symeacutetrique par rapport au milieu de la poutre il faut veacuterifier donc que

119891119911 le 119891119886119889119898 =119897

750= 08 119888119898

La longueur de traveacutee est de 600 m (sur deux appuis simple) comme indiqueacutee sur le scheacutema

Figure 46 Scheacutema statique de la poutre de roulement

119886 = (119897

2minus119890

4) = (

6

2minus36

4) = 21 119898

Figure 47 Illustrations des efforts appliqueacutes sur la poutre de roulement par le

galet et P la reacuteaction verticale max

119891119911 =119901 119886 1198972

24119864119868(3 minus

4 1198862

1198972)

Avec

L= 6000 mm

a= 2100 mm

P=89540 N

E=21104 Nmm2

71

119868119910 ge119901 119886 1198972(31198972 minus 41198862)

119891119911 241198641198972=89540 times 2100 times 60002(3 times 60002 minus 4 times 21002)

8 times 24 times 21 times 104 times 60002

119868119910 ge 421397625 1198981198984

Donc HEB360 veacuterifie la condition de la flegraveche

Tableau 45 Caracteacuteristiques du profileacute HEB360

Veacuterification de la flegraveche

Poids propre inclue (rail+poutre)

Figure 48 Scheacutema statique de la poutre de roulement sur deux appuis

119902 = 119866119901119900119906119905119903119890 + 119866119903119886119894119897 = 142 + 031 = 173 119896119899119898119897

119891119911 =119901 119886 1198972

24119864119868(3 minus

4 1198862

1198972) +

5 119902 1198974

384119864119868

119891119911 =89540 times 2100 times 60002

24 times 21 times 104 times 43190 times 104times (3 minus

4 times 21002

60002) +



119891119911 = 812 119898119898 le 119891119886119889119898 = 8 119898119898 La condition nrsquoest pas veacuterifieacutee Donc on augmente la section

profileacute

poids section Dimensions Caracteacuteristiques

G

Kgm

A cm2 h

mm

b

mm

tf

mm

tw

mm

Iy

cm4

Iz

cm4

Wply

cm3

Wplz

cm 3

HEB360 142 1806 360 300 225 125 43190 10140 2683 1032

72


119902 = 119866119901119900119906119905119903119890 + 119866119903119886119894119897 = 155 + 031 = 186 119870119873119898119897

119891119911 =119901 119886 1198972

24119864119868(3 minus

4 1198862

1198972) +

5 119902 1198974

384119864119868

119891119911 =89540 times 2100 times 60002


4 times 21002

60002) +



119891119911 = 537 119898119898 le 119891119886119889119898 = 8 119898119898 La condition est veacuterifieacutee

432 Classe du profileacute HEB 400 Tableau 531 CCM97

- Classe de lrsquoacircme fleacutechie 119889

119905119908le 72휀

Avec

휀 = radic235

119891119910

298

135le 72radic

235

235 ⟹ 2207 le 72

Lrsquoacircme est de classe 1 - Classe de la semelle comprimeacutee

119888

119905119891=1198872

119905119891le 10휀 ⟹

150

24= 625 le 10

La semelle est de classe 1 Donc la section du profileacute global est de classe 1

Veacuterification au cisaillement (ELU)

La veacuterification au cisaillement est donneacutee par les formules suivantes

profileacute


G

Kgm

A

cm2

h

mm

b

mm

tf

mm

tw

mm

Iy

cm4

Iz

cm4

Wply

cm3

Wplz

cm 3

HEB400 155 1978 400 300 24 135 57680 10820 3232 1104

73

119881119910119904119889 le 119881119901119897119903119889 119912119955119957 120787 120786 120788 (120787 120784120782)119914119914119924120791120789

119881119901119897119903119889 =119860119907119911 119891119910

radic3 1205741198980=6998 times 235

radic3 times 11= 863154 119873 = 86315 119870119873

- Effort tranchant du agrave la reacuteaction (119877119881119898119886119909) -

119881119881 = 119877119881119898119886119909 times4119886

119897=8954 times 4 times 21

6= 12535 119870119873

- Effort tranchant du au pp (rail + HEB400)

119881119875119875 =119866 119897

2=186 times 6

2= 558 119870119873

Drsquoougrave 119881119910119904119889 = 135119881119875119875 + 15119881119881 = 19556 119870119873

119881119910119904119889 le 119881119901119897119903119889


Moment sollicitant sous charges verticales

Suivant (z-z)

- Moment du a la reacuteaction (119877119881119898119886119909)

119872119881 = 119877119881119898119886119909 times(6 minus

1198902)2

4119897= 8954 times

(6 minus362 )

2

4 times 6= 6581 119870119873119898

- Moment du au poids propre (rail + HEB400)

119872119875119875 =119866 1198972

8= 837 119870119873119898

Avec 119866=(rail+HEB400)=186 KNml Drsquoougrave

119872119910119904119889 = 135119872119875119875 + 15119872119881 = 110 119870119873119898

Moment sollicitant sous charges horizontales

Suivant(y-y) - Moment du a la reacuteaction(1198771198671)

119872119911119904119889 = 119872119867 =21198771198671119871

(119871

2minus119890

4)2

74

119872119911119904119889 = 119872119867 =2 times 274

6times (

6

2minus36

4)2

= 4028 119870119873119898

433 Veacuterification de la reacutesistance de la poutre de roulement

Pour raison de la forte sensibiliteacute des poutres de roulement agrave lrsquoinstabiliteacute eacutelastique leurs

dimensionnements par le calcul en plasticiteacute nrsquoest pas admis

119873119904119889119873119901119897119903119889

+119872119910119904119889

119872119890119897119910+119872119911119904119889119872119890119897119911

le 1 120787 120785120790 ndash 119810119810119820120791120789

119873119904119889 = 15119877119871119898119886119909 = 15 times 1628 = 2442 119870119873

119872119890119897119910 =119908119890119897119910 119891119910

1205741198720= 61613 119872119890119897119911 =

119908119890119897119911 119891119910

1205741198720= 1541 119873119901119897119903119889 =

119860 119891119910

1205741198720= 422573

2442

422573+

110

61613+4028

1541= 044 le 1

Condition veacuterifieacutee La condition de reacutesistance est veacuterifieacutee pour la poutre de roulement

Reacutesistance de lrsquoacircme au voilement par cisaillement CCM97 art 561(1)

Si 119889

119905119908le 72휀 il nrsquoest pas neacutecessaire de veacuterifier le voilement par cisaillement

Avec

휀 = radic235

119891119910= 1

119889

119905119908=298

135= 2207 lt 69

Donc il nrsquoy a pas lieu de veacuterifier le voilement par cisaillement

Reacutesistance au deacuteversement

Le moment reacutesistant de deacuteversement est donneacute par la relation suivante


1205741198721

Avec 120573119908 = 1 (section de classe 1) ꭕ119871119879 Le facteur de reacuteduction pour le deacuteversement

75

Pour les poutres agrave section constante et doublement symeacutetriques (profileacutes lamineacutes I et

H) lrsquoeacutelancement 120582lt 119907119886119906119905 ∶

λ119897119905 =

119871119894119911

119888105

[

1 +120(

119871119894119911ℎ119905119891

)

2

] 025 = 6522 119808119821119821119812119831119812119809 119810119810119820120791120789

Avec 119871 = 600119888119898

1198881 = 1046 Annexe B tableau B12 CCM97 λ119897119905 =6522 λ1 = 939휀

λ119871119879 = [λ119897119905λ1] [120573119908]

05 휀 = radic235

119891119910= 1

λ119871119879 =6522

939= 0694

On calcule

ꭕ119871119879=

1


2 )le 1

empty119897119905 = 05 times [1 + 120572119897119905(λ minus 02) + λ

2] 120572119897119905 = 021 Pour les profileacutes lamineacutes

empty119897119905 = 05 times [1 + 021(0694 minus 02) + 06942] = 079 Donc

ꭕ119871119879=

1

(079 + radic0792 minus 06942)= 0856

119872119887119903119889 =0856 times 1 times 3232 times 235

11= 59104 119870119873119898

119872119910119904119889 = 110 119870119873119898

119872119910119904119889 le 119872119887119903119889 Condition veacuterifieacutee

434 Reacutesistance de lrsquoacircme agrave la charge transversale

Resistance agrave lrsquoeacutecrasement

76

Figure 49 Illustration des galets sur la poutre de roulement

Lrsquoeffort reacutesistant agrave lrsquoeacutecrasement ART 573-CCM97

119891119904119889 le 119877119910119877119889

Avec

- 119878y Longueur drsquoappui rigide

- ℎR = 65 119898119898 La hauteur du rail

- 120590119891119864119889 = 381119896119873119888119898sup2 La contrainte longitudinale dans la semelle

120590119891119864119889 =119872119910119904119889

119882119890119897119910= 381 1198701198731198881198982

119878119910 = 2(ℎ119877 + 119905119891)radic[1 minus (1205741198720120590119891119864119889

119891119910119891)

2

] = 1751 119888119898

119877119910119877119889 =119878119910 times 119905119908 times 119891119910119908

1205741198720= 505 119870119873 gt 119891119904119889 = 119877119907119898119886119909 = 8954 119870119873


Veacuterification agrave enfoncement local

Selon le CCM97 il faut satisfaire les conditions suivantes

119891119904119889 le 119877119886119877119889

119891119904119889119877119886119877119889

+119872119878119889119872119888119877119889

le 1 119808119825119827 120787 120789120790 minus 119810119810119820120791120789

Avec

77

119877119886119877119889 =

051199051199082 (119864 119891119910119908)

05[(119905119891119905119908)05

+ 3(119905119908119905119891) (119878119904119889 )]

1205741198720 119808119825119827 120787 120789120789 minus 119810119810119820120791120789

119877119886119877119889 = 108284 119870119873

119891119904119889 = 15119877119871119898119886119909 = 15 times 1628 = 2442 119870119873

119872119888119877119889 =3232 times 103 times 235

11= 69047 119870119873119898

119891119904119889119877119886119877119889

+119872119878119889119872119888119877119889

=2442

108284+

110

69047 = 018 le 15


Reacutesistance au voilement de lrsquoacircme

Selon le regraveglement CCM97

119887119890119891119891 le 119887 119808119825119827 120787 120789120791 minus 119810119810119820120791120789

119887119890119891119891 = radicℎ2 + 1198781199042 = 410 119898119898 gt 119887 = 300 119898119898

Condition non veacuterifieacutee

435 Calcul du support du chemin de roulement

Le chemin de roulement est supporteacute par une console qui est solliciteacute par les

efforts suivants

- Le poids propre de la poutre de roulement et du rail

- Les actions verticales et horizontales des galets du pont roulant

- Le poids propre de la console elle-mecircme

Charge verticale

Charge verticale non pondeacutereacutee

119901prime = 119876 119871 + 119877119898119886119909 (2 minus119890

119871) ψ

2= 186 times 6 + 814 times (2 minus

36

6) times 11

119901prime = 13651 119870119873

Charge verticale pondeacutereacutee

119901 = 135119876 119871 + 15119877119898119886119909 (2 minus119890

119871) ψ

2= 135 times 186 times 6 + 15 times 814 times (2 minus

36

6) times 11

119901 = 2031 119870119873

78

Charge horizontale

119875119867 = 15119877119867119898119886119909 (1 minus119890

119897)ψ

2= 15 times 274 times (1 minus

36

6) times 11 = 1808 119870119873

Figure 410 Coupe verticale sur le support du chemin de roulement

Dimensionnement du support de chemin de roulement

La flegraveche du support de roulement est limiteacutee

119891119911 le 119891119886119889119898 =119897

500

Figure 411 Scheacutema statique du support de chemin de roulement

119891119911 =119901prime 1198893

3119864119868le 119891119886119889119898

119868119910 =500 119901prime 1198892

3119864ge 782667 1198881198984

Selon le moment drsquoinertie obtenu on choisira un IPE 300

79

Tableau 47 Caracteacuteristiques du profileacute IPE300



119905119908le 72휀

Avec

휀 = radic235

119891119910

2486

71le 72radic

235

235 ⟹ 3501 le 72


119888

119905119891=1198872

119905119891le 10휀 ⟹

75

102= 735 le 10

La semelle est de classe 1

Donc la section du profileacute global est de classe 1



119881119910119904119889 le 119881119901119897119903119889

Avec 119860119907119911 = 257 cm2

119881119901119897119903119889 =119860119907119911 119891119910

radic3 1205741198980=257 times 235

radic3 times 11= 317 119870119873

119881119904119889 = 119901 = 2031 lt 05119881119901119897119877119889


profileacute


G

Kgm

A

cm2

h

mm

b

mm

tf

mm

tw

mm

Iy

cm4

Iz

cm4

Wply

cm3

Wplz

cm 3

IPE 300 422 5380 300 150 107 71 8353 604 628 125

80

Reacutesistance agrave la flexion (ELU)

119872119888119903119889 =119908119901119897119910 119891119910

1205741198720=628 times 235

11= 13416 119870119873119898

119872119910119904119889 = 119901 119889 = 2031 times 085 = 172635 119870119873119898

119872119910119904119889 lt 119872119888119903119889

Condition non veacuterifieacutee Donc on augmente la section

Tableau 48 Caracteacuteristiques du profileacute IPE 360


119872119888119903119889 =119908119901119897119910 119891119910

1205741198720=1019 times 235

11= 2177 119870119873119898

119872119910119904119889 = 119901 119889 = 2031 times 085 = 172635 119870119873119898

119872119910119904119889 lt 119872119888119903119889


17263

Figure 412 Diagramme du moment fleacutechissant du support de chemin de roulement

profileacute


G

Kgm

A

cm2

h

mm

b

mm

tf

mm

tw

mm

Iy

cm4

Iz

cm4

Wply

cm3

Wplz

cm3

IPE 360 571 727 360 170 127 8 16270 1043 1019 191

81


Figure 413 Coupe verticale sur la reacutepartition des charges sur le support du

chemin de roulement

119891119911 le 119891119886119889119898 =119889

500= 017

119902 = 119902119868119875119864 360 = 571 119889119886119873119898119897

119891119911 =119901prime 1198893

3119864119868+119902 1198974

8119864119868= 0082 + 0021 = 0103 119888119898 lt 017 119888119898

Conclusion Donc on adopte un profileacute IPE360 comme un support de chemin de roulement

82

Chapitre-5

Etude Sismique 51 Introduction Parmi les catastrophes naturelles le seacuteisme est le plus proche et le plus destructeur des constructions en zone urbaine ou rurale Notre pays est lrsquoun des pays les plus concerneacutes par les tremblements de terre drsquoougrave lrsquoobligation de lrsquoeacutetude sismique pour nrsquoimporte quelle construction aussi minime soit son importance En Algeacuterie les deux tremblements de terre de 1980 survenus agrave la wilaya de Chlef et de 2003 agrave Boumerdes ont certainement contribueacute agrave la prise en compte de ces pheacutenomegravenes dans la construction Lors de toute catastrophe naturelle on se doit de proteacuteger avant tout la vie humaine preacutesente dans et autour des constructions Cela implique agrave la fois une connaissance scientifique du pheacutenomegravene ainsi que la maicirctrise des moyens techniques pour y faire face Les risques du seacuteisme deacutependent de lrsquoactiviteacute tectonique ainsi que de la nature du sol les caracteacuteristiques reacutegionales Pour notre ouvrage implanteacute dans la wilaya de Ouargla le regraveglement national parasismique RPA99v2003 classe cette zone comme zone 0 (zone de sismiciteacute neacutegligeable) Ce dernier propose trois meacutethodes de calcul dont les conditions drsquoapplications diffeacuterentes et cela selon le type de la structure agrave eacutetudier le choix des meacutethodes de calcul et la modeacutelisation de la structure doivent avoir pour objectif de srsquoapprocher au mieux au comportement reacuteel de lrsquoouvrage ces meacutethodes sont les suivantes - Meacutethode statique eacutequivalente - Meacutethode drsquoanalyse modale spectrale - Meacutethode drsquoanalyse dynamique par acceacuteleacuterogramme Concernant notre projet lrsquoanalyse de la structure est effectueacutee par le logiciel Robot conccedilu agrave base de la meacutethode des eacuteleacutements finis Notre projet ne neacutecessite pas drsquoeacutetude sismique approfondie pour les raisons suivantes

-Classeacute en zone 0 consideacutereacutee zone ougrave lrsquoactiviteacute sismique est tregraves faible

-La construction est leacutegegravere et entiegraverement en charpente meacutetallique

-La hauteur de la construction est faible (1025m seulement)

Dans ce chapitre nous allons aborder lrsquoeacutetude sismique en supposant que la construction est

implanteacutee en zone 1

Afin drsquoavoir des donneacutees pratique agrave partir du RPA99v2003 et pouvoir effectuer les calculs

dynamiques

52 Analyse de la structure

83

Lrsquoanalyse eacutelastique globale peut ecirctre statique ou dynamique selon la satisfaction des conditions imposeacutees par les regraveglements sur les cas de chargement Chargement statique - Le poids propre de la structure - Les effets dus aux actions climatiques Chargement dynamique - Les effets sismiques

521 Meacutethode de calcul - Calcul de lrsquoeffort tranchant statique par la meacutethode statique eacutequivalente La meacutethode de calcul la plus adapteacutee pour le calcul dynamique des structures est celle qui est baseacutee sur lrsquoutilisation des spectres de reacuteponse Mais le RPA exige que lrsquoeffort tranchant dynamique soit supeacuterieur agrave 80 de lrsquoeffort tranchant statique donc on va calculer lrsquoeffort tranchant statique par la meacutethode statique eacutequivalente - Principe de la meacutethode Les forces reacuteelles dynamiques qui se deacuteveloppent dans la construction sont remplaceacutees par un systegraveme de forces statiques fictives dont les effets sont consideacutereacutes eacutequivalents agrave ceux de lrsquoaction sismique

522 Calcul de la force sismique totale La force totale (V) appliqueacutee agrave la base de la structure doit ecirctre calculeacutee successivement dans les deux directions horizontales et orthogonales selon la formule

119881 =119860119863 119876

119877119882

Avec A coefficient drsquoacceacuteleacuteration en fonction de la zone sismique et du groupe drsquousage du bacirctiment Dans notre cas on est dans la zone 0 une zone de sismiciteacute neacutegligeable selon le RPA donc on va prendre la plus faible valeur celle pour la zone 1 dans le tableau laquo chapitre3sect31 raquo RPA99V2003 et un groupe drsquousage 3 laquo chapitre3sect32 raquoRPA99V2003 A=005

D facteur drsquoamplification dynamique moyen qui est en fonction de la cateacutegorie du site et du facteur drsquoamortissement (η) ainsi que de la peacuteriode fondamentale de la structure (T)

119863 =

25120578 0 le 119879 le 1198792

25120578(1198792119879)23 1198792 le 119879 le 3119904

25120578 (11987923)

23 (3119879)

53 119879 gt 3119904

T1 T2 peacuteriodes caracteacuteristiques associeacutees agrave la cateacutegorie du site et donneacutees par le tableau (47) RPA99V2003 Pour notre cas en se place dans le site (S3) T1=015 s T2=050 s Le facteur de correction drsquoamortissement est donneacute par la formule

84

120578 = radic7

(2 + 120585)ge 07

Drsquoapregraves le tableau (42) RPA99V2003 on a 120585 = 5

Drsquoapregraves le RPA99V2003 article 43 si 120585 = 5 alors 120578 = 1 523 Estimation de la peacuteriode fondamentale

119879 = 119862119879 ℎ11987334 119917119926119929119924119932119923119916 (120786 120788)119929119927119912 119933120784120782120782120785

ℎN Hauteur mesureacutee agrave partir de la base jusqursquoau sommet de la structure ℎN= 1025 119898

119862t Coefficient il est en fonction du systegraveme de contreventement et du type de remplissage portique auto-stable en acier sans remplissage en maccedilonnerie Drsquoougrave 119862t = 0085

Donc 119879 = 0085times102534= 0487 119904 13T=0633 s On a 0 le 119879 le 1198791051446 = 0 le 0487 le 05 Donc 119863 = 25120578 = 25 times 1 = 25 R coefficient de comportement global de la structure sa valeur est donneacutee par le tableau (43) de RPA99V2003 en fonction du systegraveme de contreventement Sens transversal R=4 Sens longitudinal R=4 Q facteur de qualiteacute il est en fonction de la redondance geacuteomeacutetrie reacutegulariteacute en plan et en eacuteleacutevation et la qualiteacute de control de construction (ANNEXE ndash 4)

119876 = 1 +sum119875119902

6

1

Tableau 51 Peacutenaliteacutes de veacuterification

85

1-Condition minimale sur les files de contreventement non observeacutee 005 2-Redondance en plan observeacutee 0 3-Reacutegulariteacute en plan observeacutee 0 4-Reacutegulariteacute en eacuteleacutevation observeacutee 0 5-Controcircle de qualiteacute des mateacuteriaux 005 laquo supposeacute non veacuterifieacute raquo 6-Controcircle de qualiteacute de lrsquoexeacutecution non observeacute 01

119876 = 1 +sum119875119902

6

1

= 1 + 02 = 12

119882 poids total de la structure 119882 est eacutegal agrave la somme des poids Wi Calculeacutes agrave chaque niveau (i) 119882 = sum 119882119894

119899119894=1

Avec 119882119894 = 119882119866119894 + 120573119882119876119894

- 119882119866119894 poids ducirc aux charges permanentes et agrave celles drsquoeacutequipement fixes eacuteventuels solidaire de la structure - 119882119876119894 charges drsquoexploitation

- 120573 Coefficient de pondeacuteration fonction de la nature et de la dureacutee de la charge drsquoexploitation pris eacutegal agrave 050 laquo tableau 45 du RPA99V2003 raquo Le poids total de la structure peut ecirctre obtenu directement agrave partir du Logiciel ROBOT ANALYSE STRUCTURAL en introduisent la Combinaison 119882i= 119882Gi + 120573119882Qi

Le poids total de la structure est de 189475KN Force sismique totale V

119881 =119860119863 119876

119877119882

119860 = 005 119863 = 25 119876 = 12 119877 = 4 119882 = 189475119896119873

119881119909 = 119881119910 =005 times 25 times 12

4times 189475 = 7105119896119873

524 Meacutethode modale spectrale Par cette meacutethode il est rechercheacute pour chaque mode de vibration le maximum des effets engendreacutes dans la structure par les forces sismiques repreacutesenteacutees par un spectre de reacuteponse de calcul Ces effets sont par la suite combineacutes pour obtenir la reacuteponse de la structure Lrsquoaction sismique est repreacutesenteacutee par le spectre de calcul (413) du RPA2003

119904119886119892=

125119860 (119860 +

119879

1198791(25120578

119876

119877minus 1)) 0 le 119879 le 1198791

25120578(125119860) (119876

119877) 1198791 le 119879 le 1198792

25120578(125119860) (119876

119877)(1198792119879)23

1198792 le 119879 le 30119904

25120578(125119860) (11987923)

23(3

119879)

53(119876

119877) 119879 gt 30119904

86

Avec les Coefficients A η R T1 T2 Q qui sont deacutejagrave deacutetermineacutes

525 Reacutesultat du calcul dynamique - Scheacutematisation du spectre de reacuteponse suivant X et Y Paramegravetres du spectre

η = 100 A=005 1198791=015 1198792=050

Figure 51 Spectre de reacuteponse suivant la direction X

87

Figure 52 Spectre de reacuteponse suivant la direction Y

526 Veacuterification de la reacutesultante des forces sismiques

Selon lrsquoarticle 436 du RPA99V2003 la reacutesultante de la force sismique agrave la base Vt obtenue par la

combinaison des valeurs modales doit ecirctre supeacuterieure agrave 80 de la reacutesultante des forces sismiques

deacutetermineacutee par la meacutethode statique eacutequivalente

Force sismique V statique 08 V statique V dynamique Observation Sens x-x 7105 KN 5684 KN 6501 Veacuterifieacutee

Sens y-y 7105 KN 5684 KN 6378 Veacuterifieacutee

Tableau 52 Veacuterification de lrsquoeffort tranchant agrave la base

Lrsquoeffort tranchant dynamique est supeacuterieur agrave 80 de lrsquoeffort tranchant statique dans les deux sens il nrsquoy a pas lieu drsquoaugmenter les paramegravetres de reacuteponse

527 Veacuterification de la peacuteriode La peacuteriode numeacuterique donneacutee par le logiciel ROBOT ANALYSIS STRUCTURAL est de 062 s alors que la peacuteriode fondamentale calculeacutee est de 0487 s Aussi on ne prend pas en compte les peacuteriodes des quatre premiers modes car leurs masses

cumuleacutees sont nuls ou presque nuls

Tempirique = 060 lt 13 x Tfondamental=13x0487 = 0633s condition veacuterifieacutee

88

Tableau 53 Tableau des peacuteriodes

528 Veacuterification des deacuteplacements 1er Cas situation durable Drsquoapregraves lrsquoarticle 4222 du CCM97 les deacuteplacements horizontaux sont limiteacutes agrave

h150 sans charge du vent h125 avec charge du vent

Figure 53 Valeur limite des flegraveches horizontales des bacirctiments industriels

Combinaison Deacuteplacement max (cm)

Avec vent Sans vent Avec vent Sans vent

Suivant X G+ V1 G+Q 32 39

Suivant Y G+ V2 G+Q 20 10

Tableau 54 Deacuteplacement ultime en situation durable

89

ℎ

150=890

150= 594119888119898 sans vent

ℎ

125=890

125= 712119888119898 avec vent

Les deacuteplacements suivant les deux directions sont infeacuterieurs aux deacuteplacements admissibles 2eacuteme cas situation accidentelle Le RPA 99V2003 preacutecise que le deacuteplacement horizontal est calculeacute sous les forces sismiques seul lrsquoarticle 443 preacuteconise de limiter les deacuteplacements relatifs lateacuteraux drsquoun eacutetage par rapport aux eacutetages qui lui sont adjacents agrave 1 de la hauteur drsquoeacutetage article 510 Le deacuteplacement horizontal agrave chaque niveau K de la structure est calculeacute comme suit 120575k = 119877 120575ek

120575ek deacuteplacement ducirc aux forces sismiques

119877 119862119900119890119891119891119894119888119890119899119905 119889119890 119888119900119898119901 119877 = 4 Il srsquoagit de veacuterifier le point le plus haut de la toiture par rapport au sol

Niveau Deacuteplacement (cm) Deacuteplacement relatif (cm)

Suivant X Suivant Y Suivant X Suivant Y

Toiture 029 076 116 304

Tableau 55 Deacuteplacement relatif en situation accidentelle

ℎ

100=1025

100= 1025 119888119898

Tous les deacuteplacements sont infeacuterieurs agrave 1025 cm donc cette condition est satisfaite

Conclusion Les actions du vent sont les plus deacutefavorables dans les structures meacutetalliques Les systegravemes de contreventement lui assurent un bon comportement vis-agrave-vis agrave lrsquoaction du vent et le seacuteisme

90

Chapitre-6

Veacuterifications des eacuteleacutements structuraux

61 Introduction

Apregraves avoir modeacuteliseacute notre structure sur le logiciel Robot on passe aux diffeacuterentes veacuterifications exigeacutes par le CCM97 Le calcul drsquoune structure exige que sous toutes les combinaisons drsquoactions deacutefinies reacuteglementairement la stabiliteacute doit ecirctre assureacutee tant globalement au niveau de la structure qursquoindividuellement au niveau de chaque eacuteleacutement Il faut que les barres reacutesistent aux instabiliteacutes crsquoest-agrave-dire successivement au flambement ducirc agrave lrsquoaction drsquoune compression axiale au deacuteversement qui se deacuteveloppe sous lrsquoaction drsquoun moment fleacutechissant et au voilement ducirc agrave une sollicitation drsquoeffort tranchant

62 Veacuterification de la traverse IPE 400 La traverse de notre structure est un eacuteleacutement porteur constituant la partie supeacuterieur du portique supportant la panne et la couverture Sa fonction principale est de transmettre les actions agissantes sur la toiture aux poteaux La veacuterification se fait pour la traverse la plus solliciteacutee sous la combinaison drsquoaction la plus deacutefavorable

Figure 61 Illustration de la traverse la plus solliciteacutee

Pour la traverse drsquoune longueur de 91 m deacutesigneacutee en bleu qui est supposeacutee encastreacutee-encastreacutee et solliciteacutee par la combinaison drsquoaction suivante (G+15V1) les efforts sollicitant deacutetermineacutes par cette combinaison sont donneacutes par le logiciel Robot

119872119910119904119889 = 21902 kNm

119881119904119889 =7249 kN

119873119904119889 =2018 kN

91

Profileacute


IPE 400 A cm2

hmm

b mm

119905f

mm

119905w mm

119868y

cm4

119868z Cm4

119908ply

cm3

119908plz

cm3

MATERIAU ACIER S235

8446 400 180 14 90 231284 131782 123832 2256


Deacutetermination de la classe du profileacute


119888

119905119891=60

14= 59 lt 10휀 =gt 119888119897119886119904119904119890 1


119889

119905119908=98

9= 11 lt 72휀 =gt 119888119897119886119904119904119890 1

Donc la section est de classe 1

Veacuterification de la section agrave la reacutesistance

- Veacuterification agrave lrsquoeffort tranchant

Pour la veacuterification de lrsquoeffort tranchant on applique la condition suivante

Si 119881119904119889 le 05119881119901119897119903119889 ⟹ 119872119904119889 le 119872119888119903119889 119912119955119957120787 120786 120789 119914119914119924 120791120789

119872119888119903119889 Moment reacutesistant plastique

119881119898119886119909 = 119881119904119889 =7248kN

119881119901119897119911119903119889 =

119860119907119911 (119891119910

radic3)

1205741198980=

4270235

radic311

= 526674119896119873

119881119904119889 = 7247 le 05119881119901119897119911119903119889 = 52667119896119873

Lrsquoincidence de lrsquoeffort tranchant sur le moment reacutesistant est neacutegligeacutee

92

- Veacuterification de lrsquoeffort normal


119873119904119889 le 119872119894119899(025119873119901119897119903119889 05119860119908119891119910

1205741198720)

Pas drsquointeraction entre le moment reacutesistant et lrsquoeffort normal

119873119904119889 = 2018119896119873

119873119901119897119903119889 le119860 119891

119910

1205741198720=8446 235

11= 180437119896119873

025119873119901119897119903119889 =451 119896119873

119860119908 = 119860 minus 2119887 119905119891 = 34061198981198982

05119860119908119891119910

1205741198720= 36382119896119873

119873119904119889 = 2018 le 36382119896119873

Lrsquoindice de lrsquoeffort normal sur le moment fleacutechissant est neacutegligeacute

- Veacuterification au moment fleacutechissant 119872119910119904119889 = 219119896119873119898

119872119888119903119889 = 119872119901119897119910119903119889 =119908119901119897119910 119891119910

1205741198720=1238320 235

11= 26455119896119873119898

119872119910119904119889 = 219 le 119872119888119903119889 = 26455119896119873119898 Condition veacuterifieacutee

Veacuterification drsquoeacuteleacutement au pheacutenomegravene drsquoinstabiliteacute Pour les eacuteleacutements comprimeacutes et fleacutechis deux cas se preacutesentent

- Flexion composeacutee sans risque de deacuteversement Art 554 (551) CCM97 119873119904119889

120594119898119894119899 119873119901119897119903119889+119896119910 119872119910119904119889

119872119901119897119910119903119889+119896119911 119872119911119904119889119872119901119897119911119903119889

le 10helliphellip (2)

- Flexion composeacutee avec risque de deacuteversement Art 554 (552) CCM97 119873119904119889

120594119911 119873119901119897119903119889+119896119871119879 119872119910119904119889

120594119871119879119872119901119897119910119903119889+119896119911 119872119911119904119889119872119901119897119911119903119889

le 10helliphellip(2)

Calcul du coefficient de reacuteduction minimal pour le flambement

120594119898119894119899 = 119872119894119899(120594119910 120594119911)

- Flambement par rapport agrave lrsquoaxe (y-y)

93

120594119910 =1

(120601119910 +radic1206011199102 minus 1205821199102 )

120601119910 = 05[1 + 120572119910(120582119910 minus 02) + 1205821199102]

120582119910= (120582119910

1205821)radic120573119860 =

120582119910

1205821

Avec 120573119860 = 1 Classe 1

1205821 = 939

120582119910 =05119868119910

119894119910=455

166= 274

120582119910=274

939= 029

Courbe de flambement Figure 552 du CCM97

ℎ

119887=400

180= 222 gt 12 119894119898119901119897119894119902119906119890 120572 = 021

120601 = 05[1 + 120572119910(120582119910 minus 02) + 1205821199102 ] = 055

120594119910 =1

(055 + radic0552 minus 0292)= 098

- Flambement par rapport agrave lrsquoaxe (z-z)

120594119911 =1

(120601119911 +radic1206011199112 minus 120582119911

2)

120601119911 = 05[1 + 120572119911(120582119911 minus 02) + 1205821199112]

120582119911 = (1205821199111205821)radic120573119860 =

1205821199111205821

Avec 120573119860 = 1 Classe 1

120582119911 =119868119911119894119911=200

395= 5063

120582119911 =5063

939= 054


94

ℎ

119887= 222 gt 12 (119911 minus 119911)119894119898119901119897119894119902119906119890 120572 = 034

120601 = 05[1 + 034(054 minus 02) + 0542 ] = 07

120594119911 =1

(07 + radic072 minus 0542)= 087

120594119898119894119899 = 119872119894119899(120594119910 120594119911) = 087

Calcul de lrsquoeacutelancement reacuteduit vis-agrave-vis du deacuteversement

Pour les poutres agrave section constante et doublement symeacutetrique (profileacutes lamineacutes I et H)

lrsquoeacutelancement 120582119897119905 vaut

λ119897119905 =

119871119894119911

119888105

[

1 +120(

119871119894119911ℎ119905119891

)

2

] 025 = 4367 119808119821119821119812119831119812119809 119810119810119820120791120789

Avec

IPE400 119905119891 = 14119898119898 119894119911 = 395119888119898 ℎ = 400119898119898

119870 = 1 1198881=1134 Tableau B11 CCM97

L= 2 m avec L entre axe des pannes

1205821 = 939휀

휀 = radic235

119891119910= 1

120582119871119879 = [1205821198971199051205821] [120573119908]

05

120582119897119905 = 4367

120582119871119879 =4367

939= 046 gt 04

Il y a risque de deacuteversement

Donc on doit veacuterifier que

119873119904119889120594119911 119873119901119897119903119889

+119896119871119879 119872119910119904119889

120594119871119879119872119901119897119910119903119889+119896119911 119872119911119904119889119872119901119897119911119903119889


Calcul de 120594119871119879

αlt =021 et 120582119871119879 = 046 implique 120601LT = 063

95

implique 120594119871119879 = 094

Calcul de 119896119871119879

120595=-048 gtgtgtgtgt 120573MLT =2136 gtgtgtgtgtgt 120583LT =002 le15

119870119871119879 = 1 minusμLT N119904119889

120594119911 119860 119891119910= 099 lt 15

On remplace dans (2)

Donc

119873119904119889=7249 kN 119872119910119904119889=219 kNm 119872119901119897119910119903119889=26455 kNm 120594119911=087 119872119901119897119911119903119889=4819kNm

120594119897119905=094 119873119901119897119903119889=180437 kN 119896119871119879= 099 119896119911= 1 119872119911119904119889=038 kNm (neacutegligeable)

119873119904119889120594119911 119873119901119897119903119889

+119896119871119879 119872119910119904119889

120594119871119879119872119901119897119910119903119889+119896119911 119872119911119904119889

119872119901119897119911119903119889

En consideacuterant 119872119911119904119889=0

7249

087 180437+

099 219

094 26455= 055

Conclusion Le profileacute choisi IPE400 convient comme traverse pour la structure

63 Veacuterification des poteaux (HEA320)

Les poteaux de la structure ont pour fonction de transfeacuterer aux fondations les efforts

provenant des actions agissantes sur le portique Ces efforts introduits par la traverse sont

principalement un effort normal de compression etou un moment de flexion Il peut y avoir

des actions transversales dues au vent sur la faccedilade Pour le poteau drsquoune longueur de 89 m

solliciteacute par la combinaison drsquoaction suivant (135G+135Q+135V1) les efforts sollicitant

deacuteterminer de cette combinaison donneacutee par le logiciel Robot sont

Figure 62 Vue en 3D de la structure illustration des poteaux

96

119872119910119904119889 = 32083 119896119873119898

119881119904119889 = 120 119896119873

119873119904119889 = 602 119896119873

Profileacute


HEA320

A cm2

hmm

b mm

119905f

mm

119905w mm

119868y

cm4

119868z cm4

119908 ply

cm3

119908 plz

cm3

MATERIAU ACIER S235

12437 310 300 16 9 229286 698524 162823 70975

Tableau 62 Caracteacuteristiques du profileacute HEA 320



119888

119905119891=60

16= 375 lt 10휀 =gt 119888119897119886119904119904119890 1


119889

119905119908=98

9= 109 lt 72휀 =gt 119888119897119886119904119904119890 1



- Veacuterification a lrsquoeffort tranchant


Si 119881119904119889 le 05119881119901119897119903119889 ⟹ 119872119904119889 le 119872119888119903119889 119912119955119957120787 120786 120789 119914119914119924 120791120789


119881119898119886119909 = 119881119904119889 =120kN

119881119901119897119911119903119889 =

119860119907119911 (119891119910

radic3)

1205741198980=4113 235radic3

11= 50731119896119873

97

119881119904119889 le 05119881119901119897119911119903119889




119873119904119889 le 119872119894119899(025119873119901119897119903119889 05119860119908119891119910

1205741198720)


119873119904119889 =602kN

119873119901119897119903119889 le119860 119891

119910

1205741198720=12437 235

11= 2656995 119896119873

025119873119901119897119903119889 = 664248119896119873

119860119908 = 119860 minus 2119887 119905119891 = 2837 1198981198982

05119860119908119891119910

1205741198720= 30304119896119873

119873119904119889 = 602119896119873 le 30304119896119873



119872119888119903119889 = 119872119901119897119910119903119889 =119908119901119897119910 119891119910

1205741198720=1628000 times 235

11= 3478119896119873119898

119872119910119904119889 le119872119888119903119889 Condition veacuterifieacutee

Veacuterification drsquoeacuteleacutement au pheacutenomegravene drsquoinstabiliteacute Pour les eacuteleacutements comprimeacutes et fleacutechis deux cas se preacutesente


120594119898119894119899 119873119901119897119903119889+119896119910 119872119910119904119889

119872119901119897119910119903119889+119896119911 119872119911119904119889119872119901119897119911119903119889



120594119911 119873119901119897119903119889+119896119871119879 119872119910119904119889

120594119871119879119872119901119897119910119903119889+119896119911 119872119911119904119889119872119901119897119911119903119889



120594119898119894119899 = 119872119894119899(120594119910 120594119911)


98

120594119910 =1

(120601119910 +radic1206011199102 minus 1205821199102 )

120601119910 = 05[1 + 120572119910(120582119910 minus 02) + 1205821199102]

120582119910= (120582119910

1205821)radic120573119860 =

120582119910

1205821

Avec 120573119860 = 1 Classe 1

1205821 = 939

120582119910 =05119868119910

119894119910=05 890

1358= 3276

120582119910=3276

939= 034


ℎ

119887=310

300= 1 lt 12 (119910 minus 119910)119894119898119901119897119894119902119906119890 120572 = 034

120601 = 05[1 + 120572119910(120582119910 minus 02) + 1205821199102 ] = 058

120594119910 =1

058 + radic058 minus 034= 095


120594119911 =1

(120601119911 +radic1206011199112 minus 1205821199112)

120601119911 = 05[1 + 120572119911(120582119911 minus 02) + 1205821199112]

120582119911 = (1205821199111205821)radic120573119860 =

1205821199111205821

Avec 120573119860 = 1 Classe 1

1205821 = 939

120582119911 =119868119911119894119911=07 59

749= 055


ℎ

119887= 1 lt 12 (119911 minus 119911) 119894119898119901119897119894119902119906119890 120572 = 049

120601 = 05[1 + 049(055 minus 02) + 0552] = 073

99

120594119911 =1

073 + radic073 minus 055= 082

120594119898119894119899 = 119872119894119899(120594119910 120594119911) = 082


λ119897119905 =

119871119894119911

119888105

[

1 +120(

119871119894119911ℎ119905119891

)

2

] 025 = 3536

HEA320 119905119891 = 16119898119898 119894119911 = 749119888119898 ℎ = 310119898119898

119870 = 07 1198881 = 1134 Tableau B11 CCM97

L=59m avec L la hauteur du bardage au-dessus du mur de maccedilonnerie

1205821 = 939휀

휀 = radic235

119891119910= 1

120582119871119879 = [1205821198971199051205821] [120573119908]

05

120582119897119905 = 3536

120582119871119879 =3536

939= 037 lt 04 119901119886119904 119889119890 119903119894119904119902119906119890 119889119890 119889119890119907119890119903119904119890119898119890119899119905


119873119904119889120594119898119894119899 119873119901119897119903119889

+119896119910 119872119910119904119889

119872119901119897119910119903119889+119896119911 119872119911119904119889119872119901119897119911119903119889


Avec

119873119904119889 =602kN 119872119910119904119889=32083kNm 119872119911119904119889=049kNm 119872119901119897119910119903119889=3478kNm

119872119901119897119911119903119889=1516kNm 120594119898119894119899= 082 119873119901119897119903119889=26570kN 119896119910= 05 119896119911= 07

602

082 26570+05 32083

3478+07 049

1516= 034 le 10 Condition veacuterifieacutee

Conclusion Le profileacute choisi HEA320 convient comme poteau pour la structure

64 Veacuterification des eacuteleacutements de stabiliteacutes CAE (120x12) Les contreventements sont des piegraveces qui ont pour objet drsquoassurer la stabiliteacute de lrsquoossature en

srsquoopposant agrave lrsquoaction des forces horizontales ils sont geacuteneacuteralement placeacutes pour garantir le

cheminement des charges horizontales jusqursquoaux fondations ils sont disposeacutes en toiture dans le

plan des versants laquo poutres au vent raquo et doivent reprendre les efforts horizontaux appliqueacutes tant

100

sur les pignons que sur les longs pans Les contreventements sont placeacutes le plus souvent dans les

traveacutees de rive leurs diagonales sont geacuteneacuteralement des corniegraveres doubles qui sont fixeacutees sur la

traverse et leur rocircle principal est de transmettre les efforts du vent aux fondations

La diagonale est solliciteacutee sous la combinaison suivante donneacutee par le logiciel Robot

(135G+15V1)

Figure 63 Vue en 3D illustrant la position des contreventements et stabiliteacutes

119873119904119889 =69837kN

L= 75m avec L est la longueur de la diagonale la plus solliciteacute

Profileacute


2CAE (120x12)

A Cm2

hmm

b mm

Anet

Cm2

d

mm

MATERIAU ACIER S235

5508 120 248 4658 8

Tableau 63 Caracteacuteristiques du profileacute 2CAE (120x12)

Veacuterification agrave la traction

119873119904119889 le 119873119905119903119889 = 119872119894119899[119873119901119897119903119889 119873119906119903119889 119873119899119890119905119903119889]

101

119873119901119897119903119889 =119860 119891119910

1205741198720= 117671119896119873

119873119906119903119889 = 09119860119899119890119905 1198911199061205741198722

= 13719119896119873

119873119899119890119905119903119889 =119860119899119890119905 119891119910

1205741198720= 995118119896119873

119873119904119889 = 69837 lt 9951 Condition veacuterifieacutee

Conclusion Le profileacute choisi 119871 (12011990912) convient comme diagonale de la poutre au vent

Les diffeacuterents eacuteleacutements principaux veacuterifieacutes dans ce chapitre ont des sections satisfaisantes avec des

ratios convenables selon le modegravele deacutevelopper sous le logiciel ROBOT AUTODESK

Figure 64 Ratio des eacuteleacutements structuraux (agrave partir du logiciel ROBOT)

65 Veacuterification des potelets (IPE300)

Figure 65 Vue en 3D de la structure illustration des potelets

102

La combinaison la plus deacutefavorable 135G+15Q

119872119910119904119889 = 02 119896119873119898

119881119904119889 = 0048 119896119873

119873119904119889 = 5628 119896119873

Profileacute


IPE300

A cm2

hmm

b mm

119905f

mm

119905w mm

119868y

cm4

119868z cm4

119908ply

cm3

119908plz

cm3

MATERIAU ACIER S235

538 300 150 107 71 8356 746 628 125



- La classe de la section a deacutejagrave eacutetait deacuteterminer comme section de classe 1 dans le chapitre trois




Si 119881119904119889 le 05119881119901119897119903119889 ⟹ 119872119904119889 le 119872119888119903119889 119912119955119957120787 120786 120789 119914119914119924 120791120789


119881119898119886119909 = 119881119904119889 =0048kN

119881119901119897119911119903119889 =

119860119907119911 (119891119910

radic3)

1205741198980=2570 235radic3

11= 3169119896119873

119881119904119889 le 05119881119901119897119911119903119889




119873119904119889 le 119872119894119899(025119873119901119897119903119889 05119860119908119891119910

1205741198720)

103


119873119904119889 =5628kN

119873119901119897119903119889 le119860 119891

119910

1205741198720=5380 235

11= 114936 119896119873

025119873119901119897119903119889 = 28734 119896119873

119860119908 = 119860 minus 2119887 119905119891 = 2170 1198981198982

05119860119908119891119910

1205741198720= 23179119896119873

119873119904119889 = 5628119896119873 le 23179119896119873



119872119888119903119889 = 119872119901119897119910119903119889 =119908119901119897119910 119891119910

1205741198720=628000 times 235

11= 134163 119896119873119898




120594119898119894119899 119873119901119897119903119889+119896119910 119872119910119904119889

119872119901119897119910119903119889+119896119911 119872119911119904119889119872119901119897119911119903119889



120594119911 119873119901119897119903119889+119896119871119879 119872119910119904119889

120594119871119879119872119901119897119910119903119889+119896119911 119872119911119904119889119872119901119897119911119903119889



120594119898119894119899 = 119872119894119899(120594119910 120594119911)


120594119910 =1

(120601119910 +radic1206011199102 minus 1205821199102 )

120601119910 = 05[1 + 120572119910(120582119910 minus 02) + 1205821199102]

120582119910= (120582119910

1205821)radic120573119860 =

120582119910

1205821

104

Avec 120573119860 = 1 Classe 1

1205821 = 939

120582119910 =119871119910

119894119910= 960

125= 768

120582119910=768

939= 081


ℎ

119887=300

150= 05 lt 12 (119910 minus 119910)119894119898119901119897119894119902119906119890 120572 = 021

120601 = 05[1 + 120572119910(120582119910 minus 02) + 1205821199102 ] = 089

120594119910 =1

058 + radic058 minus 034= 079


120594119911 =1

(120601119911 +radic1206011199112 minus 1205821199112)

120601119911 = 05[1 + 120572119911(120582119911 minus 02) + 1205821199112]

120582119911 = (1205821199111205821)radic120573119860 =

1205821199111205821

Avec 120573119860 = 1 Classe 1

1205821 = 939

120582119911 =119868119911119894119911=125

335= 3731 120582119911 = 039


ℎ

119887= 1 lt 12 (119911 minus 119911) 119894119898119901119897119894119902119906119890 120572 = 021

120601 = 05[1 + 021(039 minus 02) + 0392] = 061

120594119911 =1

061 + radic061 minus 039= 092

120594119898119894119899 = 119872119894119899(120594119910 120594119911) = 079


105

λ119897119905 =

119871119894119911

119888105

[

1 +120(

119871119894119911ℎ119905119891

)

2

] 025 = 3433

IPE300 119905119891 = 107119898119898 119894119911 = 335119888119898 ℎ = 300119898119898

119870 = 1 1198881 = 1134 Tableau B11 CCM97


1205821 = 939휀

휀 = radic235

119891119910= 1

120582119871119879 = [1205821198971199051205821] [120573119908]

05

120582119897119905 = 3433

120582119871119879 =3433

939= 036 lt 04 119901119886119904 119889119890 119903119894119904119902119906119890 119889119890 119889119890119907119890119903119904119890119898119890119899119905


119873119904119889120594119898119894119899 119873119901119897119903119889

+119896119910 119872119910119904119889

119872119901119897119910119903119889+119896119911 119872119911119904119889119872119901119897119911119903119889


Avec

119873119904119889 =5628kN 119872119910119904119889=02kNm 119872119911119904119889=018kNm 119872119901119897119910119903119889=134163kNm

119872119901119897119911119903119889=267kNm 120594119898119894119899= 079 119873119901119897119903119889=1149kN 119896119910= 1 119896119911= 1

5628

079 1149+

02

134163+018


Conclusion Le profileacute choisi IPE300 convient largement comme potelet pour la structure

106

Chapitre-7

Calcul des assemblages

71 Introduction

Apregraves avoir veacuterifieacute les eacuteleacutements porteurs nous allons eacutetudier les assemblages Ces derniers ont un

double rocircle drsquoune part ils assurent la liaison entre les piegraveces et la transmission des sollicitations

divers entre les piegraveces Un assemblage mal conccedilu ou mal reacutealiseacute peut conduire agrave des dommages

importants sur la structure voir mecircme agrave son effondrement De ce fait cette eacutetape est drsquoune

importance cruciale Le CCM97 cite que le dimensionnement des assemblages doit ecirctre effectueacute de

sorte que la structure garde son efficaciteacute et satisfait les exigences fondamentales telles que la

seacutecuriteacute lrsquoaptitude au service et la durabiliteacute

72 Assemblage poteau ndash traverse (HEA320-IPE400)

Lrsquoassemblage poteau ndash traverse est reacutealiseacute agrave lrsquoaide drsquoune platine soudeacutee agrave la traverse et boulonneacutee

au poteau

107

Figure 71 vue en plan de lrsquoassemblage poteau-traverse

Lrsquoassemblage est solliciteacute par un moment fleacutechissant un effort tranchant et un effort normal

Les efforts sollicitant sur lrsquoassemblage sont obtenus de la combinaison 135119866 + 135119876 + 135V1 donneacutee par le logiciel Robot

119872119904119889 = 28961119896119873119898 119873119904119889 = 17878119896119873 119881119904119889 = 8941119896119873

- Disposition constructive Lrsquoassemblage est reacutealiseacute par 12 boulons HR de classe 88 de diamegravetre oslash18 mm ainsi que les

dimensions de la platine drsquoabout sont 300mm x 664mm eacutepaisseur platine = 20mm

Lrsquoeacutepaisseur la plus mince pour la deacutetermination des pinces est

119905 = 119872119894119899(119905119891 119905119901119897119886119905119894119899119890) = 135119898119898

Avec

- 119905119891 est lrsquoeacutepaisseur de la semelle (135mm)

- 119905119901119897119886119905119894119899119890 est lrsquoeacutepaisseur de la platine (20mm)

Distance entre les axes des boulons tableau 651-CCM97

Figure 72 Deacutesignation des entraxes et des pinces

12119889O = 24 119898119898 le 1198901 le 12119905 =186 119898119898 ⟹ 1198901 = 110 119898119898

15119889O = 30 119898119898 le 1198902 le 12119905 = 186 119898119898 ⟹ 1198902 = 105 119898119898

22119889O = 44 119898119898 le 1199011 le 14119905 =217 119898119898 ⟹ 1199011 = 100 119898119898

3119889O = 60 119898119898 le 1199012 le 14119905 =217 119898119898 ⟹ 1199012 = 90 119898119898 Reverification avec lrsquoANEXE J de lrsquoEC3 exgt max (mx 15do) 15doltelt2625mx 3 doltwlt525mx Avec do = 20mm et mx =80mm (distance entre la semelle de la traverse et le trou le plus preacutes )

108

exgt max (mx 15do) =80mm ex = 110 mm gt 80mm CV 15do=30mmltelt2625mx=210mm 30mm lt e= 105mm lt 210mm CV

3do=60mmltwlt525mx=420mm 60mmltw=90mmlt420mm CV

- Distribution des efforts sur les different cordons

On va choisir le cordon de soudure platine-traverse agrave lrsquoaide de lrsquoabaque de

preacutedimensionnement de la gorge (Annexe 10)

IPE 400 119905f = 135 119898119898 119905w = 86 119898119898

119886min= 26 le twle119886max= 8

119886min =35 le tf le119886max= 8

On choisit un cordon de soudure de a=7mm

721 Veacuterification de la soudure de la semelle agrave la traction

119873119904119889 le 119865119908119903119889 =119886 times sum 119897 times 119891119906

radic2 times 120573119908 times 120574119872119882

Avec pour Fe360 120573119908 = 125 120574119872119882 =08 donc 120573119908 x 120574119872119882 = 1

La longueur totale des cordons de soudure des semelles

sum119897 = 2119887 + 4(119887 minus 119905119908) = 2180 + 4(180 minus 86) = 1045119898119898

119865119908119903119889 =7times 1045 times 360

radic2= 1862119896119873

119873119904119889 =119872119904119889

ℎ=120784120790120791 120788120783

120782 120791= 120785120784120783 120789120790

119873119904119889 = 32178 le 119865119908119903119889 = 1862 119896119873 Condition veacuterifieacutee

722 Veacuterification de la soudure de lrsquoacircme au cisaillement



Avec 120573119908 = 125 120574119872119882 = 08

La longueur totale des cordons de soudure des acircmes

109

i

sum119897 = 4ℎ119894 = 4 times 373 = 1492119898119898

119865119907119903119889 =7 times 1492 times 360

radic3= 217074119896119873

119881119904119889 = 8941 le 119865119907119903119889 = 217074kN Condition veacuterifieacutee

723 Deacutetermination des efforts dans les boulons

119873119894 =119872119904119889 119889119894sum119889119894

2

Calcul de la hauteur de la partie comprimeacutee

119909 = 119905119891radic119887

119905119908= 135radic

180

86= 6176

Lrsquoaxe neutre se trouve au-dessous de la derniegravere rangeacutee de boulons ce qui fait que tous les boulons

travaillent agrave la traction

- 1198891 = 712 119898119898

- 1198892 = 612 119898119898

- 1198893 = 512 119898119898 ⟹ Σ 1198892 = 129 119898sup2

- 1198894 = 312 119898119898

- 1198895 = 212 119898119898

- 1198896 = 112 119898119898

Lrsquoeffort de traction dans les deux boulons supeacuterieurs

1198731 =28961 times 0712

129= 15984119896119873

724 Deacutetermination du diamegravetre requis des boulons Resistance des boulons au cisaillement

119865119907119903119889 = 06 times 119891119906119887 times 119860119904 tableau 653 resistance de calcul des boulons

1198731 = 119899119865119907119903119889 ⟹ 119860119904 ge119873119904119889

06 times 119891119906119887 times 119899=

15984

06 times 800 times 2= 16651198981198982

Donc on adopte des boulons M18 de classe 88 ordinaire (ANNEXE ndash 5)

Boulons d (mm) d0 (mm) A (mmsup2) AS (mmsup2) fub (mpa) dm (mm)

M18 18 20 254 192 800 291

Tableau 71 Caracteacuteristiques geacuteomeacutetriques du boulon M18

725 Veacuterification agrave la reacutesistance de lrsquoassemblage

110

Moment reacutesistant effectif de lrsquoassemblage

Remarque (notre assemblage est classeacute comme rigide pour les sollicitations causeacutes par le

deplacement des futurs ponts roulants )

119865119901 = 07 times 119891119906119887 times 119860119904 = 06 x 800 x 192 = 10752kN

119872119903119889 =119899 119865119901 sum119889119894

2

119889119894=2 times 10752 times 129

0712= 3896 gt 119872119904119889 = 28961 119896119873119898


726 Veacuterification des boulons agrave lrsquointeraction cisaillement-traction

La reacutesistance au glissement par boulons doit satisfaire la condition suivante

119865119907119904119889 le 119865119904119903119889 =119870119904 119898 120583

1205741198722(119865119901119888119889 minus 08119873119904119889) 119917119926119929119924119932119923119916 120788 120789 minus 119914119914119924120791120789

Avec

119870119904 = 10 ∶ Trous normaux

120583 = 03 ∶ Classe de surface D

119898 = 10 Plans de glissement

119865119904119903119889 = 024 (10752 minus 08 times15984

2) = 1046119896119873

119865119907119904119889 =8941

12= 745119896119873 lt 1046119896119873


727 Veacuterification au poinccedilonnement de la semelle du poteau

119865119905119904119889 le 119861119901119903119889 =06120587 times 119889119898 times 119905119901 times 119891119906

1205741198722 119813119822119825119820119828119819119812 120788 120784 minus 119810119810119820120791120789

119905119901 = 119905119891 = 135119898119898 Eacutepaisseur de la piegravece poinccedilonneacutee

119861119901119903119889 =06 times 314 times 291 times 135 times 360

125= 213157 119896119873

119865119905119904119889 =119865119901

2=10752

2= 5376119896119873 lt 119861119901 119903119889 = 213157 119896119873


111

728 Veacuterification de la pression diameacutetrale

119865119907119904119889 le 119865119887119903119889 =119870119904 times 120572119887 times 119889 times 119905 times 119891119906

1205741198722 119827119808119809119819119812119808119828 120788 120787 120785 ndash 119810119810119820120791120789

Avec 119870119904 = 25

120572119887 = min (119890131198890

(119901131198890

minus 025) 119891119906119887119891119906 1) = 1

t= 20+155=355 eacutepaisseur platine +semelle poteau


125= 46008119896119873 gt

11986511990711990411988912

= 745119896119873


729 Veacuterification de la reacutesistance de lrsquoacircme du poteau dans la zone tendue

119865119907 le 119865119905119903119889 = 119905119908119888 1198871198901198911198911198911199101205741198720

Avec

119865119905119903119889 Reacutesistance de lrsquoacircme du poteau agrave la traction

119905119908119888 Eacutepaisseur de lrsquoacircme du poteau =9mm

119887119890119891119891 = 119901 ∶ Entraxe des boulons (p=90mm)

⟹ 119865119905119903119889 = 9 times 90times23511

= 173045 119896119873

Lrsquoeffort de cisaillement vaut

119865119907 =119872119904119889

ℎ minus 119905119891=28961

029= 99865 gt 119865119905119903119889 = 173045119896119873


Donc on preacutevoit un raidisseur drsquoeacutepaisseur 14mm

7210 Veacuterification de la reacutesistance de lrsquoacircme du poteau dans la zone comprimeacutee

119873119904119889 le 119865119888119903119889 =119896119888 120588 119887119890119891119891 119905119908119888 119891119910

1205741198721radic1 + 13 (119887119890119891119891ℎ)2

119887119890119891119891 = 119905119891119887 + 2119886119901radic2 + 5(119905119891119888 + 119903119888) + 2119905119901

Avec

112

119905119891119887 ∶ Eacutepaisseur semelle-poutre = 135mm

119905119891119888 ∶ Eacutepaisseur semelle-poteau = 155mm

119905119901 ∶ Eacutepaisseur platine = 20 mm

119903119888 ∶ Rayon de raccordement acircme-semelle du poteau = 21mm

119886119901 ∶ Eacutepaisseur de la gorge de la soudure =5mm

119887119890119891119891 =25014mm

Contrainte normale de compression dans lrsquoacircme du poteau ducirce agrave lrsquoeffort de compression et au

moment fleacutechissant

120590119888119904119889 =119881119904119889119860+119872119904119889

119882119890119897119910=8941 times 103

1244+28961 times 106

1479= 196533119872119875119886

120590119888119904119889 = 19653119872119875119886 lt 119891119910 = 235119872119875119886 ⟹ 119896119888 = 1

Eacutelancement reacuteduit de la partie efficace de lrsquoacircme

119901 = 0932radic119887119890119891119891 119889119908119888 119891119910

119864 1199051199081198882= 0932radic


21 times 104 times 092= 254

119901 gt 072⟹ 120588 =119901 minus 02

1199012=254 minus 02

2542= 036

⟹ 119865119888119903119889 =1 times 036 times 2501 times 09 times 235

11 radic1 + 13 (250131

)2

= 12741119896119873

119873119904119889 = 1119873119894 =119872119904119889 sum119889119894sum119889119894

2 =29861 times 247

129= 57175119896119873

119873119904119889 = 57175 gt 119865119888119903119889 = 12741119896119873 Condition non veacuterifieacutee

La reacutesistance de lrsquoacircme du poteau en compression est faible Il faut donc preacutevoir un raidisseur

drsquoeacutepaisseur 14mm

7211 Veacuterification de la reacutesistance de lrsquoacircme du poteau dans la zone cisailleacutee

119865119907 le 119881119903119889 = 058119891119910 ℎ1199051199081205741198720

= 058 times 235 times 31 times09

11= 3457119896119873


119865119907 =119872119904119889ℎ minus 119905119891

= 46216 119896119873 gt 119881119903119889 = 3457119896119873 119888119900119899119889119894119905119894119900119899 119899119900119899 119907eacute119903119894119891119894eacute119890

On peut rajouter des eacuteclisses bilateacuterales de 2mm drsquoeacutepaisseur pour augmenter tw

113

119865119907 = 46216119896119873 le 119881119903119889 = 058119891119910 ℎ119905119908 + 04

1205741198720= 058 235 31

(09 + 04)

11= 49935119896119873


73 Assemblage Traverse-Traverse (IPE400)

Lrsquoassemblage traverse-traverse est reacutealiseacute agrave lrsquoaide de deux platines boulonneacutees entre elles et

soudeacutees avec les deux traverses

Lrsquoassemblage est solliciteacute par un moment fleacutechissant effort tranchant et un effort normal

Les efforts sollicitant sur lrsquoassemblage sont obtenus par la combinaison G+15V1 donneacutee par le

logiciel robot

119872119904119889 = 15135119896119873119898 119873119904119889 = 1324119896119873 119881119904119889 = 273119896119873

Figure 73 Vu en plan de lrsquoassemblage traverse-traverse

- Dispositions constructives

Lrsquoassemblage est reacutealiseacute par 12 boulons HR de classe 88 de diamegravetre 12060118119898119898

Les dimensions de la platine drsquoabout 180 mm x 830 mm eacutepaisseur t=20mm

Lrsquoeacutepaisseur la plus mince

119905 = min(119905119891 119905119901119897119886119905119894119899119890) = 135119898119898


114


12 d0 = 24 mm lt e1 lt12t =162 mm gtgtgt e1 =100 mm


22 d0 = 44 mm lt p1 lt14t =189 mm gtgtgt p1 =100 mm


- Distribution des efforts sur les diffeacuterents cordons

On va choisir le cordon de soudure platine-traverse agrave lrsquoaide de lrsquoabaque de preacutedimensionnement de

la gorge (Annexe 10)

IPE400

tf = 135 mm tw = 86 mm

amin = 28mm lt twlt amax = 6 mm

amin = 34mm lt tflt amax = 8 mm

On choisit un cordon de soudure de 5mm


119873119904119889 le 119865119908119903119889 =119886 times sum119871 times 119891119906

radic2 times 119861119908 120574119898119908

Avec Bw = 08 120632mw = 125 sumL = 2b + 4(b-tw) =10456 mm

Donc

119865119908119903119889 =119860 times sum119871 times 119891119906

radic2 times 119861119908 times 120574119898119908=5 times 10456 times 360

radic2 times 1= 133083119896119873

119873119904119889 =119872119904119889ℎ

=7283

08= 9103119896119873

115

119873119904119889 = 9103 le 119865119908119903119889 = 1330119896119873





Avec Bw = 08 120632mw = 125 sumL = 4hi =1492 mm

Donc

119865119907119903119889 =119886 times sum119871 times 119891119906

radic3 times 119861119908 times 120574119898119908= 5 times 1492 times 360

radic3 times 1= 155053119896119873

119881119904119889 = 437kN lt 119865119907119903119889=155053kN condition veacuterifieacutee


119873119894 =119872119904119889 119889119894sum119889119894

2


119909 = 119905119891radic119887

119905119908= 135radic

180

86= 6176119898119898

Lrsquoaxe neutre se trouve au-dessous de la derniegravere rangeacutee de boulons ce qui fait que tous les boulons travaillent agrave la traction

- 1198891 = 700 119898119898

- 1198892 = 600 119898119898

- 1198893 = 500 119898119898 ⟹ Σ1198891198942

= 124 119898sup2

- 1198894 = 300 119898119898

- 1198895 = 200 119898119898

- 1198896 = 100 119898119898

Lrsquoeffort de traction est donneacute par

1198731 =119872119904119889 times 119889119894Σ119889119894

2 =15135 times 070

124= 4111119896119873

734 Deacutetermination du diamegravetre requis pour les boulons

Lrsquoeffort de preacutecontrainte autoriseacute dans les boulons

116

119865119907 = 05 times 119891119906119887 times 119860119904 119917119926119929119924119932119923119916 120788 120787 ndash 119914119914119924120791120789

1198731 = 119899 119865119907 ⟹ 119860119904 ge119873119904119889

05 times 119891119906119887 times 119899=

13240

05 times 800 times 2= 16551198981198982

Donc on adopte des boulons M18 de classe 88

Boulon d (mm) d0 (mm) A(mm2) As(mm2) Fub (MPa) dm(mm)

M18 18 20 254 192 800 291

Tableau 72 Caracteacuteristiques geacuteomeacutetrique des boulons


Moment reacutesistant effectif de lrsquoassemblage est donneacute par

119865119901 = 07 times 119891119906119887 times 119860119904 = 10752 119896119873

119872119903119889 =119899 119865119901sum119889119894

2

119889119894=2 times 10752 times 124

07= 38092 gt 119872119904119889 = 15135119896119873119898




119865119907119904119889 le 119865119904119903119889 =119870119904 119898 120583

1205741198722(119865119901119888119889 minus 08119873119904119889) 119813119822119825119820119828119819119812 120788120789 ndash 119810119810119820120791120789

Avec

Ks = 1 trous normaux

120583 = 03 classe de surface D

m= 10 plan de glissement

119865119904119903119889 = 024 ( 10752 minus 08 times 1324) = 2326119896119873

119865119907119904119889 =273

12= 023 lt 119865119904 119903119889 = 2326119896119873




1205741198722 119813119822119825119820119828119819119812 120788 120784 ndash 119810119810119820120791120789

Avec

tp eacutepaisseur de la piegravece poinccedilonneacutee = 20mm

117


125= 31578119896119873

119865119905119904119889 =119865119901

2= 5376 lt 31578119896119873




1205741198722 119827119808119809119819119812119808119828 120788 120787 120785 ndash 119810119810119820120791120789

Avec Ks = 25

120572119887 = min (119890131198890

(119901131198890

minus 025) 119891119906119887119891119906 1) = 1

t= 40mm eacutepaisseur de deux platines

11986511990711990411988912

= 023119896119873 lt 119865119887119903119889 =1 times 25 times 18 times 40 times 360

125= 5184 119896119873


74 Assemblage des paleacutes de stabiliteacute (2L 120x120 x12)

Les boulons sont solliciteacutes en cisaillement seulement Les diagonales les plus solliciteacutees sont celles qui reprennent un effort de traction maximum

Figure 75 Assemblage des diagonales doubles corniegraveres avec gousset

Lrsquoeffort sollicitant de llsquoassemblage est Nsd =131 kN

Lrsquoeffort de cisaillement repris par un boulon est Tableau 653-CCM97

119865119907119904119889 =119873119904119889

119899119887119903 119889119890 119887119900119906119897119900119899=131

3= 4366 le 119865119907119903119889

118


1205741198722⟹ 119860119904 ge

1205741198722 times 119865119907119903119889

06 times 119891119906119887119909 119898=125 times 43666

06 times 800 times 2= 56851198981198982

m = 2 nombre des plan de cisaillement


Bien que nos boulons sont largement surdimensionner on va les garder par commoditeacute pour de

que presque tout nos assemblages soient fait a lrsquoaide de boulons M16 88 et ainsi reduire les

erreurs et les diffeculteacutes a lrsquoachat et a lrsquoexecution

Boulon d(mm) d0(mm) A(mm2) As(mm2) Fub(MPa) dm(mm)

M16 16 18 201 157 800 2458 Tableau 73 Caracteacuteristiques geacuteomeacutetrique des boulons

- Disposition constructive

Lrsquoassemblage est reacutealiseacute par 3 boulons de classe 88

Les dimensions des goussets

Gousset central 450 mm x 450 mm t = 8 mm Gousset de rive 350 mm x 350 mm t = 8 mm

Distance entre axe des boulons Tableau 651-CCM97

12119889o = 216 119898119898 le 1198901 le 12119905 = 96 119898119898 ⟹ 1198901 = 50 119898119898 15119889o = 27 119898119898 le 1198901 le 12119905 = 96 119898119898 ⟹ 1198901 = 50 119898119898 22119889o = 396 119898119898 le 1199011 le 14119905 = 112 119898119898 ⟹ 1199011 = 80 119898119898

Choix de cordon de soudure

Tmin = tgousset = 8mm

Suivant lrsquoabaque de preacutedimensionnement la gorge a= 5 mm

741 Veacuterification de la soudure gousset-semelle du poteau agrave la traction

119873119898119886119909 le 119865119908119903119889 =119886 sum119897 119891119906

119861119908 120574119898119908 radic(3 minus 1199041198941198991205722)

La longueur totale des cordons de soudure sum119897 = 700mm

120572= 30gtgtgt 11990411989411989930o = 05

119865119908119903119889 =5 times 700 times 360

1 times radic3 minus 05sup2= 85017119896119873 gt 119873119898119886119909 = 131119896119873


119

742 Veacuterification au cisaillement des boulons

119865119907119904119889 le 119865119907119903119889 =120572119907 times 120573119871119865 times 119860119904 times 119891119906119887 times119898

1205741198722 119827119808119809119819119812119808119828 120788 120787 120785 minus 119810119810119820120791120789

Avec 120573119871119865 = 1 assemblages courants

120572119907= 06

119898 = 2 nbr des plans de cisaillement


125= 12057119896119873

119865119907119904119889 =119873119904119889

3=3124

3= 10413 le 119865119907119903119889 = 12057119896119873




1205741198722 119827119808119809119819119812119808119828 120788 120787 120785 minus 119810119810119820120791120789

Avec

Ks = 25

120572119887 = min (119890131198890

(119901131198890

minus 025) 119891119906119887119891119906 1) = 092

t= 32 mm (12+12+8) somme des eacutepaisseurs


125= 33914119896119873 gt 119865119907119904119889 = 4366119896119873


744 Veacuterification agrave la reacutesistance du bloc

En considegraverent que le chargement est centreacute sur la cassure

119873119898119886119909 le 119881119890119891119891119903119889 =119860119899119905 119891119910

1205741198722+119860119899119907 119891119910

radic3 1205741198722 119812119810120785 119849119834119851119853119842119838120783 minus 120790sect120785120783120782 120784

Avec

119860119899119890119905 Section nette tendue

119860119899119890119905 = (119897

2minus11988902) 119905 = (60 minus 9)12 = 6121198981198982

119860119899119907 ∶Section nette cisailleacutee

120

119860119899119907 = (1198901 + 21199011 minus 251198890)119905 = (50 + 140 minus 45)12 = 17401198981198982

⟹ 119881119890119891119891119903119889 =612 times 235

125+1740 times 235

radic3 times 125= 303918119896119873 gt

119873119904119889

2= 655119896119873


Aucun risque de rupture par cisaillement dans cet assemblage

75 Assemblage Panne-Traverse (Echantignole)

Lrsquoassemblage panne traverse est reacutealiser agrave lrsquoaide drsquoeacutechantignole boulonner avec des boulons

ordinaires afin drsquoavoir lrsquoarticulation souhaiteacutee

Figure 76 Assemblage panne-eacutechantignole eacutechantignole-traverse

Lrsquoassemblage est solliciteacute par une reacuteaction max de Rz =36kN (voir chapitre 3)

119865119907119904119889 =119877119907119911

119899119887119900119906119897119900119899119904=36

2= 18 119896119873

119865119907119903119889 =06 times 119860119904 times 119891119906119887

120574119872119887⟹119860119904 ge

120574119872119887 times 11986511990711990311988906 times 119891119906119887

=11 times 18000

06 times 800= 41251198981198982

On adopte des boulons M10 de classe 88 avec As =58 mm2

751 Reacutesistance des boulons au cisaillement Tableau 653-CCM97

119865119907119903119889 =06 times 119860119904 times 119891119906119887

120574119872119887=06 times 58 times 800

11= 253119896119873 gt 119865119907119904119889 = 18119896119873

752 Reacutesistance des boulons agrave lrsquoeffort combineacutee traction-cisaillement

119865119905119903119889 =09 times 119860119904 times 119891119906119887

120574119872119887=09 times 58 times 800

11= 379119896119873

121

119865119907119903119889 =06 times 119860119904 times 119891119906119887

120574119872119887= 253119896119873

119865119907119904119889119865119907119903119889

+119865119905119904119889

14 119865119905119903119889= 052 lt 1 119862119900119899119889119894119905119894119900119899 119907119890119903119894119891119894eacute119890

Assemblage veacuterifieacutee

122

Chapitre-8

Veacuterification des ancrages et calcul de fondations

81 Veacuterification drsquoancrage des pieds de poteaux HEA320 811 Introduction Les portiques de notre structure possegravedent des pieds de poteaux encastreacutes ce type de liaison est neacutecessaire dans le cas drsquoun pont roulant Pour ce qui concerne la norme Algeacuterienne (CCM97) elle eacutevoque dans son paragraphe 693 les principes de calcul des pieds de poteaux articuleacutes Ce regraveglement nous oriente vers drsquoautres regravegles et conditions qursquoelles soient en accord avec les mecircmes principes qui conduisent au mecircme niveau de seacutecuriteacute Pour cela nous allons utiliser lrsquoEurocode 3 partie 1-8 calcul des assemblages Dans ce cas le poteau est solliciteacute en pied par un effort axial et un moment de flexion ce qui est eacutequivalent agrave un effort vertical excentreacute

Figure 81 Assemblage au pied de poteau rigide

123

812 Dimensionnement de la plaque drsquoassise

Le dimensionnement de la plaque drsquoassise se fait sous lrsquoaction des charges suivantes tireacutees agrave partir

de la modeacutelisation sur le logiciel ROBOT AUTODESK

Nsd=14896 kN (charge axial de compression )

Vsd = 9773 kN ( effort tranchant)

Msd=6207 kNm (moment de flexion)

813 Resistance du beacuteton agrave la compression

119865119888119896=30 MPa

119891119888119889 =085 times 119865119888119896125

= 204 MPa

814 Resistance de calcul agrave lrsquoeacutecrasement du mateacuteriau de scellement

119865119895119889 = 120572120573119895 119891119888119889

La valeur du coefficient du mateacuteriau de scellement est 120573119895=23

Les dimensions de la fondation eacutetant encore inconnues on prend 120572 = 15

119865119895119889 = 120572 120573119895 119891119888119889 = 15 times2

3times 17 = 204 119872119875119886

815 Calcul de lrsquoaire de la plaque

1198601198620 ge119873119904119889119891119888119889

=148960

204

1198601198620 ge 7266341198981198982

- Les dimensions de la platine

bp ge b+2tf = 190+2times155 = 221 mm

hp ge h+2tf = 310+2times155 = 341 mm

On prend

bp =600 hp=620

Ce qui donne Aco = 600 x 620 = 372000 mm2 gt 726634 mm2

- Calcul de la largeur drsquoappui additionnelle C

124

En posant t= 30mm comme eacutepaisseur de la platine on trouve

119862 = 119905 (119891119910119901

3119891119895119889 1205741198720)

05

= 30(235

3 times 204 times 11)05

= 5605 119898119898

119862 = 5605 lt(ℎ minus 2119905119891)

2= 1395 119898119898

Il nrsquoy a pas de recouvrement des ails en compression pour les tronccedilons des deux semelles

816 Cordon de soudure

On choisit le cordon de soudure platine-poteau agrave lrsquoaide de lrsquoabaque de preacutedimensionnement de la

gorge (a) Annexe H

HEA 320 tf=155 mm tw= 9 mm

amin= 28 mmlttwltamax =65 mm

amin= 38 mm le tf le amax = 105 mm

On choisit un cordon de soudure de 6 mm

817 Calcul de la reacutesistance agrave la flexion en preacutesence de lrsquoeffort axial

La reacutesistance agrave la flexion deacutepend de lrsquoexcentriciteacute

119890 =119872119904119889119873119904119889

= 041 119898 gt 119885119879 = 0195 119898

Moment de flexion dominant

La reacutesistance atteinte dans lrsquoune de ces parties

Tronccedilon en T tendu critique Tronccedilon en T comprimeacute critique

Figure 82 Illustration moment + effort normal

- Resistance en compression drsquoun tronccedilon en T de semelle

119865119940119955119941 = 119891119895119889 times 119887119890119891119891 times 119897119890119891119891 119812119810120785 minus 120783 120790 minus 119853119834119835119845119838119834119854120788 120786

125

Figure 83 Illustration de la partie comprimeacutee du pied de poteau

Ougrave

119871119890119891119891 = min(119887119901 119887119891119888 + 2119888) = min(600 300 + 2 times 4671) = 39342 119898119898

119887119890119891119891 = min (119888ℎ1198882minus 119905119891119888) + 119905119891119888 +min (119888

ℎ119901 minus ℎ119888

2)

119887119890119891119891 = min (4671310

2minus 155) + 155 + min (4671

620 minus 310

2) = 10892 119898119898

⟹ 119865119888119903119889 = 204 times 10892 times 39342 = 874166 119896119873

- Resistance au cisaillement de lrsquoassemblage

119865119907119903119889 = 119865119891119903119889 + 119899119887 119865119907119887119903119889

Resistance par frottement en preacutesence drsquoun effort axial de compression

119865119891119903119889 = 02119873119904119889 = 1214 119896119873

Pour 8 tiges M30 de classe 88 le choix est justifieacute avec le logiciel ROBOT

Boulon d (mm) d0 (mm) A (mm2) As (mm2) Fub (MPa) M30 30 33 707 561 800

Tableau 81 Caracteacuteristique de boulon M30

- Resistance au cisaillement drsquoun boulon drsquoancrage

119865119907119887119903119889 =120572119888119887 119891119906119887 119860119904

1205741198722

Avec 120572119888119887 = 044 minus 00003119891119910119887 = 0248

119899119887= 8 ( 8 tiges drsquoancrage )

126

119865119907119887119903119889 =0248 times 800 times 561

125= 8904 119896119873

⟹ 119865119907119903119889 = 1214 + 8 times 8904 119896119873 = 72446 119896119873

- Resistance au cisaillement de la soudure



Avec 120573119908 =08 120574119898119908 = 125 119886 = 6 mm

La longueur totale des cordons de soudure dans le sens de cisaillement

sum119897 = 470 119898119898

119865119908119903119889 =6 times 470 times 360

radic3= 58612 119896119873

119881119904119889 = 9773 119896119873 lt min(119865119907119903119889 119865119908119903119889) = 58612 119896119873


- Longueur participante du tronccedilon en T eacutequivalent tendu

Calcul de longueur efficace du tronccedilon en T EC3-18 ndashtableau 66

Figure 84 Dispositions constructives

W= 150 mm e = 55 mm ex = 40 mm mx = 40 mm

Meacutecanisme circulaire

119897119890119891119891119888119901 = 119898119894119899 2120587119898119909 = 25132 119898119898

120587119898119909 +119882 = 27566 119898119898120587119898119909 + 2119890 = 23566 119898119898

⟹ 119897119890119891119891119888119901 = 23566 119898119898

127

Meacutecanisme non circulaire

119897119890119891119891119899119888 = 119898119894119899

4119898119909 + 125119890119909 = 210 119898119898

2119898119909 + 0625119890119909 +119882

2= 180 119898119898

2119898119909 + 0625119890119909 + 119890 = 160 119898119898119887119901

2= 150 119898119898

⟹ 119897119890119891119891119899119888 = 150 119898119898

818 Veacuterification de la reacutesistance de tiges drsquoancrage

119865119905119886119899119888119903119889 = min[119865119905119887119900119899119889119903119889 119865119905119903119889]

Resistance du boulon drsquoancrage agrave la traction

119865119905119903119889 = 09 times119860119904 times 119891119906119887120574119898119887

= 09 times561 times 800

125= 32314 119896119873

- Calcul de la contrainte drsquoadheacuterence

On a d =30mm le 32 mm

119865119887119889 =036radic119891119888119896

120574119888=036 times 547

15= 1313 119872119875119886

Reacutesistance de calcul par adheacuterence entre le beacuteton et le boulon drsquoancrage

119865119905119887119900119899119889119903119889 =120587 119889 119897119887 119891119887119889

120572

Avec

1198971 = 20119889 = 600 119898119898

119903 = 3119889 = 90 119898119898

1198972 = 20119889 = 600 119898119898

d diamegravetre de la tige d = 30

119897119887Lrsquoencrage dans le beacuteton 119897119887 = (1198971 + 64119903 + 351198972) = 3276 mm

119891119888119896 Reacutesistance du beacuteton 119891119888119896 = 30 119872119875119886

120572 ∶ Facteur tenant en compte la forme de la tige 120572 = 07


07= 52929 119896119873

119865119905119886119899119888119903119889 = 119898119894119899[52929 32314] = 32314 kN

128

819 Reacutesistance de la partie tendue de lrsquoassemblage

Veacuterification de la preacutesence drsquoeffet de levier

Lb longueur drsquoallongement du boulon drsquoancrage

Lb = 8d + em +tp + twa + 05k

Avec

twa eacutepaisseur de la rondelle = 5 mm

k eacutepaisseur de lrsquoeacutecrou k = 08 d

em eacutepaisseur de mortier de calage em= 30 mm

Lb = 8times 30 + 30 + 25 + 5 + 05 times 08 times 30 = 312 119898119898

Figure 85 Longueur drsquoallongement des boulons drsquoancrages

Lb longueur limite drsquoallongement des boulons drsquoancrages

119871119887lowast =

881198981199093 119860119904

1198971198901198911198911 1199051199013 =


150 times 253= 13480 119898119898 lt 119871119887 = 312 119898119898

Lrsquoeffet de levier ne peut pas ecirctre deacuteveloppeacute et les modes de ruines 1-2 3 et 4 peuvent ecirctre

consideacutereacutes

8110 Resistance agrave la flexion de la plaque drsquoassise (par uniteacute de longueur)

119898119901119897119903119889 =1199051199012 119891119910119901

41205741198720=252 times 235

4 times 11= 3338119896119873

Resistance agrave la flexion de la plaque drsquoassise

Mode 1 1198721199011198971119903119889 = 119898119901119897119903119889 times 1198971198901198911198911 = 3338 times 015 = 5007119896119873119898

1198971198901198911198911 = min(119897119890119891119891119888119901 119897119890119891119891119899119888) = 150 119898119898

- Calcul de la reacutesistance de lrsquoassemblage agrave la traction

129

La reacutesistance finale de lrsquoassemblage drsquoun tronccedilon en T eacutequivalent tendu est prise eacutegale agrave la valeur

de la reacutesistance la plus petite des modes de ruine

119865119905119903119889 = min (1198651199051minus2119903119889 1198651199053119903119889 1198651199054119903119889) EC3-18-tableau62

Mode 1-2

1198651199051minus2119903119889 =21198721199011198971119903119889

119898119909=2 times 5

004= 250 119896119873

Mode 3

1198651199053119903119889 = 2119865119905119903119889119886119899119888ℎ119900119903 = 2 times 32314 = 646280 119896119873

Mode 4

1198651199054119903119889 =119887119890119891119891119905 119905119908 119891119910

1205741198720=150 times 9 times 235

11= 288409119896119873

Drsquoougrave

119865119905119903119889 = min(1198651199051minus2119903119889 1198651199053119903119889 1198651199054119903119889) = 250 119896119873

8111 Veacuterification de la reacutesistance en flexion


119872119904119889 le 119872119903119889 = min(minus119865119888119903119889 times 119885

119885119879119890119873minus 1

119865119879119903119889 times 119885

119885119862119890119873+ 1

) 119812119810120785 ndash 120783 120790 119827119808119809119819119812119808119828 120788 120789

119885 = 119885119879+119885119862 = 195 + 155 = 350119898119898

⟹119872119903119889 = 5646 119896119873119898 lt 6207119896119873119898

Condition non veacuterifieacutee il faut rajouter des raidisseurs bidirectionnels

82 Etude des fondations

821 Introduction

Quel que soit lrsquoouvrage il prend toujours appuis sur un sol drsquoassise Les eacuteleacutements qui jouent le rocircle

drsquointerface entre lrsquoouvrage et le sol srsquoappellent les fondations

Le dimensionnement de ces fondations est conditionneacute par le site drsquoimplantation

- Le site (S3)

- La contrainte admissible du sol 120590sol = 18 bar 180kNm2

- La profondeur drsquoancrage D= 18m

130

822 Deacutetermination des sollicitations

Pour la deacutetermination des sollicitations on considegravere les deux eacutetats limites pour le calcul des

reacuteactions drsquoappuis des poteaux

ELU 119872119880 = 6207119896119873119898 119873119880 = 9773119896119873

ELS 119872119878 = 4136119896119873119898 119873119878 = 7960119896119873

823 Dimensionnement de la semelle

Les dimensions de la semelle sont choisies de sorte qursquoelles soient homotheacutetiques avec celles du

pied de poteau avec un deacutebordement de 20 cm

119886 = 119886119901 + 119888 = 062 + 02 = 082 119898

119887 = 119887119901 + 119888 = 060 + 02 = 08 119898 Avec 119886119901 et 119887119901 dimensions de la platine

119860

119861=119886

119887= 1025 ⟹ 119860 = 1025119861

A et B dimensions de la semelle

- Calcul de lrsquoexcentriciteacute

119890 =119872119904

119873119904= 052119898

Figure 86 Les dimensions de la semelle sous poteau

Pour les semelles de dimensions B times L la valeur des contraintes extrecircmes est donneacutee par

120590119898119886119909 =119873

119860119861(1 +

6119890

119861) le 120590119904119900119897

Apres simplification

368B2 - B - 312 ge 0 ⟹ B ge0765m

On prend B =1 m et A = 25 m

- Hauteur utile de la semelle est donneacute par la condition

131

119889 = max (119861 minus 119887

4119860 minus 119886

4) = max (005 0295)

On prend d= 45 cm

ht = d+ 5cm = 50cm hauteur totale de la semelle

824 Veacuterification des contraintes

On a

119890 = 052 gt119860

6= 041

Lrsquoeffort N est agrave lrsquoexteacuterieur du noyau central

3120590119898119886119909 1205901198981198941198994

lt 120590119904119900119897

Avec

120590119898119894119899 =119873

119860119861(1 minus

6119890

119860) =

14896

2(1 minus

041

2 ) = 62191198961198731198982

120590119898119894119899 =119873

119860119861(1 +

6119890

119860) =

14896

2(1 +

041

2 ) = 86771198961198731198982

3120590119898119886119909 120590119898119894119899

4= 6835 1198961198731198982 lt 120590119904119900119897 = 180 119896119873119898

2


825 Veacuterification de la stabiliteacute au renversement La stabiliteacute au renversement des fondations doit se faire pour les semelles sous la combinaison G+Q+E ( RPA99 v 2003 Art1015)

119890 =119872

119873= 052 119898 lt

119860

4= 062 119898


826 Deacutetermination des armatures de la semelle

Le ferraillage se calcul par la meacutethode des consoles

119890 gt119886

6 119890 gt

119860

24

ELS Ferraillage dans la direction A

119860119886 =1198721119911 119904119905

132

1198721 = (119860

2minus 035119886)

2

(1 +119890

119860+14 times 119890 times 119886

1198602)1198731199042119860

1198721 = 2788119896119873119898

Avec 119911 = 09d =40cm

119904119905 = min (2

3119891119890 110radic12057811989111990528) =20163 MPa

11989111990528 = 00611989111988828 + 06 = 24 119872119875119886 120578 = 16 119867 119860 Donc

119860119886 =2788 times 106

400 times 20163= 345 1198881198982

Ferraillage dans la direction B Le ferraillage dans la direction B sera calculeacute par la meacutethode de bielle en remplaccedilant N par Nrsquo

119860119887 =119873prime(119861 minus 119887)

8119889 119904119905

Avec

119873prime = 119873119904 (1 +3119890

119860) = 796 (1 +

3 times 052

25) = 2993119896119873

119904119905 = min (2

3119891119890 110radic12057811989111990528) = 20163119872119875119886

11989111990528 = 00611989111988828 + 06 = 24119896119873 120578 = 16 119867 119860

Donc 119860119887 = 071198881198982

ELU Ferraillage dans la direction A

119860119886 =1198721119911 120590119904119905

1198721 = (119860

2minus 035119886)

2

(1 +119890

119860+14 times 119890 times 119886

1198602)1198731199062119860

1198721 = 349119896119873119898

Avec 119911 =09d = 40 cm

120590119904119905 =119891119890120574119904=400

115= 3478119872119875119886

Donc

133

119860119886 =349 times 106

400 times 3478= 251198881198982

Ferraillage dans la direction B

119860119886 =119873119906(119861 minus 119887)

8119889 120590119904119905

Avec

119873prime = 119873119906 (1 +3119890

119860) = 23833119896119873

Donc 119860119887 = 1621198881198982

La condition de non-fragiliteacute Sens A

119860119898119894119899 = 023 times11989111990528119891119890

times 119860 times ℎ119905 = 17251198881198982

Sens B

119860119898119894119899 = 023 times11989111990528119891119890

times 119861 times ℎ119905 = 691198881198982

Calcul de lrsquoespacement St ge max (6oslash + 6cm 15cm) le 30cm St ge max (6times14 + 6cm 15cm) Enrobage 3cm

Sens As (cm2) Amin (cm2) Nb de barres

A (cm2) St (cm)

A 345 1725 10T16 201 25 B 07 69 7T16 1407 25

Tableau 82 Ferraillage choisis pour la semelle au-dessous de poteau

Figure 87 Ferraillage des semelles

134

827 Calcul des longrines Les longrines sont des liaisons situeacutees agrave lrsquointeacuterieur du peacuterimegravetre de la structure elles jouent le rocircle de chainage dans les deux directions et elles sont calculeacutees sous lrsquoeffort axial de traction comme deacutefini dans le RPA99 Preacutedimensionnement Les dimensions minimales de la section transversale des longrines sont (25 x 30 cm2) Pour Site de cateacutegorieS2 et S3 [RPA99 v 2003 Art1011b]

Ferraillages longitudinaux Les longrines doivent ecirctre dimensionner pour reacutesister agrave une force de traction eacutegal agrave

119873119905 = (119873

120572) ge 20 119896119873 [119825119823119808120791120791 119855 120784120782120782120785 119808119851119853 120783120782 120783 120783 119835]

Avec N effort normal encaisseacute par le poteau le plus solliciteacute Nu =14896kN Ns =796kN 120572 coefficient en fonction de la zone sismique et de la cateacutegorie 120572 = 12 ELU

119873119905 =14896

12= 1241119896119873

ELS

119873119905 =796

12= 663119896119873

Calcul des armatures

119860119904119905 =119873119905120590119904119905

ELS

119860119904119905 =663

348= 0191198881198982

ELU

119860119904119905 =1241

348= 0351198881198982

Le ferraillage minimal doit ecirctre de 06 de la section

119860119898119894119899 = 06(b times h) = 391198881198982 Soit 6HA12 gtgtgt As =679 cm2

828 Veacuterification de la condition de non-fragiliteacute

119860119904119905 le 023 times 119887 times ℎ times11989111990528119891119890

119860119904119905 = 0905 le 119860119904 = 6791198881198982


135

829 Ferraillage transversal

120601119898119894119899 le 119898119894119899 (ℎ

35120601119897119898119894119899

119887

10) = 08 119888119898

On prend 120601119905 =8mm

8210 Calcul drsquoespacement des cadres 119878119905 lt min(20119888119898 15120601119905) = 12119888119898

On prend St=10cm

Figure 88 le ratio reacutealiseacute par cet assemblage de pied de poteau selon ROBOT

136

Conclusion geacuteneacuterale En reacutealisant ce projet de fin de cycle nous avons pu en apprendre davantage sur le preacutedimensionnement la veacuterification et lrsquoassemblage de chaque eacuteleacutement composant lrsquoossature drsquoun hangar ou drsquoune halle meacutetallique Nous avons reacuteellement saisi lrsquoimportance et lrsquoavantage que preacutesente lrsquoutilisation drsquooutils numeacuteriques pour la modeacutelisation de notre structure et la simulation des diffeacuterents efforts et charges appliqueacutees sur elle Ce fut aussi lrsquooccasion de consulter les diffeacuterentes reacuteglementations qui reacutegissent le domaine de la charpente meacutetallique en particulier et celui du geacutenie civil en geacuteneacuteral comme le CCM 97 le RNV2013 le RPA 99v2003 et le CBA 93 Nous avons aussi reacutealiseacute lrsquoimportance des stabiliteacutes et contreventements pour ce qursquoelle apporte agrave la structure comme stabiliteacute et gains de matiegravere dans les eacuteleacutements principaux Enfin le point le plus important de tous on a pu compleacuteter le grand manque drsquoinformations qursquoon avait avant ce projet et on a pu lever le voile sur pas mal drsquoincertitudes concernant le dimensionnement et la mise en œuvre des diffeacuterents assemblages de la structure Mais sans se leurrer nous restons conscients de notre eacutenorme manque drsquoinformations et de pratiques en la matiegravere nous espeacuterons que le futur nous donnera lrsquooccasion drsquoen apprendre drsquoavantage sur le domaine de la charpente agrave travers le travail ou la recherche inchaalah

137

ANNEXE - 1

138

139

140

ANNEXE - 2

141

ANNEXE - 3

142

143

ANNEXE ndash 4

144

145

ANNEXE ndash 5

Remerciements

Tout drsquoabord merci au bon dieu de nous avoir accordeacute cette vie

de nous permettre de nous instruire de grandir dlsquoeacutevoluer et de prendre soin des nocirctres

Merci agrave nos parents pour tout tout simplement

Merci agrave notre encadreur Dr KAZI TANI

Nabil il a eacuteteacute pour nous ces derniers mois comme un grand fregravere il nous a assister dans notre travail appris beaucoup de chose et nous a donneacute sans

compter de son temps et de son savoir

Merci agrave Djelti Abdessamad et Merad Sofiane pour leur aide sur diffeacuterents

points de ce modeste travail

AACHOURI et EMOUSSI

Deacutedicace











Deacutedicace














Reacutesumeacute


ملخص







Abstract































































































































Liste des tableaux

















LISTE DES NOTATIONS

Majuscules latines








16

Chapitre-1


11 Introduction


17



18

Action

permanente (γG)




Effet favorable

γGinf

10 1 0


γGsup

135 15 15




135119866119896119895 + 15119876119896119898119886119909





1 119866119896119895 + 150119882minus


sum119866119896119895119895

+ 119876119896119898119886119909

119866119896119895 + 119876119896119898119886119909


sum119866119896119895119895

+ 09sum119876119896119894119894gt1

119866119896119895 + 09119876119896119898119886119909 + 09119878 119866119896119895 + 09119876119896119898119886119909 + 09119882


19










20




21






22




23

Chapitre-2


21 Introduction










24

- Effet du site








Ouargla (Zone 4)




Kt=017 Z0=001m Zmin=1m ξ=044






Avec




119902119901(119885) = 119902119903119890119891 times 119862119890

Avec

- 119902ref = 575 119889119886119873119898sup2


2(119885) times [1 + 7119868119907] 119825119821119829120784120782120783120785 119836119841119834119849119842119853119851119838 120784 120786 sect120784 120786 120784 119834


25


119862119903(119911)

119870119905 119871119899 (1199111198981198941198991199110

) 119901119900119906119903 119911 lt 119911119898119894119899

119870119905 119871119899 (119911

1199110) 119901119900119906119903 119911119898119894119899 le 119911 le 200119898


)=0783


Zo)=1178

On retient 119862119903= 1178


119868119907(119911)

1

119862119905(119911) 119871119899 (119911

1199110) 119901119900119906119903 119911 gt 119911119898119894119899

1

119862119905(119911) 119871119899 (1199111198981198941198991199110) 119901119900119906119903 119911 le 119911119898119894119899

Pour z gt zmin 119868119907(119911) =1

1Ln(1

001)= 0217

Pour z lt zmin 119868119907(119911) =1

1Ln(1025

001)= 0144



119862119890(119911119895) = 119862119903(119911119895)2[1 + 7 119868119881]

Pour z gt zmin

119862119890(119911) = 11782 times 12 times [1 + 7(0144)] = 2786

Pour z lt zmin

119862119890(119911) = 07832 times 12 times [1 + 7(0217)] = 154


Avec

26

- 119902119903119890119891 = 575 119889119886119873119898sup2



qp = 160195Nm2 = 16 kNm2





- b=30 m

- d=36 m

- h=89 m


e = min (d 2h)


Donc e = 2x1025 = 205m



27



119862119901119890 = 1198621199011198901 119878119894 119878 le 11198982

119862119901119890 = 1198621199011198901 + (11986211990111989010 minus 1198621199011198901) times 11989711990011989210(119878) 119878119894 11198982 lt 119878 lt 101198982

119862119901119890 = 11986211990111989010 119878119894 119878 ge 101198982



Zone


Parois sous le vent


Cpe10 -10 -08 -05 +08 -03


Versant de Toiture




28







le tableau suivant


853deg F G H

-237 -123 -083



- Parois verticales


-b=36 m

29

-d=30 m

-h=1025


e=Min (b 2h) = Min (36 205) = 205 m





30

Zone


Parois sous le vent








31




853deg -22 -192 -183 -067 -057






2(5 times 4)

30 times 89= 014 = 14


μ119901 =120

160= 075



Pour μ119901=075 on lit 119862119901119894 =-016

32




2 times (5 times 4)

36 times 9575= 0116 = 116


Pour μ119901=075 rarr 119862119901119894 =-02

33





Direction V1 V3


A 1602 -10 -0154 -0846 -135529

B 1602 -08 -0154 -0646 -103489

C 1602 -05 -0154 -0346 -55429

D 1602 +08 -0154 +0954 +152831

E 1602 -03 -0154 -0146 -23389


34

Toiture


F 1602 -237 -0154 -2276 -355003

G 1602 -123 -0154 -1076 -172375

H 1602 -084 -0154 -0676 -108295

Z1 1602 -1 -0154 -0846 -135529

Z2 1602 -06 -0154 -0446 -71449


Direction V2 et V4

Parois verticales


A 1602 -10 -0162 -0838 -134247

B 1602 -08 -0162 -0638 -102207

C 1602 -05 -0162 -0338 -54147

D 1602 +08 -0162 +0962 +154112

E 1602 -03 -0162 -0138 -22107


35

Toiture


Finf 1602 -12 -0162 -1038 -1662876

Fsup 1602 -22 -0162 -2038 -3264876

G 1602 -183 -0162 -1668 -2672136

H 1602 -067 -0162 -0508 -813816

I 1602 -057 -0162 -0408 -653616









9= 015




q1= 300 Nml

q2= 500 Nml



36











- Epaisseur 50 mm

- Largeur 1000 mm





Selon le DTR BC22




37

119902 =8119875

3119871= 044 119896119873119898

119902 = 444 119889119886119873119898













38

Chapitre-3





deacutefavorable

39

(minus354 times5125


0875

6) = minus32754 1198891198861198731198982

Qeq (vent) = 3276 daN1198982















40



41


Vzsd =119902119906119911 times 119897

2=1878 kN

Mysd=119902119906119911 times 119897

2

8=2817 kNm

Mzsd=119902119906119910 times 119897

2

8=081 kNm



IPE 180 A Cm2

h mm

b mm

119905f

mm 119905w

mm 119868y

Cm4

119868z

Cm4

119908ply cm3

119908plz cm3

MATERIAU ACIER S235

239 180 91 8 53 1317 101 146 346




4

384 times 119864 119868119910lt

119897

200=



119897

200= 3 119862119900119899119889119894119905119894119900119899 119907eacute119903119894119891119894eacute119890

Plan z-z

5 times 119902119904119910 times 1198974

384 times 119864 119868119911lt

119897

200=



119897

200= 3 119862119900119899119889119894119905119894119900119899 119907eacute119903119894119891119894eacute119890

42




1205741198721 gt 119872119910119904119889 = 2817 119896119873119898

Calcul de 119872119887119903119889




λ119871119879 =

119871119894119911

119888105

[

1 +120(

119871119894119911ℎ119905119891

)

2

] 025

Avec


(Tableau B12 CCM97)

iz =224mm tf =85mm

L=Lz=3000mm h=200mm

λ119871119879 =

119871119894119911

119888105

[

1 +120(

119871119894119911ℎ119905119891

)

2

] 025 = 9457 rarr λ119871119879 =

989

939= 1007

rarr =1092

43


rarr ꭕ119871119879=

1


2)= 066 le 1

rarr 119872119887119903119889 =ꭕ119871119879times 120573

119908times 119882119901119897119910 times 119891119910

1205741198721

=066 1 166 235

11= 234 119896119873 119898








119872119872119860119883 =119901prime 119897

3=119901 1198972

8⟹ 119901 =

8 119901prime

3119897=800

18= 4444 119889119886119873119898119897

44


(ANNEXE ndash 1)

Soit

119876119890119902 =327 + 1082

2= 2176 1198891198861198731198982









45



Vzsd =119902119906119911 times 119897

2=186 kN

Mysd=119902119906119911 times 119897

2

8=279 kNm

Mzsd=119902119906119910 times 119897

2

8=0855 kNm

46



IPE 200 A Cm2

h mm

b mm

119905f

mm 119905w

mm 119868y

Cm4

119868z

Cm4

119908ply cm3

119908plz cm3

MATERIAU ACIER S235

285 200 100 85 56 1943 142 221 446




4

384 times 119864 119868119910lt

119897

200=



119897

200= 3 119862119900119899119889119894119905119894119900119899 119907eacute119903119894119891119894eacute119890

Plan z-z

5 times 119902119904119910 times 1198974

384 times 119864 119868119911lt

119897

200=



119897

200= 3 119862119900119899119889119894119905119894119900119899 119907eacute119903119894119891119894eacute119890




1205741198721 gt 119872119910119904119889 = 279 119896119873119898

Calcul de 119872119887119903119889

47




λ119871119879 =

119871119894119911

119888105

[

1 +120(

119871119894119911ℎ119905119891

)

2

] 025

Avec


(Tableau B12 CCM97)


-L=Lz=6000mm -h=200mm

λ119871119879 =

119871119894119911

119888105

[

1 +120(

119871119894119911ℎ119905119891

)

2

] 025 = 989 ⟶ λ119871119879 =

989

939= 105

rarr =114


rarr ꭕ119897119905=

1


2)= 063 le 1

rarr 119872119887119903119889 =ꭕ119897119905times 120573

119908times 119882119901119897119910 times 119891119910

1205741198721


11= 2974119896119873119898



48


Avec

119881119901119897119911119903119889 =

119860119907119911 (119891119910

radic3)

11 119890119905 119860119907119911 = 1400 1198981198982

Donc

05119881119901119897119911119903119889 = 05

1400 (235

radic3)

11= 8634 119896119873



Si 119889


CCM97 art 561(1)

119889

119905119908 =

159





(119872119910119904119889

119872119901119897119910119903119889)

120572

+ (119872119911119904119889119872119901119897119911119903119889

)

120573

le 1 119912119955119957 120787 120786 120790 (120783120783)119914119914119924 120791120789


119872119901119897119910119903119889 =119882119901119897119910 times 119891119910

11=221 times 235

11= 4721 119896119873119898

119872119901119897119911119903119889 =119882119901119897119911 times 119891119910

11=446 times 235

11= 952 119896119873119898

119872119910119904119889 = 279 119896119873119898

119872119911119904119889 = 0855 119896119873119898

(279

4721)2

+ (0855

952) = 044 lt 1 119888119900119899119889119894119905119894119900119899 119907eacute119903119894119891119894eacute119890

49











Effort rampant


Lrsquoexcentrement


2 (119887

2) le 119905 le 3(

119887

2)


50

2 (10

2) = 10 le 119905 le 3(

10

2) = 15

On prend t=10 cm


119877119911 = 119902119906119911 times119897

2= 6 times

6

2= 18 119896119873

119877119910 = 119902119906119910 times119897

2= 054 119896119873


119877119911 = 18 times 2 = 36 119896119873

119877119910 = 054 times 2 = 108 119896119873


119872119877 = 119877119911 times 119905 + 119877119910 timesℎ

2= 36 times 10 + 108 times 10 = 3708 119896119873 119888119898 = 37119896119873119898


119872119890119897119877119889 =119908119890119897 times 119891119910

1205741198720 119912119955119957 120787 120786 120787 120783 (120784)119914119914119924120791120789

119872119890119897119877119889 =119908119890119897 times 1198911199101205741198720

=gt 119908119890119897 ge119872119890119897119877119889 times 1205741198720

119891119910=gt 119908119890119897 ge

00037 times 11

235

= 173 times 10minus51198983

119908119890119897 = 17321198881198983




119908119890119897 =119887 1198902


6 times 1732

119887= radic

6 times 1732

180

119890 ge 076


Donc on prend e=1cm

51





















52












qsy =(133 + 5) times 125=2288daNml

qsy = 0228 kN

quy=135G=03kN



W += 1541 daN m2


quz=15W

quz=288kN

53



qsz=19262daN=192kN


119891119911 =5 times 119902119904119911 times 119897

4

384 times 119864119910 times 119868le 119891119886119889119873 =

119897

200=600

200= 3 119888119898

119868119910 ge5 times 192 times 6004



Profileacute


UPN 140 A Cm2

h mm

b mm

119905f mm

119905w mm

Iy

Cm4

Iz

Cm4

119908pSy

cm3

119908pSz

cm3

MATERIAU ACIER S235

20 140 60 10 7 605 627 103 283







qsy =(133 + 5) times 125 +1568 = 3856daNml

qsy = 038 kN

quy=135G

quy =053kN


qsz=192kN

quz=15W

quz=288kN

54




119888

119905119891=60

10= 6 lt 10휀 =gt 119888119897119886119904119904119890 1


119889

119905119908=98

7= 14 lt 72휀 =gt 119888119897119886119904119904119890 1


(119872119910119904119889

119872119890119897119910119877119889)

1

+ (119872119911119904119889

119872119890119897119911119877119889)1

le 1


119872119910 =119902119906119911 times 119897

2

8=288 times 62

8= 1296 119896119873119898


119872119911 =119902119906119910 times 119897

2

8=058 times 62

8= 261119896119873119898

119872119890119897119910119877119889 =119908119890119897119910 times 119891119910

1205741198720=864 times 103 times 235

11= 1845 119896119873119898

119872119890119897119911119877119889 =119908119890119897119911 times 119891119910

1205741198720=148 times 103 times 235

11= 316 119896119873119898

Donc

(1296

1845)1+ (

261



55

Nouveau 119872119911

119872119911 =119902119906119910 times 119897

2

8=058 times 32

8= 065119896119873119898

(1296

1845)1+ (

065




119881119911119904119889 =15119882119871

2= 1296 119896119873

119881119901119897119877119889 =119860119907119911 times 119891119910

radic3times 1205741198720= 12855 119896119873





1205741198721gt 119872119910119904119889 119912119955119957 120787 120787 120784 (120787 120786120790)119914119914119924120791120789

Avec

119872119888119903 = 11986211205872 119864 1198681199111198712

radic119868119908119868119911+1198712 119866 1198681199051205872 119864 119868119911

119912119925119925119916119935119916 119913 (119913 120783 120785) minus 119914119914119924120791120789

119872119888119903=311713762 Ncm


119872119888119903


119882119901119897119910 (upn140) =103 cm3

56

λ119897119905 = 0881


2 ]


empty119897119905 = 0959

ꭕ119897119905=

1


2 )

le 1

ꭕ119897119905= 075

119872119887119903119889 = 1652 119896119873119898

119872119887119903119889 = 1652 119896119873119898 gt 119872119910119904119889 = 1296 119896119873119898 119862119900119899119889119894119905119894119900119899 119907eacute119903119894119891119894eacute119890







57

119877 = 125119902119910 times 119897

2

Avec 119902119910 = [135(119866119880119875119873140 + 119866119888119900119906119907119890119903119905119906119903119890)]

119902119910 = 0837119896119873

119897 = 6 119898

119877 = 125119902119910 times 119897

2= 125 times 0837 times 3 = 32119896119873


1198791 =119877

2= 16119896119873

1198792 = 1198791 + 119877=48 kN

1198793 =1198792

2 sin 120579= 374 119896119873 119860119907119890119888 120579 = 119886119903119888 119905119892

25 119898

3 119898= 398deg



119873119905119904119889 =119860 times 119891119910

1205741198720= 4800 119873 =gt 119860 ge

11 times 4800

235 =gt 119860 ge 22461198981198982

119860 =120587empty2

4=gt empty ge radic

4119860

120587= radic

4 times 2246

314= 534 119898119898



Introduction



58



119878ge

63

radic119904

119889times119875

Avec








Srsquo=273

4=6825 m2








59



















96=8989 daNm2





60

119891119910 =5 times119882 times 1198974

384 times 119864 times 119868119910le 119891119886119889119898 =

119897

200


384 times E= 59136 1198881198984


Profileacute


IPE300 A Cm2

h mm

b mm

tf mm

tw

mm 119868y

Cm4

119868z Cm4

Wply

cm3

Wplz

cm3

MATERIAU ACIER S235

538 300 150 107 71 8356 746 628 125





119888

119905119891=

75

107= 7 lt 10 = 10 119878119890119898119890119897119897119890 119889119890 119888119897119886119904119904119890 1


119889

119905119908=2486

71= 35 lt 38 = 38 Acirc119898119890 119889119890 119888119897119886119904119904119890 1



Si 119881119904119889 le 05 119881119901119897119903119889 ⟹119872119904119889 le 119872119888119903119889 119912119955119957120787 120786 120789 119914119914119924 120791120789

61

119881119904119889 =15 times119882 times 119897


2= 388 119896119873 lt 05 119881119901119897119903119889 = 05 (

2570 times 235

radic3 times 11) = 1585 119896119873





Si

119873119904119889 le 119872119894119899 (025119873119901119897119903119889 05119860119908 119891119910

1205741198980)


025119873119901119897119903119889 = 025119860 times 119891119910

1205741198720= 025

5380 times 235

11= 28734 119896119873

05119860119908 times 119891119910

1205741198720= 05

2170 times 235

11= 2317 119896119873

119873119904119889 = 135119866 = 1337 119896119873 lt 119898119894119899 (025119873119901119897119903119889 05119860119908 times 119891119910

1205741198720)





119872119910119904119889 =15119882 times 1198972

8= 9313119896119873119898 119872119911119904119889 = 0 119872119901119897119910119903119889 = 13416 119896119873119898

λ119897119905 =

119871119911119894119911

119888105

[

1 +120(

119871119911119894119911ℎ119905119891

)

2

] 025


62

119871119911 = 1250 119898119898 119894119911 = 335 119898119898 ℎ = 300 119898119898 119905119891 = 107 119898119898




119873119904119889ꭕ119898119894119899

119873119901119897119903119889+119870119910 119872119910119904119889

119872119901119897119910119903119889+119870119911 119872119911119904119889119872119901119897119911119903119889


Avec

λ119910 =119871119910

119894119910=960

125= 768 rarr λ119910 =

768

939= 081

=gt 120583119910 = λ119910(2119861119898119910 minus 4) +119882119901119897119910 minus119882119890119897119910

119882119890119897119910= minus1134 + 0127 = minus1007 lt 09

120572 = 021 λ119910 = 081

empty119910 = 05 [1 + 120572119910(λ119910 minus 02) + λ1199102]

empty119910 = 05[1 + 021(081 minus 02) + 0812] = 089

ꭕ119910=

1


ꭕ119910= 0794 rarr 119870119910 = 1 minus


0794 times 538 times 2350= 101

120582119911 =125

335= 3731 =gt 120582119911 = 0397 rarr empty119911 = 0611 =gt ꭕ

119911= 092

ꭕ119898119894119899

= ꭕ119910= 0794

119873119901119897119903119889 =119860119891119910

1205741198980=5380 times 235

11= 114936 119896119873

119872119910119904119889 =151198821198712

8= 9313 119896119873119898

119872119901119897119910119903119889 = 13416 119896119873119898

119873119904119889 = 135119866 = 1337 119896119873

119896119910 = 101

119872119911119904119889 = 0

63

119873119904119889120594119898119894119899 119873119901119897119903119889

+119896119910 119872119910119904119889

119872119901119897119910119903119889+119896119911 119872119911119904119889119872119901119897119911119903119889

le 10

1337

0794 times 114836+101 times 9313

13416= 071 lt 1 119862119900119899119889119894119905119894119900119899 119907eacute119903119894119891119894eacute119890




64

Chapitre 4


41 Introduction




- Le pont roulant










poteaux de la halle

65





Puissances

N (t)

Porteacutee

L(m)



B

Chariot

K

Total

B+K

Rmax Rmin

125 18 085 520 1040 6809 1151 796 814 194


66


1 035 06 2 36



I 02 11 11 A-2















Groupes II






67
















119877119898119886119909 = 814 119870119873 119877119898119894119899 = 194 119870119873

Charges verticales

119877119881119898119886119909 = Ψ1 119877119898119886119909 = 115 times 814 = 8954 119870119873

119877119881119898119894119899 = Ψ2 119877119898119894119899 = 11 times 194 = 2134 119870119873


68

119877119871119898119886119909 = 119862 119877119898119886119909 = 02 times 814 = 1628 119870119873

119877119871119898119894119899 = 119862 119877119898119894119899 = 02 times 194 = 388 119870119873



1198771198671119898119886119909 = plusmn [0024(119870 + 119873 + 119861)119871

119890+ 0021(119873 + 119870)]

= plusmn [0024(1151 + 125 + 6809)18

36+ 0021(125 + 1151)]

1198771198671119898119886119909 = plusmn274 119905

1198771198671119898119894119899 = plusmn [0024(119870 + 119873 + 119861)119871

119890minus 0021(119873 + 119870)]

= plusmn [0024(1151 + 125 + 6809)18

36minus 0021(125 + 1151)]

1198771198671119898119894119899 = plusmn2168 119905


1198771198672119898119886119909 = plusmn [00052(119870 + 119873 + 5119861)119871

119890+ 0021(119873 + 119870)]

= plusmn [00052(1151 + 125 + 5 times 6809)18

36+ 0021(125 + 1151)]

1198771198672119898119886119909 = plusmn1526 119905

1198771198672119898119894119899 = plusmn [00052(119870 + 119873 + 5119861)119871

119890minus 0021(119873 + 119870)]

= plusmn [00052(1151 + 125 + 5 times 6809)18

36minus 0021(125 + 1151)]

1198771198672119898119894119899 = plusmn0953 119905




69





Rail

Poids

(Kgm)

B

(mm)

H

(mm)

P

(mm)

Section

A (cm2)

I x

(cm4)

I y

(cm4)

A55

318

55

65

150

407

178

337



70



119891119911 le 119891119886119889119898 =119897

750= 08 119888119898



119886 = (119897

2minus119890

4) = (

6

2minus36

4) = 21 119898



119891119911 =119901 119886 1198972

24119864119868(3 minus

4 1198862

1198972)

Avec

L= 6000 mm

a= 2100 mm

P=89540 N

E=21104 Nmm2

71

119868119910 ge119901 119886 1198972(31198972 minus 41198862)



119868119910 ge 421397625 1198981198984






119902 = 119866119901119900119906119905119903119890 + 119866119903119886119894119897 = 142 + 031 = 173 119896119899119898119897

119891119911 =119901 119886 1198972

24119864119868(3 minus

4 1198862

1198972) +

5 119902 1198974

384119864119868

119891119911 =89540 times 2100 times 60002


4 times 21002

60002) +




profileacute


G

Kgm

A cm2 h

mm

b

mm

tf

mm

tw

mm

Iy

cm4

Iz

cm4

Wply

cm3

Wplz

cm 3

HEB360 142 1806 360 300 225 125 43190 10140 2683 1032

72


119902 = 119866119901119900119906119905119903119890 + 119866119903119886119894119897 = 155 + 031 = 186 119870119873119898119897

119891119911 =119901 119886 1198972

24119864119868(3 minus

4 1198862

1198972) +

5 119902 1198974

384119864119868

119891119911 =89540 times 2100 times 60002


4 times 21002

60002) +






119905119908le 72휀

Avec

휀 = radic235

119891119910

298

135le 72radic

235

235 ⟹ 2207 le 72


119888

119905119891=1198872

119905119891le 10휀 ⟹

150

24= 625 le 10




profileacute


G

Kgm

A

cm2

h

mm

b

mm

tf

mm

tw

mm

Iy

cm4

Iz

cm4

Wply

cm3

Wplz

cm 3

HEB400 155 1978 400 300 24 135 57680 10820 3232 1104

73

119881119910119904119889 le 119881119901119897119903119889 119912119955119957 120787 120786 120788 (120787 120784120782)119914119914119924120791120789

119881119901119897119903119889 =119860119907119911 119891119910

radic3 1205741198980=6998 times 235

radic3 times 11= 863154 119873 = 86315 119870119873


119881119881 = 119877119881119898119886119909 times4119886

119897=8954 times 4 times 21

6= 12535 119870119873


119881119875119875 =119866 119897

2=186 times 6

2= 558 119870119873

Drsquoougrave 119881119910119904119889 = 135119881119875119875 + 15119881119881 = 19556 119870119873

119881119910119904119889 le 119881119901119897119903119889



Suivant (z-z)


119872119881 = 119877119881119898119886119909 times(6 minus

1198902)2

4119897= 8954 times

(6 minus362 )

2

4 times 6= 6581 119870119873119898


119872119875119875 =119866 1198972

8= 837 119870119873119898


119872119910119904119889 = 135119872119875119875 + 15119872119881 = 110 119870119873119898



119872119911119904119889 = 119872119867 =21198771198671119871

(119871

2minus119890

4)2

74

119872119911119904119889 = 119872119867 =2 times 274

6times (

6

2minus36

4)2

= 4028 119870119873119898




119873119904119889119873119901119897119903119889

+119872119910119904119889

119872119890119897119910+119872119911119904119889119872119890119897119911

le 1 120787 120785120790 ndash 119810119810119820120791120789

119873119904119889 = 15119877119871119898119886119909 = 15 times 1628 = 2442 119870119873

119872119890119897119910 =119908119890119897119910 119891119910

1205741198720= 61613 119872119890119897119911 =

119908119890119897119911 119891119910

1205741198720= 1541 119873119901119897119903119889 =

119860 119891119910

1205741198720= 422573

2442

422573+

110

61613+4028

1541= 044 le 1



Si 119889


Avec

휀 = radic235

119891119910= 1

119889

119905119908=298

135= 2207 lt 69





1205741198721


75



λ119897119905 =

119871119894119911

119888105

[

1 +120(

119871119894119911ℎ119905119891

)

2

] 025 = 6522 119808119821119821119812119831119812119809 119810119810119820120791120789

Avec 119871 = 600119888119898


λ119871119879 = [λ119897119905λ1] [120573119908]

05 휀 = radic235

119891119910= 1

λ119871119879 =6522

939= 0694

On calcule

ꭕ119871119879=

1


2 )le 1




ꭕ119871119879=

1

(079 + radic0792 minus 06942)= 0856


11= 59104 119870119873119898

119872119910119904119889 = 110 119870119873119898




76



119891119904119889 le 119877119910119877119889

Avec




120590119891119864119889 =119872119910119904119889

119882119890119897119910= 381 1198701198731198881198982

119878119910 = 2(ℎ119877 + 119905119891)radic[1 minus (1205741198720120590119891119864119889

119891119910119891)

2

] = 1751 119888119898

119877119910119877119889 =119878119910 times 119905119908 times 119891119910119908

1205741198720= 505 119870119873 gt 119891119904119889 = 119877119907119898119886119909 = 8954 119870119873




119891119904119889 le 119877119886119877119889

119891119904119889119877119886119877119889

+119872119878119889119872119888119877119889

le 1 119808119825119827 120787 120789120790 minus 119810119810119820120791120789

Avec

77

119877119886119877119889 =

051199051199082 (119864 119891119910119908)

05[(119905119891119905119908)05

+ 3(119905119908119905119891) (119878119904119889 )]

1205741198720 119808119825119827 120787 120789120789 minus 119810119810119820120791120789

119877119886119877119889 = 108284 119870119873

119891119904119889 = 15119877119871119898119886119909 = 15 times 1628 = 2442 119870119873

119872119888119877119889 =3232 times 103 times 235

11= 69047 119870119873119898

119891119904119889119877119886119877119889

+119872119878119889119872119888119877119889

=2442

108284+

110

69047 = 018 le 15




119887119890119891119891 le 119887 119808119825119827 120787 120789120791 minus 119810119810119820120791120789

119887119890119891119891 = radicℎ2 + 1198781199042 = 410 119898119898 gt 119887 = 300 119898119898




efforts suivants




Charge verticale


119901prime = 119876 119871 + 119877119898119886119909 (2 minus119890

119871) ψ


36

6) times 11

119901prime = 13651 119870119873


119901 = 135119876 119871 + 15119877119898119886119909 (2 minus119890

119871) ψ


36

6) times 11

119901 = 2031 119870119873

78

Charge horizontale

119875119867 = 15119877119867119898119886119909 (1 minus119890

119897)ψ


36

6) times 11 = 1808 119870119873




119891119911 le 119891119886119889119898 =119897

500


119891119911 =119901prime 1198893

3119864119868le 119891119886119889119898

119868119910 =500 119901prime 1198892

3119864ge 782667 1198881198984


79




119905119908le 72휀

Avec

휀 = radic235

119891119910

2486

71le 72radic

235

235 ⟹ 3501 le 72


119888

119905119891=1198872

119905119891le 10휀 ⟹

75

102= 735 le 10





119881119910119904119889 le 119881119901119897119903119889

Avec 119860119907119911 = 257 cm2

119881119901119897119903119889 =119860119907119911 119891119910

radic3 1205741198980=257 times 235

radic3 times 11= 317 119870119873

119881119904119889 = 119901 = 2031 lt 05119881119901119897119877119889


profileacute


G

Kgm

A

cm2

h

mm

b

mm

tf

mm

tw

mm

Iy

cm4

Iz

cm4

Wply

cm3

Wplz

cm 3

IPE 300 422 5380 300 150 107 71 8353 604 628 125

80


119872119888119903119889 =119908119901119897119910 119891119910

1205741198720=628 times 235

11= 13416 119870119873119898

119872119910119904119889 = 119901 119889 = 2031 times 085 = 172635 119870119873119898

119872119910119904119889 lt 119872119888119903119889




119872119888119903119889 =119908119901119897119910 119891119910

1205741198720=1019 times 235

11= 2177 119870119873119898

119872119910119904119889 = 119901 119889 = 2031 times 085 = 172635 119870119873119898

119872119910119904119889 lt 119872119888119903119889


17263


profileacute


G

Kgm

A

cm2

h

mm

b

mm

tf

mm

tw

mm

Iy

cm4

Iz

cm4

Wply

cm3

Wplz

cm3

IPE 360 571 727 360 170 127 8 16270 1043 1019 191

81



chemin de roulement

119891119911 le 119891119886119889119898 =119889

500= 017

119902 = 119902119868119875119864 360 = 571 119889119886119873119898119897

119891119911 =119901prime 1198893

3119864119868+119902 1198974

8119864119868= 0082 + 0021 = 0103 119888119898 lt 017 119888119898


82

Chapitre-5








dynamiques


83




119881 =119860119863 119876

119877119882



119863 =

25120578 0 le 119879 le 1198792

25120578(1198792119879)23 1198792 le 119879 le 3119904

25120578 (11987923)

23 (3119879)

53 119879 gt 3119904


84

120578 = radic7

(2 + 120585)ge 07



119879 = 119862119879 ℎ11987334 119917119926119929119924119932119923119916 (120786 120788)119929119927119912 119933120784120782120782120785




119876 = 1 +sum119875119902

6

1


85


119876 = 1 +sum119875119902

6

1

= 1 + 02 = 12


119899119894=1

Avec 119882119894 = 119882119866119894 + 120573119882119876119894




119881 =119860119863 119876

119877119882

119860 = 005 119863 = 25 119876 = 12 119877 = 4 119882 = 189475119896119873

119881119909 = 119881119910 =005 times 25 times 12

4times 189475 = 7105119896119873


119904119886119892=

125119860 (119860 +

119879

1198791(25120578

119876

119877minus 1)) 0 le 119879 le 1198791

25120578(125119860) (119876

119877) 1198791 le 119879 le 1198792

25120578(125119860) (119876

119877)(1198792119879)23

1198792 le 119879 le 30119904

25120578(125119860) (11987923)

23(3

119879)

53(119876

119877) 119879 gt 30119904

86



η = 100 A=005 1198791=015 1198792=050


87













88










89

ℎ

150=890

150= 594119888119898 sans vent

ℎ

125=890

125= 712119888119898 avec vent






Toiture 029 076 116 304


ℎ

100=1025

100= 1025 119888119898



90

Chapitre-6


61 Introduction





119872119910119904119889 = 21902 kNm

119881119904119889 =7249 kN

119873119904119889 =2018 kN

91

Profileacute


IPE 400 A cm2

hmm

b mm

119905f

mm

119905w mm

119868y

cm4

119868z Cm4

119908ply

cm3

119908plz

cm3

MATERIAU ACIER S235

8446 400 180 14 90 231284 131782 123832 2256




119888

119905119891=60

14= 59 lt 10휀 =gt 119888119897119886119904119904119890 1


119889

119905119908=98

9= 11 lt 72휀 =gt 119888119897119886119904119904119890 1





Si 119881119904119889 le 05119881119901119897119903119889 ⟹ 119872119904119889 le 119872119888119903119889 119912119955119957120787 120786 120789 119914119914119924 120791120789


119881119898119886119909 = 119881119904119889 =7248kN

119881119901119897119911119903119889 =

119860119907119911 (119891119910

radic3)

1205741198980=

4270235

radic311

= 526674119896119873

119881119904119889 = 7247 le 05119881119901119897119911119903119889 = 52667119896119873


92



119873119904119889 le 119872119894119899(025119873119901119897119903119889 05119860119908119891119910

1205741198720)


119873119904119889 = 2018119896119873

119873119901119897119903119889 le119860 119891

119910

1205741198720=8446 235

11= 180437119896119873

025119873119901119897119903119889 =451 119896119873

119860119908 = 119860 minus 2119887 119905119891 = 34061198981198982

05119860119908119891119910

1205741198720= 36382119896119873

119873119904119889 = 2018 le 36382119896119873



119872119888119903119889 = 119872119901119897119910119903119889 =119908119901119897119910 119891119910

1205741198720=1238320 235

11= 26455119896119873119898




120594119898119894119899 119873119901119897119903119889+119896119910 119872119910119904119889

119872119901119897119910119903119889+119896119911 119872119911119904119889119872119901119897119911119903119889



120594119911 119873119901119897119903119889+119896119871119879 119872119910119904119889

120594119871119879119872119901119897119910119903119889+119896119911 119872119911119904119889119872119901119897119911119903119889



120594119898119894119899 = 119872119894119899(120594119910 120594119911)


93

120594119910 =1

(120601119910 +radic1206011199102 minus 1205821199102 )

120601119910 = 05[1 + 120572119910(120582119910 minus 02) + 1205821199102]

120582119910= (120582119910

1205821)radic120573119860 =

120582119910

1205821

Avec 120573119860 = 1 Classe 1

1205821 = 939

120582119910 =05119868119910

119894119910=455

166= 274

120582119910=274

939= 029


ℎ

119887=400

180= 222 gt 12 119894119898119901119897119894119902119906119890 120572 = 021

120601 = 05[1 + 120572119910(120582119910 minus 02) + 1205821199102 ] = 055

120594119910 =1

(055 + radic0552 minus 0292)= 098


120594119911 =1

(120601119911 +radic1206011199112 minus 120582119911

2)

120601119911 = 05[1 + 120572119911(120582119911 minus 02) + 1205821199112]

120582119911 = (1205821199111205821)radic120573119860 =

1205821199111205821

Avec 120573119860 = 1 Classe 1

120582119911 =119868119911119894119911=200

395= 5063

120582119911 =5063

939= 054


94

ℎ

119887= 222 gt 12 (119911 minus 119911)119894119898119901119897119894119902119906119890 120572 = 034

120601 = 05[1 + 034(054 minus 02) + 0542 ] = 07

120594119911 =1

(07 + radic072 minus 0542)= 087

120594119898119894119899 = 119872119894119899(120594119910 120594119911) = 087




λ119897119905 =

119871119894119911

119888105

[

1 +120(

119871119894119911ℎ119905119891

)

2

] 025 = 4367 119808119821119821119812119831119812119809 119810119810119820120791120789

Avec

IPE400 119905119891 = 14119898119898 119894119911 = 395119888119898 ℎ = 400119898119898

119870 = 1 1198881=1134 Tableau B11 CCM97


1205821 = 939휀

휀 = radic235

119891119910= 1

120582119871119879 = [1205821198971199051205821] [120573119908]

05

120582119897119905 = 4367

120582119871119879 =4367

939= 046 gt 04



119873119904119889120594119911 119873119901119897119903119889

+119896119871119879 119872119910119904119889

120594119871119879119872119901119897119910119903119889+119896119911 119872119911119904119889119872119901119897119911119903119889


Calcul de 120594119871119879


95

implique 120594119871119879 = 094

Calcul de 119896119871119879


119870119871119879 = 1 minusμLT N119904119889

120594119911 119860 119891119910= 099 lt 15


Donc

119873119904119889=7249 kN 119872119910119904119889=219 kNm 119872119901119897119910119903119889=26455 kNm 120594119911=087 119872119901119897119911119903119889=4819kNm


119873119904119889120594119911 119873119901119897119903119889

+119896119871119879 119872119910119904119889

120594119871119879119872119901119897119910119903119889+119896119911 119872119911119904119889

119872119901119897119911119903119889


7249

087 180437+

099 219

094 26455= 055










96

119872119910119904119889 = 32083 119896119873119898

119881119904119889 = 120 119896119873

119873119904119889 = 602 119896119873

Profileacute


HEA320

A cm2

hmm

b mm

119905f

mm

119905w mm

119868y

cm4

119868z cm4

119908 ply

cm3

119908 plz

cm3

MATERIAU ACIER S235

12437 310 300 16 9 229286 698524 162823 70975




119888

119905119891=60

16= 375 lt 10휀 =gt 119888119897119886119904119904119890 1


119889

119905119908=98

9= 109 lt 72휀 =gt 119888119897119886119904119904119890 1





Si 119881119904119889 le 05119881119901119897119903119889 ⟹ 119872119904119889 le 119872119888119903119889 119912119955119957120787 120786 120789 119914119914119924 120791120789


119881119898119886119909 = 119881119904119889 =120kN

119881119901119897119911119903119889 =

119860119907119911 (119891119910

radic3)

1205741198980=4113 235radic3

11= 50731119896119873

97

119881119904119889 le 05119881119901119897119911119903119889




119873119904119889 le 119872119894119899(025119873119901119897119903119889 05119860119908119891119910

1205741198720)


119873119904119889 =602kN

119873119901119897119903119889 le119860 119891

119910

1205741198720=12437 235

11= 2656995 119896119873

025119873119901119897119903119889 = 664248119896119873

119860119908 = 119860 minus 2119887 119905119891 = 2837 1198981198982

05119860119908119891119910

1205741198720= 30304119896119873

119873119904119889 = 602119896119873 le 30304119896119873



119872119888119903119889 = 119872119901119897119910119903119889 =119908119901119897119910 119891119910

1205741198720=1628000 times 235

11= 3478119896119873119898




120594119898119894119899 119873119901119897119903119889+119896119910 119872119910119904119889

119872119901119897119910119903119889+119896119911 119872119911119904119889119872119901119897119911119903119889



120594119911 119873119901119897119903119889+119896119871119879 119872119910119904119889

120594119871119879119872119901119897119910119903119889+119896119911 119872119911119904119889119872119901119897119911119903119889



120594119898119894119899 = 119872119894119899(120594119910 120594119911)


98

120594119910 =1

(120601119910 +radic1206011199102 minus 1205821199102 )

120601119910 = 05[1 + 120572119910(120582119910 minus 02) + 1205821199102]

120582119910= (120582119910

1205821)radic120573119860 =

120582119910

1205821

Avec 120573119860 = 1 Classe 1

1205821 = 939

120582119910 =05119868119910

119894119910=05 890

1358= 3276

120582119910=3276

939= 034


ℎ

119887=310

300= 1 lt 12 (119910 minus 119910)119894119898119901119897119894119902119906119890 120572 = 034

120601 = 05[1 + 120572119910(120582119910 minus 02) + 1205821199102 ] = 058

120594119910 =1

058 + radic058 minus 034= 095


120594119911 =1

(120601119911 +radic1206011199112 minus 1205821199112)

120601119911 = 05[1 + 120572119911(120582119911 minus 02) + 1205821199112]

120582119911 = (1205821199111205821)radic120573119860 =

1205821199111205821

Avec 120573119860 = 1 Classe 1

1205821 = 939

120582119911 =119868119911119894119911=07 59

749= 055


ℎ

119887= 1 lt 12 (119911 minus 119911) 119894119898119901119897119894119902119906119890 120572 = 049

120601 = 05[1 + 049(055 minus 02) + 0552] = 073

99

120594119911 =1

073 + radic073 minus 055= 082

120594119898119894119899 = 119872119894119899(120594119910 120594119911) = 082


λ119897119905 =

119871119894119911

119888105

[

1 +120(

119871119894119911ℎ119905119891

)

2

] 025 = 3536

HEA320 119905119891 = 16119898119898 119894119911 = 749119888119898 ℎ = 310119898119898

119870 = 07 1198881 = 1134 Tableau B11 CCM97


1205821 = 939휀

휀 = radic235

119891119910= 1

120582119871119879 = [1205821198971199051205821] [120573119908]

05

120582119897119905 = 3536

120582119871119879 =3536

939= 037 lt 04 119901119886119904 119889119890 119903119894119904119902119906119890 119889119890 119889119890119907119890119903119904119890119898119890119899119905


119873119904119889120594119898119894119899 119873119901119897119903119889

+119896119910 119872119910119904119889

119872119901119897119910119903119889+119896119911 119872119911119904119889119872119901119897119911119903119889


Avec

119873119904119889 =602kN 119872119910119904119889=32083kNm 119872119911119904119889=049kNm 119872119901119897119910119903119889=3478kNm

119872119901119897119911119903119889=1516kNm 120594119898119894119899= 082 119873119901119897119903119889=26570kN 119896119910= 05 119896119911= 07

602

082 26570+05 32083

3478+07 049







100





(135G+15V1)


119873119904119889 =69837kN


Profileacute


2CAE (120x12)

A Cm2

hmm

b mm

Anet

Cm2

d

mm

MATERIAU ACIER S235

5508 120 248 4658 8



119873119904119889 le 119873119905119903119889 = 119872119894119899[119873119901119897119903119889 119873119906119903119889 119873119899119890119905119903119889]

101

119873119901119897119903119889 =119860 119891119910

1205741198720= 117671119896119873

119873119906119903119889 = 09119860119899119890119905 1198911199061205741198722

= 13719119896119873

119873119899119890119905119903119889 =119860119899119890119905 119891119910

1205741198720= 995118119896119873








102


119872119910119904119889 = 02 119896119873119898

119881119904119889 = 0048 119896119873

119873119904119889 = 5628 119896119873

Profileacute


IPE300

A cm2

hmm

b mm

119905f

mm

119905w mm

119868y

cm4

119868z cm4

119908ply

cm3

119908plz

cm3

MATERIAU ACIER S235

538 300 150 107 71 8356 746 628 125







Si 119881119904119889 le 05119881119901119897119903119889 ⟹ 119872119904119889 le 119872119888119903119889 119912119955119957120787 120786 120789 119914119914119924 120791120789


119881119898119886119909 = 119881119904119889 =0048kN

119881119901119897119911119903119889 =

119860119907119911 (119891119910

radic3)

1205741198980=2570 235radic3

11= 3169119896119873

119881119904119889 le 05119881119901119897119911119903119889




119873119904119889 le 119872119894119899(025119873119901119897119903119889 05119860119908119891119910

1205741198720)

103


119873119904119889 =5628kN

119873119901119897119903119889 le119860 119891

119910

1205741198720=5380 235

11= 114936 119896119873

025119873119901119897119903119889 = 28734 119896119873

119860119908 = 119860 minus 2119887 119905119891 = 2170 1198981198982

05119860119908119891119910

1205741198720= 23179119896119873

119873119904119889 = 5628119896119873 le 23179119896119873



119872119888119903119889 = 119872119901119897119910119903119889 =119908119901119897119910 119891119910

1205741198720=628000 times 235

11= 134163 119896119873119898




120594119898119894119899 119873119901119897119903119889+119896119910 119872119910119904119889

119872119901119897119910119903119889+119896119911 119872119911119904119889119872119901119897119911119903119889



120594119911 119873119901119897119903119889+119896119871119879 119872119910119904119889

120594119871119879119872119901119897119910119903119889+119896119911 119872119911119904119889119872119901119897119911119903119889



120594119898119894119899 = 119872119894119899(120594119910 120594119911)


120594119910 =1

(120601119910 +radic1206011199102 minus 1205821199102 )

120601119910 = 05[1 + 120572119910(120582119910 minus 02) + 1205821199102]

120582119910= (120582119910

1205821)radic120573119860 =

120582119910

1205821

104

Avec 120573119860 = 1 Classe 1

1205821 = 939

120582119910 =119871119910

119894119910= 960

125= 768

120582119910=768

939= 081


ℎ

119887=300

150= 05 lt 12 (119910 minus 119910)119894119898119901119897119894119902119906119890 120572 = 021

120601 = 05[1 + 120572119910(120582119910 minus 02) + 1205821199102 ] = 089

120594119910 =1

058 + radic058 minus 034= 079


120594119911 =1

(120601119911 +radic1206011199112 minus 1205821199112)

120601119911 = 05[1 + 120572119911(120582119911 minus 02) + 1205821199112]

120582119911 = (1205821199111205821)radic120573119860 =

1205821199111205821

Avec 120573119860 = 1 Classe 1

1205821 = 939

120582119911 =119868119911119894119911=125

335= 3731 120582119911 = 039


ℎ

119887= 1 lt 12 (119911 minus 119911) 119894119898119901119897119894119902119906119890 120572 = 021

120601 = 05[1 + 021(039 minus 02) + 0392] = 061

120594119911 =1

061 + radic061 minus 039= 092

120594119898119894119899 = 119872119894119899(120594119910 120594119911) = 079


105

λ119897119905 =

119871119894119911

119888105

[

1 +120(

119871119894119911ℎ119905119891

)

2

] 025 = 3433

IPE300 119905119891 = 107119898119898 119894119911 = 335119888119898 ℎ = 300119898119898

119870 = 1 1198881 = 1134 Tableau B11 CCM97


1205821 = 939휀

휀 = radic235

119891119910= 1

120582119871119879 = [1205821198971199051205821] [120573119908]

05

120582119897119905 = 3433

120582119871119879 =3433

939= 036 lt 04 119901119886119904 119889119890 119903119894119904119902119906119890 119889119890 119889119890119907119890119903119904119890119898119890119899119905


119873119904119889120594119898119894119899 119873119901119897119903119889

+119896119910 119872119910119904119889

119872119901119897119910119903119889+119896119911 119872119911119904119889119872119901119897119911119903119889


Avec

119873119904119889 =5628kN 119872119910119904119889=02kNm 119872119911119904119889=018kNm 119872119901119897119910119903119889=134163kNm

119872119901119897119911119903119889=267kNm 120594119898119894119899= 079 119873119901119897119903119889=1149kN 119896119910= 1 119896119911= 1

5628

079 1149+

02

134163+018



106

Chapitre-7


71 Introduction










au poteau

107




119872119904119889 = 28961119896119873119898 119873119904119889 = 17878119896119873 119881119904119889 = 8941119896119873




119905 = 119872119894119899(119905119891 119905119901119897119886119905119894119899119890) = 135119898119898

Avec





12119889O = 24 119898119898 le 1198901 le 12119905 =186 119898119898 ⟹ 1198901 = 110 119898119898

15119889O = 30 119898119898 le 1198902 le 12119905 = 186 119898119898 ⟹ 1198902 = 105 119898119898

22119889O = 44 119898119898 le 1199011 le 14119905 =217 119898119898 ⟹ 1199011 = 100 119898119898


108






IPE 400 119905f = 135 119898119898 119905w = 86 119898119898

119886min= 26 le twle119886max= 8

119886min =35 le tf le119886max= 8







sum119897 = 2119887 + 4(119887 minus 119905119908) = 2180 + 4(180 minus 86) = 1045119898119898

119865119908119903119889 =7times 1045 times 360

radic2= 1862119896119873

119873119904119889 =119872119904119889

ℎ=120784120790120791 120788120783

120782 120791= 120785120784120783 120789120790





Avec 120573119908 = 125 120574119872119882 = 08


109

i

sum119897 = 4ℎ119894 = 4 times 373 = 1492119898119898

119865119907119903119889 =7 times 1492 times 360

radic3= 217074119896119873



119873119894 =119872119904119889 119889119894sum119889119894

2


119909 = 119905119891radic119887

119905119908= 135radic

180

86= 6176



- 1198891 = 712 119898119898

- 1198892 = 612 119898119898

- 1198893 = 512 119898119898 ⟹ Σ 1198892 = 129 119898sup2

- 1198894 = 312 119898119898

- 1198895 = 212 119898119898

- 1198896 = 112 119898119898


1198731 =28961 times 0712

129= 15984119896119873



1198731 = 119899119865119907119903119889 ⟹ 119860119904 ge119873119904119889

06 times 119891119906119887 times 119899=

15984

06 times 800 times 2= 16651198981198982



M18 18 20 254 192 800 291



110




119865119901 = 07 times 119891119906119887 times 119860119904 = 06 x 800 x 192 = 10752kN

119872119903119889 =119899 119865119901 sum119889119894

2

119889119894=2 times 10752 times 129

0712= 3896 gt 119872119904119889 = 28961 119896119873119898




119865119907119904119889 le 119865119904119903119889 =119870119904 119898 120583

1205741198722(119865119901119888119889 minus 08119873119904119889) 119917119926119929119924119932119923119916 120788 120789 minus 119914119914119924120791120789

Avec

119870119904 = 10 ∶ Trous normaux



119865119904119903119889 = 024 (10752 minus 08 times15984

2) = 1046119896119873

119865119907119904119889 =8941

12= 745119896119873 lt 1046119896119873




1205741198722 119813119822119825119820119828119819119812 120788 120784 minus 119810119810119820120791120789



125= 213157 119896119873

119865119905119904119889 =119865119901

2=10752

2= 5376119896119873 lt 119861119901 119903119889 = 213157 119896119873


111



1205741198722 119827119808119809119819119812119808119828 120788 120787 120785 ndash 119810119810119820120791120789

Avec 119870119904 = 25

120572119887 = min (119890131198890

(119901131198890

minus 025) 119891119906119887119891119906 1) = 1



125= 46008119896119873 gt

11986511990711990411988912

= 745119896119873



119865119907 le 119865119905119903119889 = 119905119908119888 1198871198901198911198911198911199101205741198720

Avec




⟹ 119865119905119903119889 = 9 times 90times23511

= 173045 119896119873


119865119907 =119872119904119889

ℎ minus 119905119891=28961

029= 99865 gt 119865119905119903119889 = 173045119896119873




119873119904119889 le 119865119888119903119889 =119896119888 120588 119887119890119891119891 119905119908119888 119891119910

1205741198721radic1 + 13 (119887119890119891119891ℎ)2

119887119890119891119891 = 119905119891119887 + 2119886119901radic2 + 5(119905119891119888 + 119903119888) + 2119905119901

Avec

112






119887119890119891119891 =25014mm



120590119888119904119889 =119881119904119889119860+119872119904119889

119882119890119897119910=8941 times 103

1244+28961 times 106

1479= 196533119872119875119886

120590119888119904119889 = 19653119872119875119886 lt 119891119910 = 235119872119875119886 ⟹ 119896119888 = 1


119901 = 0932radic119887119890119891119891 119889119908119888 119891119910

119864 1199051199081198882= 0932radic


21 times 104 times 092= 254

119901 gt 072⟹ 120588 =119901 minus 02

1199012=254 minus 02

2542= 036


11 radic1 + 13 (250131

)2

= 12741119896119873

119873119904119889 = 1119873119894 =119872119904119889 sum119889119894sum119889119894

2 =29861 times 247

129= 57175119896119873





119865119907 le 119881119903119889 = 058119891119910 ℎ1199051199081205741198720


11= 3457119896119873


119865119907 =119872119904119889ℎ minus 119905119891

= 46216 119896119873 gt 119881119903119889 = 3457119896119873 119888119900119899119889119894119905119894119900119899 119899119900119899 119907eacute119903119894119891119894eacute119890


113

119865119907 = 46216119896119873 le 119881119903119889 = 058119891119910 ℎ119905119908 + 04

1205741198720= 058 235 31

(09 + 04)

11= 49935119896119873







logiciel robot

119872119904119889 = 15135119896119873119898 119873119904119889 = 1324119896119873 119881119904119889 = 273119896119873






119905 = min(119905119891 119905119901119897119886119905119894119899119890) = 135119898119898


114









IPE400

tf = 135 mm tw = 86 mm






radic2 times 119861119908 120574119898119908


Donc

119865119908119903119889 =119860 times sum119871 times 119891119906


radic2 times 1= 133083119896119873

119873119904119889 =119872119904119889ℎ

=7283

08= 9103119896119873

115

119873119904119889 = 9103 le 119865119908119903119889 = 1330119896119873






Donc

119865119907119903119889 =119886 times sum119871 times 119891119906


radic3 times 1= 155053119896119873



119873119894 =119872119904119889 119889119894sum119889119894

2


119909 = 119905119891radic119887

119905119908= 135radic

180

86= 6176119898119898


- 1198891 = 700 119898119898

- 1198892 = 600 119898119898

- 1198893 = 500 119898119898 ⟹ Σ1198891198942

= 124 119898sup2

- 1198894 = 300 119898119898

- 1198895 = 200 119898119898

- 1198896 = 100 119898119898


1198731 =119872119904119889 times 119889119894Σ119889119894

2 =15135 times 070

124= 4111119896119873



116


1198731 = 119899 119865119907 ⟹ 119860119904 ge119873119904119889

05 times 119891119906119887 times 119899=

13240

05 times 800 times 2= 16551198981198982



M18 18 20 254 192 800 291




119865119901 = 07 times 119891119906119887 times 119860119904 = 10752 119896119873

119872119903119889 =119899 119865119901sum119889119894

2

119889119894=2 times 10752 times 124

07= 38092 gt 119872119904119889 = 15135119896119873119898




119865119907119904119889 le 119865119904119903119889 =119870119904 119898 120583

1205741198722(119865119901119888119889 minus 08119873119904119889) 119813119822119825119820119828119819119812 120788120789 ndash 119810119810119820120791120789

Avec




119865119904119903119889 = 024 ( 10752 minus 08 times 1324) = 2326119896119873

119865119907119904119889 =273

12= 023 lt 119865119904 119903119889 = 2326119896119873




1205741198722 119813119822119825119820119828119819119812 120788 120784 ndash 119810119810119820120791120789

Avec


117


125= 31578119896119873

119865119905119904119889 =119865119901

2= 5376 lt 31578119896119873




1205741198722 119827119808119809119819119812119808119828 120788 120787 120785 ndash 119810119810119820120791120789

Avec Ks = 25

120572119887 = min (119890131198890

(119901131198890

minus 025) 119891119906119887119891119906 1) = 1


11986511990711990411988912


125= 5184 119896119873







119865119907119904119889 =119873119904119889

119899119887119903 119889119890 119887119900119906119897119900119899=131

3= 4366 le 119865119907119903119889

118


1205741198722⟹ 119860119904 ge

1205741198722 times 119865119907119903119889

06 times 119891119906119887119909 119898=125 times 43666

06 times 800 times 2= 56851198981198982


















119873119898119886119909 le 119865119908119903119889 =119886 sum119897 119891119906

119861119908 120574119898119908 radic(3 minus 1199041198941198991205722)


120572= 30gtgtgt 11990411989411989930o = 05

119865119908119903119889 =5 times 700 times 360



119



1205741198722 119827119808119809119819119812119808119828 120788 120787 120785 minus 119810119810119820120791120789


120572119907= 06



125= 12057119896119873

119865119907119904119889 =119873119904119889

3=3124

3= 10413 le 119865119907119903119889 = 12057119896119873




1205741198722 119827119808119809119819119812119808119828 120788 120787 120785 minus 119810119810119820120791120789

Avec

Ks = 25

120572119887 = min (119890131198890

(119901131198890

minus 025) 119891119906119887119891119906 1) = 092



125= 33914119896119873 gt 119865119907119904119889 = 4366119896119873




119873119898119886119909 le 119881119890119891119891119903119889 =119860119899119905 119891119910

1205741198722+119860119899119907 119891119910

radic3 1205741198722 119812119810120785 119849119834119851119853119842119838120783 minus 120790sect120785120783120782 120784

Avec


119860119899119890119905 = (119897

2minus11988902) 119905 = (60 minus 9)12 = 6121198981198982


120

119860119899119907 = (1198901 + 21199011 minus 251198890)119905 = (50 + 140 minus 45)12 = 17401198981198982

⟹ 119881119890119891119891119903119889 =612 times 235

125+1740 times 235

radic3 times 125= 303918119896119873 gt

119873119904119889

2= 655119896119873








119865119907119904119889 =119877119907119911

119899119887119900119906119897119900119899119904=36

2= 18 119896119873

119865119907119903119889 =06 times 119860119904 times 119891119906119887

120574119872119887⟹119860119904 ge

120574119872119887 times 11986511990711990311988906 times 119891119906119887

=11 times 18000

06 times 800= 41251198981198982



119865119907119903119889 =06 times 119860119904 times 119891119906119887

120574119872119887=06 times 58 times 800

11= 253119896119873 gt 119865119907119904119889 = 18119896119873


119865119905119903119889 =09 times 119860119904 times 119891119906119887

120574119872119887=09 times 58 times 800

11= 379119896119873

121

119865119907119903119889 =06 times 119860119904 times 119891119906119887

120574119872119887= 253119896119873

119865119907119904119889119865119907119903119889

+119865119905119904119889

14 119865119905119903119889= 052 lt 1 119862119900119899119889119894119905119894119900119899 119907119890119903119894119891119894eacute119890


122

Chapitre-8




123








119865119888119896=30 MPa

119891119888119889 =085 times 119865119888119896125

= 204 MPa


119865119895119889 = 120572120573119895 119891119888119889



119865119895119889 = 120572 120573119895 119891119888119889 = 15 times2

3times 17 = 204 119872119875119886


1198601198620 ge119873119904119889119891119888119889

=148960

204

1198601198620 ge 7266341198981198982


bp ge b+2tf = 190+2times155 = 221 mm

hp ge h+2tf = 310+2times155 = 341 mm

On prend

bp =600 hp=620



124


119862 = 119905 (119891119910119901

3119891119895119889 1205741198720)

05

= 30(235


= 5605 119898119898

119862 = 5605 lt(ℎ minus 2119905119891)

2= 1395 119898119898




gorge (a) Annexe H







119890 =119872119904119889119873119904119889

= 041 119898 gt 119885119879 = 0195 119898







125


Ougrave

119871119890119891119891 = min(119887119901 119887119891119888 + 2119888) = min(600 300 + 2 times 4671) = 39342 119898119898

119887119890119891119891 = min (119888ℎ1198882minus 119905119891119888) + 119905119891119888 +min (119888

ℎ119901 minus ℎ119888

2)

119887119890119891119891 = min (4671310

2minus 155) + 155 + min (4671

620 minus 310

2) = 10892 119898119898

⟹ 119865119888119903119889 = 204 times 10892 times 39342 = 874166 119896119873


119865119907119903119889 = 119865119891119903119889 + 119899119887 119865119907119887119903119889


119865119891119903119889 = 02119873119904119889 = 1214 119896119873





119865119907119887119903119889 =120572119888119887 119891119906119887 119860119904

1205741198722

Avec 120572119888119887 = 044 minus 00003119891119910119887 = 0248


126

119865119907119887119903119889 =0248 times 800 times 561

125= 8904 119896119873

⟹ 119865119907119903119889 = 1214 + 8 times 8904 119896119873 = 72446 119896119873




Avec 120573119908 =08 120574119898119908 = 125 119886 = 6 mm


sum119897 = 470 119898119898

119865119908119903119889 =6 times 470 times 360

radic3= 58612 119896119873

119881119904119889 = 9773 119896119873 lt min(119865119907119903119889 119865119908119903119889) = 58612 119896119873





W= 150 mm e = 55 mm ex = 40 mm mx = 40 mm


119897119890119891119891119888119901 = 119898119894119899 2120587119898119909 = 25132 119898119898

120587119898119909 +119882 = 27566 119898119898120587119898119909 + 2119890 = 23566 119898119898

⟹ 119897119890119891119891119888119901 = 23566 119898119898

127


119897119890119891119891119899119888 = 119898119894119899

4119898119909 + 125119890119909 = 210 119898119898

2119898119909 + 0625119890119909 +119882

2= 180 119898119898

2119898119909 + 0625119890119909 + 119890 = 160 119898119898119887119901

2= 150 119898119898

⟹ 119897119890119891119891119899119888 = 150 119898119898


119865119905119886119899119888119903119889 = min[119865119905119887119900119899119889119903119889 119865119905119903119889]


119865119905119903119889 = 09 times119860119904 times 119891119906119887120574119898119887


125= 32314 119896119873



119865119887119889 =036radic119891119888119896

120574119888=036 times 547

15= 1313 119872119875119886


119865119905119887119900119899119889119903119889 =120587 119889 119897119887 119891119887119889

120572

Avec

1198971 = 20119889 = 600 119898119898

119903 = 3119889 = 90 119898119898

1198972 = 20119889 = 600 119898119898






07= 52929 119896119873

119865119905119886119899119888119903119889 = 119898119894119899[52929 32314] = 32314 kN

128




Lb = 8d + em +tp + twa + 05k

Avec







119871119887lowast =

881198981199093 119860119904

1198971198901198911198911 1199051199013 =


150 times 253= 13480 119898119898 lt 119871119887 = 312 119898119898




119898119901119897119903119889 =1199051199012 119891119910119901

41205741198720=252 times 235

4 times 11= 3338119896119873


Mode 1 1198721199011198971119903119889 = 119898119901119897119903119889 times 1198971198901198911198911 = 3338 times 015 = 5007119896119873119898

1198971198901198911198911 = min(119897119890119891119891119888119901 119897119890119891119891119899119888) = 150 119898119898


129




Mode 1-2

1198651199051minus2119903119889 =21198721199011198971119903119889

119898119909=2 times 5

004= 250 119896119873

Mode 3

1198651199053119903119889 = 2119865119905119903119889119886119899119888ℎ119900119903 = 2 times 32314 = 646280 119896119873

Mode 4

1198651199054119903119889 =119887119890119891119891119905 119905119908 119891119910

1205741198720=150 times 9 times 235

11= 288409119896119873

Drsquoougrave

119865119905119903119889 = min(1198651199051minus2119903119889 1198651199053119903119889 1198651199054119903119889) = 250 119896119873




119885119879119890119873minus 1

119865119879119903119889 times 119885

119885119862119890119873+ 1

) 119812119810120785 ndash 120783 120790 119827119808119809119819119812119808119828 120788 120789

119885 = 119885119879+119885119862 = 195 + 155 = 350119898119898

⟹119872119903119889 = 5646 119896119873119898 lt 6207119896119873119898



821 Introduction




- Le site (S3)



130




ELU 119872119880 = 6207119896119873119898 119873119880 = 9773119896119873

ELS 119872119878 = 4136119896119873119898 119873119878 = 7960119896119873




119886 = 119886119901 + 119888 = 062 + 02 = 082 119898


119860

119861=119886

119887= 1025 ⟹ 119860 = 1025119861



119890 =119872119904

119873119904= 052119898



120590119898119886119909 =119873

119860119861(1 +

6119890

119861) le 120590119904119900119897


368B2 - B - 312 ge 0 ⟹ B ge0765m



131

119889 = max (119861 minus 119887

4119860 minus 119886

4) = max (005 0295)

On prend d= 45 cm



On a

119890 = 052 gt119860

6= 041


3120590119898119886119909 1205901198981198941198994

lt 120590119904119900119897

Avec

120590119898119894119899 =119873

119860119861(1 minus

6119890

119860) =

14896

2(1 minus

041

2 ) = 62191198961198731198982

120590119898119894119899 =119873

119860119861(1 +

6119890

119860) =

14896

2(1 +

041

2 ) = 86771198961198731198982

3120590119898119886119909 120590119898119894119899

4= 6835 1198961198731198982 lt 120590119904119900119897 = 180 119896119873119898

2



119890 =119872

119873= 052 119898 lt

119860

4= 062 119898




119890 gt119886

6 119890 gt

119860

24


119860119886 =1198721119911 119904119905

132

1198721 = (119860

2minus 035119886)

2

(1 +119890

119860+14 times 119890 times 119886

1198602)1198731199042119860

1198721 = 2788119896119873119898

Avec 119911 = 09d =40cm

119904119905 = min (2

3119891119890 110radic12057811989111990528) =20163 MPa

11989111990528 = 00611989111988828 + 06 = 24 119872119875119886 120578 = 16 119867 119860 Donc

119860119886 =2788 times 106

400 times 20163= 345 1198881198982


119860119887 =119873prime(119861 minus 119887)

8119889 119904119905

Avec

119873prime = 119873119904 (1 +3119890

119860) = 796 (1 +

3 times 052

25) = 2993119896119873

119904119905 = min (2

3119891119890 110radic12057811989111990528) = 20163119872119875119886

11989111990528 = 00611989111988828 + 06 = 24119896119873 120578 = 16 119867 119860

Donc 119860119887 = 071198881198982


119860119886 =1198721119911 120590119904119905

1198721 = (119860

2minus 035119886)

2

(1 +119890

119860+14 times 119890 times 119886

1198602)1198731199062119860

1198721 = 349119896119873119898

Avec 119911 =09d = 40 cm

120590119904119905 =119891119890120574119904=400

115= 3478119872119875119886

Donc

133

119860119886 =349 times 106

400 times 3478= 251198881198982


119860119886 =119873119906(119861 minus 119887)

8119889 120590119904119905

Avec

119873prime = 119873119906 (1 +3119890

119860) = 23833119896119873

Donc 119860119887 = 1621198881198982


119860119898119894119899 = 023 times11989111990528119891119890

times 119860 times ℎ119905 = 17251198881198982

Sens B

119860119898119894119899 = 023 times11989111990528119891119890

times 119861 times ℎ119905 = 691198881198982



A (cm2) St (cm)

A 345 1725 10T16 201 25 B 07 69 7T16 1407 25



134



119873119905 = (119873

120572) ge 20 119896119873 [119825119823119808120791120791 119855 120784120782120782120785 119808119851119853 120783120782 120783 120783 119835]


119873119905 =14896

12= 1241119896119873

ELS

119873119905 =796

12= 663119896119873


119860119904119905 =119873119905120590119904119905

ELS

119860119904119905 =663

348= 0191198881198982

ELU

119860119904119905 =1241

348= 0351198881198982





119860119904119905 = 0905 le 119860119904 = 6791198881198982


135


120601119898119894119899 le 119898119894119899 (ℎ

35120601119897119898119894119899

119887

10) = 08 119888119898

On prend 120601119905 =8mm


On prend St=10cm


136


137

ANNEXE - 1

138

139

140

ANNEXE - 2

141

ANNEXE - 3

142

143

ANNEXE ndash 4

144

145

ANNEXE ndash 5

Deacutedicace











Deacutedicace














Reacutesumeacute


ملخص







Abstract































































































































Liste des tableaux

















LISTE DES NOTATIONS

Majuscules latines








16

Chapitre-1


11 Introduction


17



18

Action

permanente (γG)




Effet favorable

γGinf

10 1 0


γGsup

135 15 15




135119866119896119895 + 15119876119896119898119886119909





1 119866119896119895 + 150119882minus


sum119866119896119895119895

+ 119876119896119898119886119909

119866119896119895 + 119876119896119898119886119909


sum119866119896119895119895

+ 09sum119876119896119894119894gt1

119866119896119895 + 09119876119896119898119886119909 + 09119878 119866119896119895 + 09119876119896119898119886119909 + 09119882


19










20




21






22




23

Chapitre-2


21 Introduction










24

- Effet du site








Ouargla (Zone 4)




Kt=017 Z0=001m Zmin=1m ξ=044






Avec




119902119901(119885) = 119902119903119890119891 times 119862119890

Avec

- 119902ref = 575 119889119886119873119898sup2


2(119885) times [1 + 7119868119907] 119825119821119829120784120782120783120785 119836119841119834119849119842119853119851119838 120784 120786 sect120784 120786 120784 119834


25


119862119903(119911)

119870119905 119871119899 (1199111198981198941198991199110

) 119901119900119906119903 119911 lt 119911119898119894119899

119870119905 119871119899 (119911

1199110) 119901119900119906119903 119911119898119894119899 le 119911 le 200119898


)=0783


Zo)=1178

On retient 119862119903= 1178


119868119907(119911)

1

119862119905(119911) 119871119899 (119911

1199110) 119901119900119906119903 119911 gt 119911119898119894119899

1

119862119905(119911) 119871119899 (1199111198981198941198991199110) 119901119900119906119903 119911 le 119911119898119894119899

Pour z gt zmin 119868119907(119911) =1

1Ln(1

001)= 0217

Pour z lt zmin 119868119907(119911) =1

1Ln(1025

001)= 0144



119862119890(119911119895) = 119862119903(119911119895)2[1 + 7 119868119881]

Pour z gt zmin

119862119890(119911) = 11782 times 12 times [1 + 7(0144)] = 2786

Pour z lt zmin

119862119890(119911) = 07832 times 12 times [1 + 7(0217)] = 154


Avec

26

- 119902119903119890119891 = 575 119889119886119873119898sup2



qp = 160195Nm2 = 16 kNm2





- b=30 m

- d=36 m

- h=89 m


e = min (d 2h)


Donc e = 2x1025 = 205m



27



119862119901119890 = 1198621199011198901 119878119894 119878 le 11198982

119862119901119890 = 1198621199011198901 + (11986211990111989010 minus 1198621199011198901) times 11989711990011989210(119878) 119878119894 11198982 lt 119878 lt 101198982

119862119901119890 = 11986211990111989010 119878119894 119878 ge 101198982



Zone


Parois sous le vent


Cpe10 -10 -08 -05 +08 -03


Versant de Toiture




28







le tableau suivant


853deg F G H

-237 -123 -083



- Parois verticales


-b=36 m

29

-d=30 m

-h=1025


e=Min (b 2h) = Min (36 205) = 205 m





30

Zone


Parois sous le vent








31




853deg -22 -192 -183 -067 -057






2(5 times 4)

30 times 89= 014 = 14


μ119901 =120

160= 075



Pour μ119901=075 on lit 119862119901119894 =-016

32




2 times (5 times 4)

36 times 9575= 0116 = 116


Pour μ119901=075 rarr 119862119901119894 =-02

33





Direction V1 V3


A 1602 -10 -0154 -0846 -135529

B 1602 -08 -0154 -0646 -103489

C 1602 -05 -0154 -0346 -55429

D 1602 +08 -0154 +0954 +152831

E 1602 -03 -0154 -0146 -23389


34

Toiture


F 1602 -237 -0154 -2276 -355003

G 1602 -123 -0154 -1076 -172375

H 1602 -084 -0154 -0676 -108295

Z1 1602 -1 -0154 -0846 -135529

Z2 1602 -06 -0154 -0446 -71449


Direction V2 et V4

Parois verticales


A 1602 -10 -0162 -0838 -134247

B 1602 -08 -0162 -0638 -102207

C 1602 -05 -0162 -0338 -54147

D 1602 +08 -0162 +0962 +154112

E 1602 -03 -0162 -0138 -22107


35

Toiture


Finf 1602 -12 -0162 -1038 -1662876

Fsup 1602 -22 -0162 -2038 -3264876

G 1602 -183 -0162 -1668 -2672136

H 1602 -067 -0162 -0508 -813816

I 1602 -057 -0162 -0408 -653616









9= 015




q1= 300 Nml

q2= 500 Nml



36











- Epaisseur 50 mm

- Largeur 1000 mm





Selon le DTR BC22




37

119902 =8119875

3119871= 044 119896119873119898

119902 = 444 119889119886119873119898













38

Chapitre-3





deacutefavorable

39

(minus354 times5125


0875

6) = minus32754 1198891198861198731198982

Qeq (vent) = 3276 daN1198982















40



41


Vzsd =119902119906119911 times 119897

2=1878 kN

Mysd=119902119906119911 times 119897

2

8=2817 kNm

Mzsd=119902119906119910 times 119897

2

8=081 kNm



IPE 180 A Cm2

h mm

b mm

119905f

mm 119905w

mm 119868y

Cm4

119868z

Cm4

119908ply cm3

119908plz cm3

MATERIAU ACIER S235

239 180 91 8 53 1317 101 146 346




4

384 times 119864 119868119910lt

119897

200=



119897

200= 3 119862119900119899119889119894119905119894119900119899 119907eacute119903119894119891119894eacute119890

Plan z-z

5 times 119902119904119910 times 1198974

384 times 119864 119868119911lt

119897

200=



119897

200= 3 119862119900119899119889119894119905119894119900119899 119907eacute119903119894119891119894eacute119890

42




1205741198721 gt 119872119910119904119889 = 2817 119896119873119898

Calcul de 119872119887119903119889




λ119871119879 =

119871119894119911

119888105

[

1 +120(

119871119894119911ℎ119905119891

)

2

] 025

Avec


(Tableau B12 CCM97)

iz =224mm tf =85mm

L=Lz=3000mm h=200mm

λ119871119879 =

119871119894119911

119888105

[

1 +120(

119871119894119911ℎ119905119891

)

2

] 025 = 9457 rarr λ119871119879 =

989

939= 1007

rarr =1092

43


rarr ꭕ119871119879=

1


2)= 066 le 1

rarr 119872119887119903119889 =ꭕ119871119879times 120573

119908times 119882119901119897119910 times 119891119910

1205741198721

=066 1 166 235

11= 234 119896119873 119898








119872119872119860119883 =119901prime 119897

3=119901 1198972

8⟹ 119901 =

8 119901prime

3119897=800

18= 4444 119889119886119873119898119897

44


(ANNEXE ndash 1)

Soit

119876119890119902 =327 + 1082

2= 2176 1198891198861198731198982









45



Vzsd =119902119906119911 times 119897

2=186 kN

Mysd=119902119906119911 times 119897

2

8=279 kNm

Mzsd=119902119906119910 times 119897

2

8=0855 kNm

46



IPE 200 A Cm2

h mm

b mm

119905f

mm 119905w

mm 119868y

Cm4

119868z

Cm4

119908ply cm3

119908plz cm3

MATERIAU ACIER S235

285 200 100 85 56 1943 142 221 446




4

384 times 119864 119868119910lt

119897

200=



119897

200= 3 119862119900119899119889119894119905119894119900119899 119907eacute119903119894119891119894eacute119890

Plan z-z

5 times 119902119904119910 times 1198974

384 times 119864 119868119911lt

119897

200=



119897

200= 3 119862119900119899119889119894119905119894119900119899 119907eacute119903119894119891119894eacute119890




1205741198721 gt 119872119910119904119889 = 279 119896119873119898

Calcul de 119872119887119903119889

47




λ119871119879 =

119871119894119911

119888105

[

1 +120(

119871119894119911ℎ119905119891

)

2

] 025

Avec


(Tableau B12 CCM97)


-L=Lz=6000mm -h=200mm

λ119871119879 =

119871119894119911

119888105

[

1 +120(

119871119894119911ℎ119905119891

)

2

] 025 = 989 ⟶ λ119871119879 =

989

939= 105

rarr =114


rarr ꭕ119897119905=

1


2)= 063 le 1

rarr 119872119887119903119889 =ꭕ119897119905times 120573

119908times 119882119901119897119910 times 119891119910

1205741198721


11= 2974119896119873119898



48


Avec

119881119901119897119911119903119889 =

119860119907119911 (119891119910

radic3)

11 119890119905 119860119907119911 = 1400 1198981198982

Donc

05119881119901119897119911119903119889 = 05

1400 (235

radic3)

11= 8634 119896119873



Si 119889


CCM97 art 561(1)

119889

119905119908 =

159





(119872119910119904119889

119872119901119897119910119903119889)

120572

+ (119872119911119904119889119872119901119897119911119903119889

)

120573

le 1 119912119955119957 120787 120786 120790 (120783120783)119914119914119924 120791120789


119872119901119897119910119903119889 =119882119901119897119910 times 119891119910

11=221 times 235

11= 4721 119896119873119898

119872119901119897119911119903119889 =119882119901119897119911 times 119891119910

11=446 times 235

11= 952 119896119873119898

119872119910119904119889 = 279 119896119873119898

119872119911119904119889 = 0855 119896119873119898

(279

4721)2

+ (0855

952) = 044 lt 1 119888119900119899119889119894119905119894119900119899 119907eacute119903119894119891119894eacute119890

49











Effort rampant


Lrsquoexcentrement


2 (119887

2) le 119905 le 3(

119887

2)


50

2 (10

2) = 10 le 119905 le 3(

10

2) = 15

On prend t=10 cm


119877119911 = 119902119906119911 times119897

2= 6 times

6

2= 18 119896119873

119877119910 = 119902119906119910 times119897

2= 054 119896119873


119877119911 = 18 times 2 = 36 119896119873

119877119910 = 054 times 2 = 108 119896119873


119872119877 = 119877119911 times 119905 + 119877119910 timesℎ

2= 36 times 10 + 108 times 10 = 3708 119896119873 119888119898 = 37119896119873119898


119872119890119897119877119889 =119908119890119897 times 119891119910

1205741198720 119912119955119957 120787 120786 120787 120783 (120784)119914119914119924120791120789

119872119890119897119877119889 =119908119890119897 times 1198911199101205741198720

=gt 119908119890119897 ge119872119890119897119877119889 times 1205741198720

119891119910=gt 119908119890119897 ge

00037 times 11

235

= 173 times 10minus51198983

119908119890119897 = 17321198881198983




119908119890119897 =119887 1198902


6 times 1732

119887= radic

6 times 1732

180

119890 ge 076


Donc on prend e=1cm

51





















52












qsy =(133 + 5) times 125=2288daNml

qsy = 0228 kN

quy=135G=03kN



W += 1541 daN m2


quz=15W

quz=288kN

53



qsz=19262daN=192kN


119891119911 =5 times 119902119904119911 times 119897

4

384 times 119864119910 times 119868le 119891119886119889119873 =

119897

200=600

200= 3 119888119898

119868119910 ge5 times 192 times 6004



Profileacute


UPN 140 A Cm2

h mm

b mm

119905f mm

119905w mm

Iy

Cm4

Iz

Cm4

119908pSy

cm3

119908pSz

cm3

MATERIAU ACIER S235

20 140 60 10 7 605 627 103 283







qsy =(133 + 5) times 125 +1568 = 3856daNml

qsy = 038 kN

quy=135G

quy =053kN


qsz=192kN

quz=15W

quz=288kN

54




119888

119905119891=60

10= 6 lt 10휀 =gt 119888119897119886119904119904119890 1


119889

119905119908=98

7= 14 lt 72휀 =gt 119888119897119886119904119904119890 1


(119872119910119904119889

119872119890119897119910119877119889)

1

+ (119872119911119904119889

119872119890119897119911119877119889)1

le 1


119872119910 =119902119906119911 times 119897

2

8=288 times 62

8= 1296 119896119873119898


119872119911 =119902119906119910 times 119897

2

8=058 times 62

8= 261119896119873119898

119872119890119897119910119877119889 =119908119890119897119910 times 119891119910

1205741198720=864 times 103 times 235

11= 1845 119896119873119898

119872119890119897119911119877119889 =119908119890119897119911 times 119891119910

1205741198720=148 times 103 times 235

11= 316 119896119873119898

Donc

(1296

1845)1+ (

261



55

Nouveau 119872119911

119872119911 =119902119906119910 times 119897

2

8=058 times 32

8= 065119896119873119898

(1296

1845)1+ (

065




119881119911119904119889 =15119882119871

2= 1296 119896119873

119881119901119897119877119889 =119860119907119911 times 119891119910

radic3times 1205741198720= 12855 119896119873





1205741198721gt 119872119910119904119889 119912119955119957 120787 120787 120784 (120787 120786120790)119914119914119924120791120789

Avec

119872119888119903 = 11986211205872 119864 1198681199111198712

radic119868119908119868119911+1198712 119866 1198681199051205872 119864 119868119911

119912119925119925119916119935119916 119913 (119913 120783 120785) minus 119914119914119924120791120789

119872119888119903=311713762 Ncm


119872119888119903


119882119901119897119910 (upn140) =103 cm3

56

λ119897119905 = 0881


2 ]


empty119897119905 = 0959

ꭕ119897119905=

1


2 )

le 1

ꭕ119897119905= 075

119872119887119903119889 = 1652 119896119873119898

119872119887119903119889 = 1652 119896119873119898 gt 119872119910119904119889 = 1296 119896119873119898 119862119900119899119889119894119905119894119900119899 119907eacute119903119894119891119894eacute119890







57

119877 = 125119902119910 times 119897

2

Avec 119902119910 = [135(119866119880119875119873140 + 119866119888119900119906119907119890119903119905119906119903119890)]

119902119910 = 0837119896119873

119897 = 6 119898

119877 = 125119902119910 times 119897

2= 125 times 0837 times 3 = 32119896119873


1198791 =119877

2= 16119896119873

1198792 = 1198791 + 119877=48 kN

1198793 =1198792

2 sin 120579= 374 119896119873 119860119907119890119888 120579 = 119886119903119888 119905119892

25 119898

3 119898= 398deg



119873119905119904119889 =119860 times 119891119910

1205741198720= 4800 119873 =gt 119860 ge

11 times 4800

235 =gt 119860 ge 22461198981198982

119860 =120587empty2

4=gt empty ge radic

4119860

120587= radic

4 times 2246

314= 534 119898119898



Introduction



58



119878ge

63

radic119904

119889times119875

Avec








Srsquo=273

4=6825 m2








59



















96=8989 daNm2





60

119891119910 =5 times119882 times 1198974

384 times 119864 times 119868119910le 119891119886119889119898 =

119897

200


384 times E= 59136 1198881198984


Profileacute


IPE300 A Cm2

h mm

b mm

tf mm

tw

mm 119868y

Cm4

119868z Cm4

Wply

cm3

Wplz

cm3

MATERIAU ACIER S235

538 300 150 107 71 8356 746 628 125





119888

119905119891=

75

107= 7 lt 10 = 10 119878119890119898119890119897119897119890 119889119890 119888119897119886119904119904119890 1


119889

119905119908=2486

71= 35 lt 38 = 38 Acirc119898119890 119889119890 119888119897119886119904119904119890 1



Si 119881119904119889 le 05 119881119901119897119903119889 ⟹119872119904119889 le 119872119888119903119889 119912119955119957120787 120786 120789 119914119914119924 120791120789

61

119881119904119889 =15 times119882 times 119897


2= 388 119896119873 lt 05 119881119901119897119903119889 = 05 (

2570 times 235

radic3 times 11) = 1585 119896119873





Si

119873119904119889 le 119872119894119899 (025119873119901119897119903119889 05119860119908 119891119910

1205741198980)


025119873119901119897119903119889 = 025119860 times 119891119910

1205741198720= 025

5380 times 235

11= 28734 119896119873

05119860119908 times 119891119910

1205741198720= 05

2170 times 235

11= 2317 119896119873

119873119904119889 = 135119866 = 1337 119896119873 lt 119898119894119899 (025119873119901119897119903119889 05119860119908 times 119891119910

1205741198720)





119872119910119904119889 =15119882 times 1198972

8= 9313119896119873119898 119872119911119904119889 = 0 119872119901119897119910119903119889 = 13416 119896119873119898

λ119897119905 =

119871119911119894119911

119888105

[

1 +120(

119871119911119894119911ℎ119905119891

)

2

] 025


62

119871119911 = 1250 119898119898 119894119911 = 335 119898119898 ℎ = 300 119898119898 119905119891 = 107 119898119898




119873119904119889ꭕ119898119894119899

119873119901119897119903119889+119870119910 119872119910119904119889

119872119901119897119910119903119889+119870119911 119872119911119904119889119872119901119897119911119903119889


Avec

λ119910 =119871119910

119894119910=960

125= 768 rarr λ119910 =

768

939= 081

=gt 120583119910 = λ119910(2119861119898119910 minus 4) +119882119901119897119910 minus119882119890119897119910

119882119890119897119910= minus1134 + 0127 = minus1007 lt 09

120572 = 021 λ119910 = 081

empty119910 = 05 [1 + 120572119910(λ119910 minus 02) + λ1199102]

empty119910 = 05[1 + 021(081 minus 02) + 0812] = 089

ꭕ119910=

1


ꭕ119910= 0794 rarr 119870119910 = 1 minus


0794 times 538 times 2350= 101

120582119911 =125

335= 3731 =gt 120582119911 = 0397 rarr empty119911 = 0611 =gt ꭕ

119911= 092

ꭕ119898119894119899

= ꭕ119910= 0794

119873119901119897119903119889 =119860119891119910

1205741198980=5380 times 235

11= 114936 119896119873

119872119910119904119889 =151198821198712

8= 9313 119896119873119898

119872119901119897119910119903119889 = 13416 119896119873119898

119873119904119889 = 135119866 = 1337 119896119873

119896119910 = 101

119872119911119904119889 = 0

63

119873119904119889120594119898119894119899 119873119901119897119903119889

+119896119910 119872119910119904119889

119872119901119897119910119903119889+119896119911 119872119911119904119889119872119901119897119911119903119889

le 10

1337

0794 times 114836+101 times 9313

13416= 071 lt 1 119862119900119899119889119894119905119894119900119899 119907eacute119903119894119891119894eacute119890




64

Chapitre 4


41 Introduction




- Le pont roulant










poteaux de la halle

65





Puissances

N (t)

Porteacutee

L(m)



B

Chariot

K

Total

B+K

Rmax Rmin

125 18 085 520 1040 6809 1151 796 814 194


66


1 035 06 2 36



I 02 11 11 A-2















Groupes II






67
















119877119898119886119909 = 814 119870119873 119877119898119894119899 = 194 119870119873

Charges verticales

119877119881119898119886119909 = Ψ1 119877119898119886119909 = 115 times 814 = 8954 119870119873

119877119881119898119894119899 = Ψ2 119877119898119894119899 = 11 times 194 = 2134 119870119873


68

119877119871119898119886119909 = 119862 119877119898119886119909 = 02 times 814 = 1628 119870119873

119877119871119898119894119899 = 119862 119877119898119894119899 = 02 times 194 = 388 119870119873



1198771198671119898119886119909 = plusmn [0024(119870 + 119873 + 119861)119871

119890+ 0021(119873 + 119870)]

= plusmn [0024(1151 + 125 + 6809)18

36+ 0021(125 + 1151)]

1198771198671119898119886119909 = plusmn274 119905

1198771198671119898119894119899 = plusmn [0024(119870 + 119873 + 119861)119871

119890minus 0021(119873 + 119870)]

= plusmn [0024(1151 + 125 + 6809)18

36minus 0021(125 + 1151)]

1198771198671119898119894119899 = plusmn2168 119905


1198771198672119898119886119909 = plusmn [00052(119870 + 119873 + 5119861)119871

119890+ 0021(119873 + 119870)]

= plusmn [00052(1151 + 125 + 5 times 6809)18

36+ 0021(125 + 1151)]

1198771198672119898119886119909 = plusmn1526 119905

1198771198672119898119894119899 = plusmn [00052(119870 + 119873 + 5119861)119871

119890minus 0021(119873 + 119870)]

= plusmn [00052(1151 + 125 + 5 times 6809)18

36minus 0021(125 + 1151)]

1198771198672119898119894119899 = plusmn0953 119905




69





Rail

Poids

(Kgm)

B

(mm)

H

(mm)

P

(mm)

Section

A (cm2)

I x

(cm4)

I y

(cm4)

A55

318

55

65

150

407

178

337



70



119891119911 le 119891119886119889119898 =119897

750= 08 119888119898



119886 = (119897

2minus119890

4) = (

6

2minus36

4) = 21 119898



119891119911 =119901 119886 1198972

24119864119868(3 minus

4 1198862

1198972)

Avec

L= 6000 mm

a= 2100 mm

P=89540 N

E=21104 Nmm2

71

119868119910 ge119901 119886 1198972(31198972 minus 41198862)



119868119910 ge 421397625 1198981198984






119902 = 119866119901119900119906119905119903119890 + 119866119903119886119894119897 = 142 + 031 = 173 119896119899119898119897

119891119911 =119901 119886 1198972

24119864119868(3 minus

4 1198862

1198972) +

5 119902 1198974

384119864119868

119891119911 =89540 times 2100 times 60002


4 times 21002

60002) +




profileacute


G

Kgm

A cm2 h

mm

b

mm

tf

mm

tw

mm

Iy

cm4

Iz

cm4

Wply

cm3

Wplz

cm 3

HEB360 142 1806 360 300 225 125 43190 10140 2683 1032

72


119902 = 119866119901119900119906119905119903119890 + 119866119903119886119894119897 = 155 + 031 = 186 119870119873119898119897

119891119911 =119901 119886 1198972

24119864119868(3 minus

4 1198862

1198972) +

5 119902 1198974

384119864119868

119891119911 =89540 times 2100 times 60002


4 times 21002

60002) +






119905119908le 72휀

Avec

휀 = radic235

119891119910

298

135le 72radic

235

235 ⟹ 2207 le 72


119888

119905119891=1198872

119905119891le 10휀 ⟹

150

24= 625 le 10




profileacute


G

Kgm

A

cm2

h

mm

b

mm

tf

mm

tw

mm

Iy

cm4

Iz

cm4

Wply

cm3

Wplz

cm 3

HEB400 155 1978 400 300 24 135 57680 10820 3232 1104

73

119881119910119904119889 le 119881119901119897119903119889 119912119955119957 120787 120786 120788 (120787 120784120782)119914119914119924120791120789

119881119901119897119903119889 =119860119907119911 119891119910

radic3 1205741198980=6998 times 235

radic3 times 11= 863154 119873 = 86315 119870119873


119881119881 = 119877119881119898119886119909 times4119886

119897=8954 times 4 times 21

6= 12535 119870119873


119881119875119875 =119866 119897

2=186 times 6

2= 558 119870119873

Drsquoougrave 119881119910119904119889 = 135119881119875119875 + 15119881119881 = 19556 119870119873

119881119910119904119889 le 119881119901119897119903119889



Suivant (z-z)


119872119881 = 119877119881119898119886119909 times(6 minus

1198902)2

4119897= 8954 times

(6 minus362 )

2

4 times 6= 6581 119870119873119898


119872119875119875 =119866 1198972

8= 837 119870119873119898


119872119910119904119889 = 135119872119875119875 + 15119872119881 = 110 119870119873119898



119872119911119904119889 = 119872119867 =21198771198671119871

(119871

2minus119890

4)2

74

119872119911119904119889 = 119872119867 =2 times 274

6times (

6

2minus36

4)2

= 4028 119870119873119898




119873119904119889119873119901119897119903119889

+119872119910119904119889

119872119890119897119910+119872119911119904119889119872119890119897119911

le 1 120787 120785120790 ndash 119810119810119820120791120789

119873119904119889 = 15119877119871119898119886119909 = 15 times 1628 = 2442 119870119873

119872119890119897119910 =119908119890119897119910 119891119910

1205741198720= 61613 119872119890119897119911 =

119908119890119897119911 119891119910

1205741198720= 1541 119873119901119897119903119889 =

119860 119891119910

1205741198720= 422573

2442

422573+

110

61613+4028

1541= 044 le 1



Si 119889


Avec

휀 = radic235

119891119910= 1

119889

119905119908=298

135= 2207 lt 69





1205741198721


75



λ119897119905 =

119871119894119911

119888105

[

1 +120(

119871119894119911ℎ119905119891

)

2

] 025 = 6522 119808119821119821119812119831119812119809 119810119810119820120791120789

Avec 119871 = 600119888119898


λ119871119879 = [λ119897119905λ1] [120573119908]

05 휀 = radic235

119891119910= 1

λ119871119879 =6522

939= 0694

On calcule

ꭕ119871119879=

1


2 )le 1




ꭕ119871119879=

1

(079 + radic0792 minus 06942)= 0856


11= 59104 119870119873119898

119872119910119904119889 = 110 119870119873119898




76



119891119904119889 le 119877119910119877119889

Avec




120590119891119864119889 =119872119910119904119889

119882119890119897119910= 381 1198701198731198881198982

119878119910 = 2(ℎ119877 + 119905119891)radic[1 minus (1205741198720120590119891119864119889

119891119910119891)

2

] = 1751 119888119898

119877119910119877119889 =119878119910 times 119905119908 times 119891119910119908

1205741198720= 505 119870119873 gt 119891119904119889 = 119877119907119898119886119909 = 8954 119870119873




119891119904119889 le 119877119886119877119889

119891119904119889119877119886119877119889

+119872119878119889119872119888119877119889

le 1 119808119825119827 120787 120789120790 minus 119810119810119820120791120789

Avec

77

119877119886119877119889 =

051199051199082 (119864 119891119910119908)

05[(119905119891119905119908)05

+ 3(119905119908119905119891) (119878119904119889 )]

1205741198720 119808119825119827 120787 120789120789 minus 119810119810119820120791120789

119877119886119877119889 = 108284 119870119873

119891119904119889 = 15119877119871119898119886119909 = 15 times 1628 = 2442 119870119873

119872119888119877119889 =3232 times 103 times 235

11= 69047 119870119873119898

119891119904119889119877119886119877119889

+119872119878119889119872119888119877119889

=2442

108284+

110

69047 = 018 le 15




119887119890119891119891 le 119887 119808119825119827 120787 120789120791 minus 119810119810119820120791120789

119887119890119891119891 = radicℎ2 + 1198781199042 = 410 119898119898 gt 119887 = 300 119898119898




efforts suivants




Charge verticale


119901prime = 119876 119871 + 119877119898119886119909 (2 minus119890

119871) ψ


36

6) times 11

119901prime = 13651 119870119873


119901 = 135119876 119871 + 15119877119898119886119909 (2 minus119890

119871) ψ


36

6) times 11

119901 = 2031 119870119873

78

Charge horizontale

119875119867 = 15119877119867119898119886119909 (1 minus119890

119897)ψ


36

6) times 11 = 1808 119870119873




119891119911 le 119891119886119889119898 =119897

500


119891119911 =119901prime 1198893

3119864119868le 119891119886119889119898

119868119910 =500 119901prime 1198892

3119864ge 782667 1198881198984


79




119905119908le 72휀

Avec

휀 = radic235

119891119910

2486

71le 72radic

235

235 ⟹ 3501 le 72


119888

119905119891=1198872

119905119891le 10휀 ⟹

75

102= 735 le 10





119881119910119904119889 le 119881119901119897119903119889

Avec 119860119907119911 = 257 cm2

119881119901119897119903119889 =119860119907119911 119891119910

radic3 1205741198980=257 times 235

radic3 times 11= 317 119870119873

119881119904119889 = 119901 = 2031 lt 05119881119901119897119877119889


profileacute


G

Kgm

A

cm2

h

mm

b

mm

tf

mm

tw

mm

Iy

cm4

Iz

cm4

Wply

cm3

Wplz

cm 3

IPE 300 422 5380 300 150 107 71 8353 604 628 125

80


119872119888119903119889 =119908119901119897119910 119891119910

1205741198720=628 times 235

11= 13416 119870119873119898

119872119910119904119889 = 119901 119889 = 2031 times 085 = 172635 119870119873119898

119872119910119904119889 lt 119872119888119903119889




119872119888119903119889 =119908119901119897119910 119891119910

1205741198720=1019 times 235

11= 2177 119870119873119898

119872119910119904119889 = 119901 119889 = 2031 times 085 = 172635 119870119873119898

119872119910119904119889 lt 119872119888119903119889


17263


profileacute


G

Kgm

A

cm2

h

mm

b

mm

tf

mm

tw

mm

Iy

cm4

Iz

cm4

Wply

cm3

Wplz

cm3

IPE 360 571 727 360 170 127 8 16270 1043 1019 191

81



chemin de roulement

119891119911 le 119891119886119889119898 =119889

500= 017

119902 = 119902119868119875119864 360 = 571 119889119886119873119898119897

119891119911 =119901prime 1198893

3119864119868+119902 1198974

8119864119868= 0082 + 0021 = 0103 119888119898 lt 017 119888119898


82

Chapitre-5








dynamiques


83




119881 =119860119863 119876

119877119882



119863 =

25120578 0 le 119879 le 1198792

25120578(1198792119879)23 1198792 le 119879 le 3119904

25120578 (11987923)

23 (3119879)

53 119879 gt 3119904


84

120578 = radic7

(2 + 120585)ge 07



119879 = 119862119879 ℎ11987334 119917119926119929119924119932119923119916 (120786 120788)119929119927119912 119933120784120782120782120785




119876 = 1 +sum119875119902

6

1


85


119876 = 1 +sum119875119902

6

1

= 1 + 02 = 12


119899119894=1

Avec 119882119894 = 119882119866119894 + 120573119882119876119894




119881 =119860119863 119876

119877119882

119860 = 005 119863 = 25 119876 = 12 119877 = 4 119882 = 189475119896119873

119881119909 = 119881119910 =005 times 25 times 12

4times 189475 = 7105119896119873


119904119886119892=

125119860 (119860 +

119879

1198791(25120578

119876

119877minus 1)) 0 le 119879 le 1198791

25120578(125119860) (119876

119877) 1198791 le 119879 le 1198792

25120578(125119860) (119876

119877)(1198792119879)23

1198792 le 119879 le 30119904

25120578(125119860) (11987923)

23(3

119879)

53(119876

119877) 119879 gt 30119904

86



η = 100 A=005 1198791=015 1198792=050


87













88










89

ℎ

150=890

150= 594119888119898 sans vent

ℎ

125=890

125= 712119888119898 avec vent






Toiture 029 076 116 304


ℎ

100=1025

100= 1025 119888119898



90

Chapitre-6


61 Introduction





119872119910119904119889 = 21902 kNm

119881119904119889 =7249 kN

119873119904119889 =2018 kN

91

Profileacute


IPE 400 A cm2

hmm

b mm

119905f

mm

119905w mm

119868y

cm4

119868z Cm4

119908ply

cm3

119908plz

cm3

MATERIAU ACIER S235

8446 400 180 14 90 231284 131782 123832 2256




119888

119905119891=60

14= 59 lt 10휀 =gt 119888119897119886119904119904119890 1


119889

119905119908=98

9= 11 lt 72휀 =gt 119888119897119886119904119904119890 1





Si 119881119904119889 le 05119881119901119897119903119889 ⟹ 119872119904119889 le 119872119888119903119889 119912119955119957120787 120786 120789 119914119914119924 120791120789


119881119898119886119909 = 119881119904119889 =7248kN

119881119901119897119911119903119889 =

119860119907119911 (119891119910

radic3)

1205741198980=

4270235

radic311

= 526674119896119873

119881119904119889 = 7247 le 05119881119901119897119911119903119889 = 52667119896119873


92



119873119904119889 le 119872119894119899(025119873119901119897119903119889 05119860119908119891119910

1205741198720)


119873119904119889 = 2018119896119873

119873119901119897119903119889 le119860 119891

119910

1205741198720=8446 235

11= 180437119896119873

025119873119901119897119903119889 =451 119896119873

119860119908 = 119860 minus 2119887 119905119891 = 34061198981198982

05119860119908119891119910

1205741198720= 36382119896119873

119873119904119889 = 2018 le 36382119896119873



119872119888119903119889 = 119872119901119897119910119903119889 =119908119901119897119910 119891119910

1205741198720=1238320 235

11= 26455119896119873119898




120594119898119894119899 119873119901119897119903119889+119896119910 119872119910119904119889

119872119901119897119910119903119889+119896119911 119872119911119904119889119872119901119897119911119903119889



120594119911 119873119901119897119903119889+119896119871119879 119872119910119904119889

120594119871119879119872119901119897119910119903119889+119896119911 119872119911119904119889119872119901119897119911119903119889



120594119898119894119899 = 119872119894119899(120594119910 120594119911)


93

120594119910 =1

(120601119910 +radic1206011199102 minus 1205821199102 )

120601119910 = 05[1 + 120572119910(120582119910 minus 02) + 1205821199102]

120582119910= (120582119910

1205821)radic120573119860 =

120582119910

1205821

Avec 120573119860 = 1 Classe 1

1205821 = 939

120582119910 =05119868119910

119894119910=455

166= 274

120582119910=274

939= 029


ℎ

119887=400

180= 222 gt 12 119894119898119901119897119894119902119906119890 120572 = 021

120601 = 05[1 + 120572119910(120582119910 minus 02) + 1205821199102 ] = 055

120594119910 =1

(055 + radic0552 minus 0292)= 098


120594119911 =1

(120601119911 +radic1206011199112 minus 120582119911

2)

120601119911 = 05[1 + 120572119911(120582119911 minus 02) + 1205821199112]

120582119911 = (1205821199111205821)radic120573119860 =

1205821199111205821

Avec 120573119860 = 1 Classe 1

120582119911 =119868119911119894119911=200

395= 5063

120582119911 =5063

939= 054


94

ℎ

119887= 222 gt 12 (119911 minus 119911)119894119898119901119897119894119902119906119890 120572 = 034

120601 = 05[1 + 034(054 minus 02) + 0542 ] = 07

120594119911 =1

(07 + radic072 minus 0542)= 087

120594119898119894119899 = 119872119894119899(120594119910 120594119911) = 087




λ119897119905 =

119871119894119911

119888105

[

1 +120(

119871119894119911ℎ119905119891

)

2

] 025 = 4367 119808119821119821119812119831119812119809 119810119810119820120791120789

Avec

IPE400 119905119891 = 14119898119898 119894119911 = 395119888119898 ℎ = 400119898119898

119870 = 1 1198881=1134 Tableau B11 CCM97


1205821 = 939휀

휀 = radic235

119891119910= 1

120582119871119879 = [1205821198971199051205821] [120573119908]

05

120582119897119905 = 4367

120582119871119879 =4367

939= 046 gt 04



119873119904119889120594119911 119873119901119897119903119889

+119896119871119879 119872119910119904119889

120594119871119879119872119901119897119910119903119889+119896119911 119872119911119904119889119872119901119897119911119903119889


Calcul de 120594119871119879


95

implique 120594119871119879 = 094

Calcul de 119896119871119879


119870119871119879 = 1 minusμLT N119904119889

120594119911 119860 119891119910= 099 lt 15


Donc

119873119904119889=7249 kN 119872119910119904119889=219 kNm 119872119901119897119910119903119889=26455 kNm 120594119911=087 119872119901119897119911119903119889=4819kNm


119873119904119889120594119911 119873119901119897119903119889

+119896119871119879 119872119910119904119889

120594119871119879119872119901119897119910119903119889+119896119911 119872119911119904119889

119872119901119897119911119903119889


7249

087 180437+

099 219

094 26455= 055










96

119872119910119904119889 = 32083 119896119873119898

119881119904119889 = 120 119896119873

119873119904119889 = 602 119896119873

Profileacute


HEA320

A cm2

hmm

b mm

119905f

mm

119905w mm

119868y

cm4

119868z cm4

119908 ply

cm3

119908 plz

cm3

MATERIAU ACIER S235

12437 310 300 16 9 229286 698524 162823 70975




119888

119905119891=60

16= 375 lt 10휀 =gt 119888119897119886119904119904119890 1


119889

119905119908=98

9= 109 lt 72휀 =gt 119888119897119886119904119904119890 1





Si 119881119904119889 le 05119881119901119897119903119889 ⟹ 119872119904119889 le 119872119888119903119889 119912119955119957120787 120786 120789 119914119914119924 120791120789


119881119898119886119909 = 119881119904119889 =120kN

119881119901119897119911119903119889 =

119860119907119911 (119891119910

radic3)

1205741198980=4113 235radic3

11= 50731119896119873

97

119881119904119889 le 05119881119901119897119911119903119889




119873119904119889 le 119872119894119899(025119873119901119897119903119889 05119860119908119891119910

1205741198720)


119873119904119889 =602kN

119873119901119897119903119889 le119860 119891

119910

1205741198720=12437 235

11= 2656995 119896119873

025119873119901119897119903119889 = 664248119896119873

119860119908 = 119860 minus 2119887 119905119891 = 2837 1198981198982

05119860119908119891119910

1205741198720= 30304119896119873

119873119904119889 = 602119896119873 le 30304119896119873



119872119888119903119889 = 119872119901119897119910119903119889 =119908119901119897119910 119891119910

1205741198720=1628000 times 235

11= 3478119896119873119898




120594119898119894119899 119873119901119897119903119889+119896119910 119872119910119904119889

119872119901119897119910119903119889+119896119911 119872119911119904119889119872119901119897119911119903119889



120594119911 119873119901119897119903119889+119896119871119879 119872119910119904119889

120594119871119879119872119901119897119910119903119889+119896119911 119872119911119904119889119872119901119897119911119903119889



120594119898119894119899 = 119872119894119899(120594119910 120594119911)


98

120594119910 =1

(120601119910 +radic1206011199102 minus 1205821199102 )

120601119910 = 05[1 + 120572119910(120582119910 minus 02) + 1205821199102]

120582119910= (120582119910

1205821)radic120573119860 =

120582119910

1205821

Avec 120573119860 = 1 Classe 1

1205821 = 939

120582119910 =05119868119910

119894119910=05 890

1358= 3276

120582119910=3276

939= 034


ℎ

119887=310

300= 1 lt 12 (119910 minus 119910)119894119898119901119897119894119902119906119890 120572 = 034

120601 = 05[1 + 120572119910(120582119910 minus 02) + 1205821199102 ] = 058

120594119910 =1

058 + radic058 minus 034= 095


120594119911 =1

(120601119911 +radic1206011199112 minus 1205821199112)

120601119911 = 05[1 + 120572119911(120582119911 minus 02) + 1205821199112]

120582119911 = (1205821199111205821)radic120573119860 =

1205821199111205821

Avec 120573119860 = 1 Classe 1

1205821 = 939

120582119911 =119868119911119894119911=07 59

749= 055


ℎ

119887= 1 lt 12 (119911 minus 119911) 119894119898119901119897119894119902119906119890 120572 = 049

120601 = 05[1 + 049(055 minus 02) + 0552] = 073

99

120594119911 =1

073 + radic073 minus 055= 082

120594119898119894119899 = 119872119894119899(120594119910 120594119911) = 082


λ119897119905 =

119871119894119911

119888105

[

1 +120(

119871119894119911ℎ119905119891

)

2

] 025 = 3536

HEA320 119905119891 = 16119898119898 119894119911 = 749119888119898 ℎ = 310119898119898

119870 = 07 1198881 = 1134 Tableau B11 CCM97


1205821 = 939휀

휀 = radic235

119891119910= 1

120582119871119879 = [1205821198971199051205821] [120573119908]

05

120582119897119905 = 3536

120582119871119879 =3536

939= 037 lt 04 119901119886119904 119889119890 119903119894119904119902119906119890 119889119890 119889119890119907119890119903119904119890119898119890119899119905


119873119904119889120594119898119894119899 119873119901119897119903119889

+119896119910 119872119910119904119889

119872119901119897119910119903119889+119896119911 119872119911119904119889119872119901119897119911119903119889


Avec

119873119904119889 =602kN 119872119910119904119889=32083kNm 119872119911119904119889=049kNm 119872119901119897119910119903119889=3478kNm

119872119901119897119911119903119889=1516kNm 120594119898119894119899= 082 119873119901119897119903119889=26570kN 119896119910= 05 119896119911= 07

602

082 26570+05 32083

3478+07 049







100





(135G+15V1)


119873119904119889 =69837kN


Profileacute


2CAE (120x12)

A Cm2

hmm

b mm

Anet

Cm2

d

mm

MATERIAU ACIER S235

5508 120 248 4658 8



119873119904119889 le 119873119905119903119889 = 119872119894119899[119873119901119897119903119889 119873119906119903119889 119873119899119890119905119903119889]

101

119873119901119897119903119889 =119860 119891119910

1205741198720= 117671119896119873

119873119906119903119889 = 09119860119899119890119905 1198911199061205741198722

= 13719119896119873

119873119899119890119905119903119889 =119860119899119890119905 119891119910

1205741198720= 995118119896119873








102


119872119910119904119889 = 02 119896119873119898

119881119904119889 = 0048 119896119873

119873119904119889 = 5628 119896119873

Profileacute


IPE300

A cm2

hmm

b mm

119905f

mm

119905w mm

119868y

cm4

119868z cm4

119908ply

cm3

119908plz

cm3

MATERIAU ACIER S235

538 300 150 107 71 8356 746 628 125







Si 119881119904119889 le 05119881119901119897119903119889 ⟹ 119872119904119889 le 119872119888119903119889 119912119955119957120787 120786 120789 119914119914119924 120791120789


119881119898119886119909 = 119881119904119889 =0048kN

119881119901119897119911119903119889 =

119860119907119911 (119891119910

radic3)

1205741198980=2570 235radic3

11= 3169119896119873

119881119904119889 le 05119881119901119897119911119903119889




119873119904119889 le 119872119894119899(025119873119901119897119903119889 05119860119908119891119910

1205741198720)

103


119873119904119889 =5628kN

119873119901119897119903119889 le119860 119891

119910

1205741198720=5380 235

11= 114936 119896119873

025119873119901119897119903119889 = 28734 119896119873

119860119908 = 119860 minus 2119887 119905119891 = 2170 1198981198982

05119860119908119891119910

1205741198720= 23179119896119873

119873119904119889 = 5628119896119873 le 23179119896119873



119872119888119903119889 = 119872119901119897119910119903119889 =119908119901119897119910 119891119910

1205741198720=628000 times 235

11= 134163 119896119873119898




120594119898119894119899 119873119901119897119903119889+119896119910 119872119910119904119889

119872119901119897119910119903119889+119896119911 119872119911119904119889119872119901119897119911119903119889



120594119911 119873119901119897119903119889+119896119871119879 119872119910119904119889

120594119871119879119872119901119897119910119903119889+119896119911 119872119911119904119889119872119901119897119911119903119889



120594119898119894119899 = 119872119894119899(120594119910 120594119911)


120594119910 =1

(120601119910 +radic1206011199102 minus 1205821199102 )

120601119910 = 05[1 + 120572119910(120582119910 minus 02) + 1205821199102]

120582119910= (120582119910

1205821)radic120573119860 =

120582119910

1205821

104

Avec 120573119860 = 1 Classe 1

1205821 = 939

120582119910 =119871119910

119894119910= 960

125= 768

120582119910=768

939= 081


ℎ

119887=300

150= 05 lt 12 (119910 minus 119910)119894119898119901119897119894119902119906119890 120572 = 021

120601 = 05[1 + 120572119910(120582119910 minus 02) + 1205821199102 ] = 089

120594119910 =1

058 + radic058 minus 034= 079


120594119911 =1

(120601119911 +radic1206011199112 minus 1205821199112)

120601119911 = 05[1 + 120572119911(120582119911 minus 02) + 1205821199112]

120582119911 = (1205821199111205821)radic120573119860 =

1205821199111205821

Avec 120573119860 = 1 Classe 1

1205821 = 939

120582119911 =119868119911119894119911=125

335= 3731 120582119911 = 039


ℎ

119887= 1 lt 12 (119911 minus 119911) 119894119898119901119897119894119902119906119890 120572 = 021

120601 = 05[1 + 021(039 minus 02) + 0392] = 061

120594119911 =1

061 + radic061 minus 039= 092

120594119898119894119899 = 119872119894119899(120594119910 120594119911) = 079


105

λ119897119905 =

119871119894119911

119888105

[

1 +120(

119871119894119911ℎ119905119891

)

2

] 025 = 3433

IPE300 119905119891 = 107119898119898 119894119911 = 335119888119898 ℎ = 300119898119898

119870 = 1 1198881 = 1134 Tableau B11 CCM97


1205821 = 939휀

휀 = radic235

119891119910= 1

120582119871119879 = [1205821198971199051205821] [120573119908]

05

120582119897119905 = 3433

120582119871119879 =3433

939= 036 lt 04 119901119886119904 119889119890 119903119894119904119902119906119890 119889119890 119889119890119907119890119903119904119890119898119890119899119905


119873119904119889120594119898119894119899 119873119901119897119903119889

+119896119910 119872119910119904119889

119872119901119897119910119903119889+119896119911 119872119911119904119889119872119901119897119911119903119889


Avec

119873119904119889 =5628kN 119872119910119904119889=02kNm 119872119911119904119889=018kNm 119872119901119897119910119903119889=134163kNm

119872119901119897119911119903119889=267kNm 120594119898119894119899= 079 119873119901119897119903119889=1149kN 119896119910= 1 119896119911= 1

5628

079 1149+

02

134163+018



106

Chapitre-7


71 Introduction










au poteau

107




119872119904119889 = 28961119896119873119898 119873119904119889 = 17878119896119873 119881119904119889 = 8941119896119873




119905 = 119872119894119899(119905119891 119905119901119897119886119905119894119899119890) = 135119898119898

Avec





12119889O = 24 119898119898 le 1198901 le 12119905 =186 119898119898 ⟹ 1198901 = 110 119898119898

15119889O = 30 119898119898 le 1198902 le 12119905 = 186 119898119898 ⟹ 1198902 = 105 119898119898

22119889O = 44 119898119898 le 1199011 le 14119905 =217 119898119898 ⟹ 1199011 = 100 119898119898


108






IPE 400 119905f = 135 119898119898 119905w = 86 119898119898

119886min= 26 le twle119886max= 8

119886min =35 le tf le119886max= 8







sum119897 = 2119887 + 4(119887 minus 119905119908) = 2180 + 4(180 minus 86) = 1045119898119898

119865119908119903119889 =7times 1045 times 360

radic2= 1862119896119873

119873119904119889 =119872119904119889

ℎ=120784120790120791 120788120783

120782 120791= 120785120784120783 120789120790





Avec 120573119908 = 125 120574119872119882 = 08


109

i

sum119897 = 4ℎ119894 = 4 times 373 = 1492119898119898

119865119907119903119889 =7 times 1492 times 360

radic3= 217074119896119873



119873119894 =119872119904119889 119889119894sum119889119894

2


119909 = 119905119891radic119887

119905119908= 135radic

180

86= 6176



- 1198891 = 712 119898119898

- 1198892 = 612 119898119898

- 1198893 = 512 119898119898 ⟹ Σ 1198892 = 129 119898sup2

- 1198894 = 312 119898119898

- 1198895 = 212 119898119898

- 1198896 = 112 119898119898


1198731 =28961 times 0712

129= 15984119896119873



1198731 = 119899119865119907119903119889 ⟹ 119860119904 ge119873119904119889

06 times 119891119906119887 times 119899=

15984

06 times 800 times 2= 16651198981198982



M18 18 20 254 192 800 291



110




119865119901 = 07 times 119891119906119887 times 119860119904 = 06 x 800 x 192 = 10752kN

119872119903119889 =119899 119865119901 sum119889119894

2

119889119894=2 times 10752 times 129

0712= 3896 gt 119872119904119889 = 28961 119896119873119898




119865119907119904119889 le 119865119904119903119889 =119870119904 119898 120583

1205741198722(119865119901119888119889 minus 08119873119904119889) 119917119926119929119924119932119923119916 120788 120789 minus 119914119914119924120791120789

Avec

119870119904 = 10 ∶ Trous normaux



119865119904119903119889 = 024 (10752 minus 08 times15984

2) = 1046119896119873

119865119907119904119889 =8941

12= 745119896119873 lt 1046119896119873




1205741198722 119813119822119825119820119828119819119812 120788 120784 minus 119810119810119820120791120789



125= 213157 119896119873

119865119905119904119889 =119865119901

2=10752

2= 5376119896119873 lt 119861119901 119903119889 = 213157 119896119873


111



1205741198722 119827119808119809119819119812119808119828 120788 120787 120785 ndash 119810119810119820120791120789

Avec 119870119904 = 25

120572119887 = min (119890131198890

(119901131198890

minus 025) 119891119906119887119891119906 1) = 1



125= 46008119896119873 gt

11986511990711990411988912

= 745119896119873



119865119907 le 119865119905119903119889 = 119905119908119888 1198871198901198911198911198911199101205741198720

Avec




⟹ 119865119905119903119889 = 9 times 90times23511

= 173045 119896119873


119865119907 =119872119904119889

ℎ minus 119905119891=28961

029= 99865 gt 119865119905119903119889 = 173045119896119873




119873119904119889 le 119865119888119903119889 =119896119888 120588 119887119890119891119891 119905119908119888 119891119910

1205741198721radic1 + 13 (119887119890119891119891ℎ)2

119887119890119891119891 = 119905119891119887 + 2119886119901radic2 + 5(119905119891119888 + 119903119888) + 2119905119901

Avec

112






119887119890119891119891 =25014mm



120590119888119904119889 =119881119904119889119860+119872119904119889

119882119890119897119910=8941 times 103

1244+28961 times 106

1479= 196533119872119875119886

120590119888119904119889 = 19653119872119875119886 lt 119891119910 = 235119872119875119886 ⟹ 119896119888 = 1


119901 = 0932radic119887119890119891119891 119889119908119888 119891119910

119864 1199051199081198882= 0932radic


21 times 104 times 092= 254

119901 gt 072⟹ 120588 =119901 minus 02

1199012=254 minus 02

2542= 036


11 radic1 + 13 (250131

)2

= 12741119896119873

119873119904119889 = 1119873119894 =119872119904119889 sum119889119894sum119889119894

2 =29861 times 247

129= 57175119896119873





119865119907 le 119881119903119889 = 058119891119910 ℎ1199051199081205741198720


11= 3457119896119873


119865119907 =119872119904119889ℎ minus 119905119891

= 46216 119896119873 gt 119881119903119889 = 3457119896119873 119888119900119899119889119894119905119894119900119899 119899119900119899 119907eacute119903119894119891119894eacute119890


113

119865119907 = 46216119896119873 le 119881119903119889 = 058119891119910 ℎ119905119908 + 04

1205741198720= 058 235 31

(09 + 04)

11= 49935119896119873







logiciel robot

119872119904119889 = 15135119896119873119898 119873119904119889 = 1324119896119873 119881119904119889 = 273119896119873






119905 = min(119905119891 119905119901119897119886119905119894119899119890) = 135119898119898


114









IPE400

tf = 135 mm tw = 86 mm






radic2 times 119861119908 120574119898119908


Donc

119865119908119903119889 =119860 times sum119871 times 119891119906


radic2 times 1= 133083119896119873

119873119904119889 =119872119904119889ℎ

=7283

08= 9103119896119873

115

119873119904119889 = 9103 le 119865119908119903119889 = 1330119896119873






Donc

119865119907119903119889 =119886 times sum119871 times 119891119906


radic3 times 1= 155053119896119873



119873119894 =119872119904119889 119889119894sum119889119894

2


119909 = 119905119891radic119887

119905119908= 135radic

180

86= 6176119898119898


- 1198891 = 700 119898119898

- 1198892 = 600 119898119898

- 1198893 = 500 119898119898 ⟹ Σ1198891198942

= 124 119898sup2

- 1198894 = 300 119898119898

- 1198895 = 200 119898119898

- 1198896 = 100 119898119898


1198731 =119872119904119889 times 119889119894Σ119889119894

2 =15135 times 070

124= 4111119896119873



116


1198731 = 119899 119865119907 ⟹ 119860119904 ge119873119904119889

05 times 119891119906119887 times 119899=

13240

05 times 800 times 2= 16551198981198982



M18 18 20 254 192 800 291




119865119901 = 07 times 119891119906119887 times 119860119904 = 10752 119896119873

119872119903119889 =119899 119865119901sum119889119894

2

119889119894=2 times 10752 times 124

07= 38092 gt 119872119904119889 = 15135119896119873119898




119865119907119904119889 le 119865119904119903119889 =119870119904 119898 120583

1205741198722(119865119901119888119889 minus 08119873119904119889) 119813119822119825119820119828119819119812 120788120789 ndash 119810119810119820120791120789

Avec




119865119904119903119889 = 024 ( 10752 minus 08 times 1324) = 2326119896119873

119865119907119904119889 =273

12= 023 lt 119865119904 119903119889 = 2326119896119873




1205741198722 119813119822119825119820119828119819119812 120788 120784 ndash 119810119810119820120791120789

Avec


117


125= 31578119896119873

119865119905119904119889 =119865119901

2= 5376 lt 31578119896119873




1205741198722 119827119808119809119819119812119808119828 120788 120787 120785 ndash 119810119810119820120791120789

Avec Ks = 25

120572119887 = min (119890131198890

(119901131198890

minus 025) 119891119906119887119891119906 1) = 1


11986511990711990411988912


125= 5184 119896119873







119865119907119904119889 =119873119904119889

119899119887119903 119889119890 119887119900119906119897119900119899=131

3= 4366 le 119865119907119903119889

118


1205741198722⟹ 119860119904 ge

1205741198722 times 119865119907119903119889

06 times 119891119906119887119909 119898=125 times 43666

06 times 800 times 2= 56851198981198982


















119873119898119886119909 le 119865119908119903119889 =119886 sum119897 119891119906

119861119908 120574119898119908 radic(3 minus 1199041198941198991205722)


120572= 30gtgtgt 11990411989411989930o = 05

119865119908119903119889 =5 times 700 times 360



119



1205741198722 119827119808119809119819119812119808119828 120788 120787 120785 minus 119810119810119820120791120789


120572119907= 06



125= 12057119896119873

119865119907119904119889 =119873119904119889

3=3124

3= 10413 le 119865119907119903119889 = 12057119896119873




1205741198722 119827119808119809119819119812119808119828 120788 120787 120785 minus 119810119810119820120791120789

Avec

Ks = 25

120572119887 = min (119890131198890

(119901131198890

minus 025) 119891119906119887119891119906 1) = 092



125= 33914119896119873 gt 119865119907119904119889 = 4366119896119873




119873119898119886119909 le 119881119890119891119891119903119889 =119860119899119905 119891119910

1205741198722+119860119899119907 119891119910

radic3 1205741198722 119812119810120785 119849119834119851119853119842119838120783 minus 120790sect120785120783120782 120784

Avec


119860119899119890119905 = (119897

2minus11988902) 119905 = (60 minus 9)12 = 6121198981198982


120

119860119899119907 = (1198901 + 21199011 minus 251198890)119905 = (50 + 140 minus 45)12 = 17401198981198982

⟹ 119881119890119891119891119903119889 =612 times 235

125+1740 times 235

radic3 times 125= 303918119896119873 gt

119873119904119889

2= 655119896119873








119865119907119904119889 =119877119907119911

119899119887119900119906119897119900119899119904=36

2= 18 119896119873

119865119907119903119889 =06 times 119860119904 times 119891119906119887

120574119872119887⟹119860119904 ge

120574119872119887 times 11986511990711990311988906 times 119891119906119887

=11 times 18000

06 times 800= 41251198981198982



119865119907119903119889 =06 times 119860119904 times 119891119906119887

120574119872119887=06 times 58 times 800

11= 253119896119873 gt 119865119907119904119889 = 18119896119873


119865119905119903119889 =09 times 119860119904 times 119891119906119887

120574119872119887=09 times 58 times 800

11= 379119896119873

121

119865119907119903119889 =06 times 119860119904 times 119891119906119887

120574119872119887= 253119896119873

119865119907119904119889119865119907119903119889

+119865119905119904119889

14 119865119905119903119889= 052 lt 1 119862119900119899119889119894119905119894119900119899 119907119890119903119894119891119894eacute119890


122

Chapitre-8




123








119865119888119896=30 MPa

119891119888119889 =085 times 119865119888119896125

= 204 MPa


119865119895119889 = 120572120573119895 119891119888119889



119865119895119889 = 120572 120573119895 119891119888119889 = 15 times2

3times 17 = 204 119872119875119886


1198601198620 ge119873119904119889119891119888119889

=148960

204

1198601198620 ge 7266341198981198982


bp ge b+2tf = 190+2times155 = 221 mm

hp ge h+2tf = 310+2times155 = 341 mm

On prend

bp =600 hp=620



124


119862 = 119905 (119891119910119901

3119891119895119889 1205741198720)

05

= 30(235


= 5605 119898119898

119862 = 5605 lt(ℎ minus 2119905119891)

2= 1395 119898119898




gorge (a) Annexe H







119890 =119872119904119889119873119904119889

= 041 119898 gt 119885119879 = 0195 119898







125


Ougrave

119871119890119891119891 = min(119887119901 119887119891119888 + 2119888) = min(600 300 + 2 times 4671) = 39342 119898119898

119887119890119891119891 = min (119888ℎ1198882minus 119905119891119888) + 119905119891119888 +min (119888

ℎ119901 minus ℎ119888

2)

119887119890119891119891 = min (4671310

2minus 155) + 155 + min (4671

620 minus 310

2) = 10892 119898119898

⟹ 119865119888119903119889 = 204 times 10892 times 39342 = 874166 119896119873


119865119907119903119889 = 119865119891119903119889 + 119899119887 119865119907119887119903119889


119865119891119903119889 = 02119873119904119889 = 1214 119896119873





119865119907119887119903119889 =120572119888119887 119891119906119887 119860119904

1205741198722

Avec 120572119888119887 = 044 minus 00003119891119910119887 = 0248


126

119865119907119887119903119889 =0248 times 800 times 561

125= 8904 119896119873

⟹ 119865119907119903119889 = 1214 + 8 times 8904 119896119873 = 72446 119896119873




Avec 120573119908 =08 120574119898119908 = 125 119886 = 6 mm


sum119897 = 470 119898119898

119865119908119903119889 =6 times 470 times 360

radic3= 58612 119896119873

119881119904119889 = 9773 119896119873 lt min(119865119907119903119889 119865119908119903119889) = 58612 119896119873





W= 150 mm e = 55 mm ex = 40 mm mx = 40 mm


119897119890119891119891119888119901 = 119898119894119899 2120587119898119909 = 25132 119898119898

120587119898119909 +119882 = 27566 119898119898120587119898119909 + 2119890 = 23566 119898119898

⟹ 119897119890119891119891119888119901 = 23566 119898119898

127


119897119890119891119891119899119888 = 119898119894119899

4119898119909 + 125119890119909 = 210 119898119898

2119898119909 + 0625119890119909 +119882

2= 180 119898119898

2119898119909 + 0625119890119909 + 119890 = 160 119898119898119887119901

2= 150 119898119898

⟹ 119897119890119891119891119899119888 = 150 119898119898


119865119905119886119899119888119903119889 = min[119865119905119887119900119899119889119903119889 119865119905119903119889]


119865119905119903119889 = 09 times119860119904 times 119891119906119887120574119898119887


125= 32314 119896119873



119865119887119889 =036radic119891119888119896

120574119888=036 times 547

15= 1313 119872119875119886


119865119905119887119900119899119889119903119889 =120587 119889 119897119887 119891119887119889

120572

Avec

1198971 = 20119889 = 600 119898119898

119903 = 3119889 = 90 119898119898

1198972 = 20119889 = 600 119898119898






07= 52929 119896119873

119865119905119886119899119888119903119889 = 119898119894119899[52929 32314] = 32314 kN

128




Lb = 8d + em +tp + twa + 05k

Avec







119871119887lowast =

881198981199093 119860119904

1198971198901198911198911 1199051199013 =


150 times 253= 13480 119898119898 lt 119871119887 = 312 119898119898




119898119901119897119903119889 =1199051199012 119891119910119901

41205741198720=252 times 235

4 times 11= 3338119896119873


Mode 1 1198721199011198971119903119889 = 119898119901119897119903119889 times 1198971198901198911198911 = 3338 times 015 = 5007119896119873119898

1198971198901198911198911 = min(119897119890119891119891119888119901 119897119890119891119891119899119888) = 150 119898119898


129




Mode 1-2

1198651199051minus2119903119889 =21198721199011198971119903119889

119898119909=2 times 5

004= 250 119896119873

Mode 3

1198651199053119903119889 = 2119865119905119903119889119886119899119888ℎ119900119903 = 2 times 32314 = 646280 119896119873

Mode 4

1198651199054119903119889 =119887119890119891119891119905 119905119908 119891119910

1205741198720=150 times 9 times 235

11= 288409119896119873

Drsquoougrave

119865119905119903119889 = min(1198651199051minus2119903119889 1198651199053119903119889 1198651199054119903119889) = 250 119896119873




119885119879119890119873minus 1

119865119879119903119889 times 119885

119885119862119890119873+ 1

) 119812119810120785 ndash 120783 120790 119827119808119809119819119812119808119828 120788 120789

119885 = 119885119879+119885119862 = 195 + 155 = 350119898119898

⟹119872119903119889 = 5646 119896119873119898 lt 6207119896119873119898



821 Introduction




- Le site (S3)



130




ELU 119872119880 = 6207119896119873119898 119873119880 = 9773119896119873

ELS 119872119878 = 4136119896119873119898 119873119878 = 7960119896119873




119886 = 119886119901 + 119888 = 062 + 02 = 082 119898


119860

119861=119886

119887= 1025 ⟹ 119860 = 1025119861



119890 =119872119904

119873119904= 052119898



120590119898119886119909 =119873

119860119861(1 +

6119890

119861) le 120590119904119900119897


368B2 - B - 312 ge 0 ⟹ B ge0765m



131

119889 = max (119861 minus 119887

4119860 minus 119886

4) = max (005 0295)

On prend d= 45 cm



On a

119890 = 052 gt119860

6= 041


3120590119898119886119909 1205901198981198941198994

lt 120590119904119900119897

Avec

120590119898119894119899 =119873

119860119861(1 minus

6119890

119860) =

14896

2(1 minus

041

2 ) = 62191198961198731198982

120590119898119894119899 =119873

119860119861(1 +

6119890

119860) =

14896

2(1 +

041

2 ) = 86771198961198731198982

3120590119898119886119909 120590119898119894119899

4= 6835 1198961198731198982 lt 120590119904119900119897 = 180 119896119873119898

2



119890 =119872

119873= 052 119898 lt

119860

4= 062 119898




119890 gt119886

6 119890 gt

119860

24


119860119886 =1198721119911 119904119905

132

1198721 = (119860

2minus 035119886)

2

(1 +119890

119860+14 times 119890 times 119886

1198602)1198731199042119860

1198721 = 2788119896119873119898

Avec 119911 = 09d =40cm

119904119905 = min (2

3119891119890 110radic12057811989111990528) =20163 MPa

11989111990528 = 00611989111988828 + 06 = 24 119872119875119886 120578 = 16 119867 119860 Donc

119860119886 =2788 times 106

400 times 20163= 345 1198881198982


119860119887 =119873prime(119861 minus 119887)

8119889 119904119905

Avec

119873prime = 119873119904 (1 +3119890

119860) = 796 (1 +

3 times 052

25) = 2993119896119873

119904119905 = min (2

3119891119890 110radic12057811989111990528) = 20163119872119875119886

11989111990528 = 00611989111988828 + 06 = 24119896119873 120578 = 16 119867 119860

Donc 119860119887 = 071198881198982


119860119886 =1198721119911 120590119904119905

1198721 = (119860

2minus 035119886)

2

(1 +119890

119860+14 times 119890 times 119886

1198602)1198731199062119860

1198721 = 349119896119873119898

Avec 119911 =09d = 40 cm

120590119904119905 =119891119890120574119904=400

115= 3478119872119875119886

Donc

133

119860119886 =349 times 106

400 times 3478= 251198881198982


119860119886 =119873119906(119861 minus 119887)

8119889 120590119904119905

Avec

119873prime = 119873119906 (1 +3119890

119860) = 23833119896119873

Donc 119860119887 = 1621198881198982


119860119898119894119899 = 023 times11989111990528119891119890

times 119860 times ℎ119905 = 17251198881198982

Sens B

119860119898119894119899 = 023 times11989111990528119891119890

times 119861 times ℎ119905 = 691198881198982



A (cm2) St (cm)

A 345 1725 10T16 201 25 B 07 69 7T16 1407 25



134



119873119905 = (119873

120572) ge 20 119896119873 [119825119823119808120791120791 119855 120784120782120782120785 119808119851119853 120783120782 120783 120783 119835]


119873119905 =14896

12= 1241119896119873

ELS

119873119905 =796

12= 663119896119873


119860119904119905 =119873119905120590119904119905

ELS

119860119904119905 =663

348= 0191198881198982

ELU

119860119904119905 =1241

348= 0351198881198982





119860119904119905 = 0905 le 119860119904 = 6791198881198982


135


120601119898119894119899 le 119898119894119899 (ℎ

35120601119897119898119894119899

119887

10) = 08 119888119898

On prend 120601119905 =8mm


On prend St=10cm


136


137

ANNEXE - 1

138

139

140

ANNEXE - 2

141

ANNEXE - 3

142

143

ANNEXE ndash 4

144

145

ANNEXE ndash 5

Deacutedicace














Reacutesumeacute


ملخص







Abstract































































































































Liste des tableaux

















LISTE DES NOTATIONS

Majuscules latines








16

Chapitre-1


11 Introduction


17



18

Action

permanente (γG)




Effet favorable

γGinf

10 1 0


γGsup

135 15 15




135119866119896119895 + 15119876119896119898119886119909





1 119866119896119895 + 150119882minus


sum119866119896119895119895

+ 119876119896119898119886119909

119866119896119895 + 119876119896119898119886119909


sum119866119896119895119895

+ 09sum119876119896119894119894gt1

119866119896119895 + 09119876119896119898119886119909 + 09119878 119866119896119895 + 09119876119896119898119886119909 + 09119882


19










20




21






22




23

Chapitre-2


21 Introduction










24

- Effet du site








Ouargla (Zone 4)




Kt=017 Z0=001m Zmin=1m ξ=044






Avec




119902119901(119885) = 119902119903119890119891 times 119862119890

Avec

- 119902ref = 575 119889119886119873119898sup2


2(119885) times [1 + 7119868119907] 119825119821119829120784120782120783120785 119836119841119834119849119842119853119851119838 120784 120786 sect120784 120786 120784 119834


25


119862119903(119911)

119870119905 119871119899 (1199111198981198941198991199110

) 119901119900119906119903 119911 lt 119911119898119894119899

119870119905 119871119899 (119911

1199110) 119901119900119906119903 119911119898119894119899 le 119911 le 200119898


)=0783


Zo)=1178

On retient 119862119903= 1178


119868119907(119911)

1

119862119905(119911) 119871119899 (119911

1199110) 119901119900119906119903 119911 gt 119911119898119894119899

1

119862119905(119911) 119871119899 (1199111198981198941198991199110) 119901119900119906119903 119911 le 119911119898119894119899

Pour z gt zmin 119868119907(119911) =1

1Ln(1

001)= 0217

Pour z lt zmin 119868119907(119911) =1

1Ln(1025

001)= 0144



119862119890(119911119895) = 119862119903(119911119895)2[1 + 7 119868119881]

Pour z gt zmin

119862119890(119911) = 11782 times 12 times [1 + 7(0144)] = 2786

Pour z lt zmin

119862119890(119911) = 07832 times 12 times [1 + 7(0217)] = 154


Avec

26

- 119902119903119890119891 = 575 119889119886119873119898sup2



qp = 160195Nm2 = 16 kNm2





- b=30 m

- d=36 m

- h=89 m


e = min (d 2h)


Donc e = 2x1025 = 205m



27



119862119901119890 = 1198621199011198901 119878119894 119878 le 11198982

119862119901119890 = 1198621199011198901 + (11986211990111989010 minus 1198621199011198901) times 11989711990011989210(119878) 119878119894 11198982 lt 119878 lt 101198982

119862119901119890 = 11986211990111989010 119878119894 119878 ge 101198982



Zone


Parois sous le vent


Cpe10 -10 -08 -05 +08 -03


Versant de Toiture




28







le tableau suivant


853deg F G H

-237 -123 -083



- Parois verticales


-b=36 m

29

-d=30 m

-h=1025


e=Min (b 2h) = Min (36 205) = 205 m





30

Zone


Parois sous le vent








31




853deg -22 -192 -183 -067 -057






2(5 times 4)

30 times 89= 014 = 14


μ119901 =120

160= 075



Pour μ119901=075 on lit 119862119901119894 =-016

32




2 times (5 times 4)

36 times 9575= 0116 = 116


Pour μ119901=075 rarr 119862119901119894 =-02

33





Direction V1 V3


A 1602 -10 -0154 -0846 -135529

B 1602 -08 -0154 -0646 -103489

C 1602 -05 -0154 -0346 -55429

D 1602 +08 -0154 +0954 +152831

E 1602 -03 -0154 -0146 -23389


34

Toiture


F 1602 -237 -0154 -2276 -355003

G 1602 -123 -0154 -1076 -172375

H 1602 -084 -0154 -0676 -108295

Z1 1602 -1 -0154 -0846 -135529

Z2 1602 -06 -0154 -0446 -71449


Direction V2 et V4

Parois verticales


A 1602 -10 -0162 -0838 -134247

B 1602 -08 -0162 -0638 -102207

C 1602 -05 -0162 -0338 -54147

D 1602 +08 -0162 +0962 +154112

E 1602 -03 -0162 -0138 -22107


35

Toiture


Finf 1602 -12 -0162 -1038 -1662876

Fsup 1602 -22 -0162 -2038 -3264876

G 1602 -183 -0162 -1668 -2672136

H 1602 -067 -0162 -0508 -813816

I 1602 -057 -0162 -0408 -653616









9= 015




q1= 300 Nml

q2= 500 Nml



36











- Epaisseur 50 mm

- Largeur 1000 mm





Selon le DTR BC22




37

119902 =8119875

3119871= 044 119896119873119898

119902 = 444 119889119886119873119898













38

Chapitre-3





deacutefavorable

39

(minus354 times5125


0875

6) = minus32754 1198891198861198731198982

Qeq (vent) = 3276 daN1198982















40



41


Vzsd =119902119906119911 times 119897

2=1878 kN

Mysd=119902119906119911 times 119897

2

8=2817 kNm

Mzsd=119902119906119910 times 119897

2

8=081 kNm



IPE 180 A Cm2

h mm

b mm

119905f

mm 119905w

mm 119868y

Cm4

119868z

Cm4

119908ply cm3

119908plz cm3

MATERIAU ACIER S235

239 180 91 8 53 1317 101 146 346




4

384 times 119864 119868119910lt

119897

200=



119897

200= 3 119862119900119899119889119894119905119894119900119899 119907eacute119903119894119891119894eacute119890

Plan z-z

5 times 119902119904119910 times 1198974

384 times 119864 119868119911lt

119897

200=



119897

200= 3 119862119900119899119889119894119905119894119900119899 119907eacute119903119894119891119894eacute119890

42




1205741198721 gt 119872119910119904119889 = 2817 119896119873119898

Calcul de 119872119887119903119889




λ119871119879 =

119871119894119911

119888105

[

1 +120(

119871119894119911ℎ119905119891

)

2

] 025

Avec


(Tableau B12 CCM97)

iz =224mm tf =85mm

L=Lz=3000mm h=200mm

λ119871119879 =

119871119894119911

119888105

[

1 +120(

119871119894119911ℎ119905119891

)

2

] 025 = 9457 rarr λ119871119879 =

989

939= 1007

rarr =1092

43


rarr ꭕ119871119879=

1


2)= 066 le 1

rarr 119872119887119903119889 =ꭕ119871119879times 120573

119908times 119882119901119897119910 times 119891119910

1205741198721

=066 1 166 235

11= 234 119896119873 119898








119872119872119860119883 =119901prime 119897

3=119901 1198972

8⟹ 119901 =

8 119901prime

3119897=800

18= 4444 119889119886119873119898119897

44


(ANNEXE ndash 1)

Soit

119876119890119902 =327 + 1082

2= 2176 1198891198861198731198982









45



Vzsd =119902119906119911 times 119897

2=186 kN

Mysd=119902119906119911 times 119897

2

8=279 kNm

Mzsd=119902119906119910 times 119897

2

8=0855 kNm

46



IPE 200 A Cm2

h mm

b mm

119905f

mm 119905w

mm 119868y

Cm4

119868z

Cm4

119908ply cm3

119908plz cm3

MATERIAU ACIER S235

285 200 100 85 56 1943 142 221 446




4

384 times 119864 119868119910lt

119897

200=



119897

200= 3 119862119900119899119889119894119905119894119900119899 119907eacute119903119894119891119894eacute119890

Plan z-z

5 times 119902119904119910 times 1198974

384 times 119864 119868119911lt

119897

200=



119897

200= 3 119862119900119899119889119894119905119894119900119899 119907eacute119903119894119891119894eacute119890




1205741198721 gt 119872119910119904119889 = 279 119896119873119898

Calcul de 119872119887119903119889

47




λ119871119879 =

119871119894119911

119888105

[

1 +120(

119871119894119911ℎ119905119891

)

2

] 025

Avec


(Tableau B12 CCM97)


-L=Lz=6000mm -h=200mm

λ119871119879 =

119871119894119911

119888105

[

1 +120(

119871119894119911ℎ119905119891

)

2

] 025 = 989 ⟶ λ119871119879 =

989

939= 105

rarr =114


rarr ꭕ119897119905=

1


2)= 063 le 1

rarr 119872119887119903119889 =ꭕ119897119905times 120573

119908times 119882119901119897119910 times 119891119910

1205741198721


11= 2974119896119873119898



48


Avec

119881119901119897119911119903119889 =

119860119907119911 (119891119910

radic3)

11 119890119905 119860119907119911 = 1400 1198981198982

Donc

05119881119901119897119911119903119889 = 05

1400 (235

radic3)

11= 8634 119896119873



Si 119889


CCM97 art 561(1)

119889

119905119908 =

159





(119872119910119904119889

119872119901119897119910119903119889)

120572

+ (119872119911119904119889119872119901119897119911119903119889

)

120573

le 1 119912119955119957 120787 120786 120790 (120783120783)119914119914119924 120791120789


119872119901119897119910119903119889 =119882119901119897119910 times 119891119910

11=221 times 235

11= 4721 119896119873119898

119872119901119897119911119903119889 =119882119901119897119911 times 119891119910

11=446 times 235

11= 952 119896119873119898

119872119910119904119889 = 279 119896119873119898

119872119911119904119889 = 0855 119896119873119898

(279

4721)2

+ (0855

952) = 044 lt 1 119888119900119899119889119894119905119894119900119899 119907eacute119903119894119891119894eacute119890

49











Effort rampant


Lrsquoexcentrement


2 (119887

2) le 119905 le 3(

119887

2)


50

2 (10

2) = 10 le 119905 le 3(

10

2) = 15

On prend t=10 cm


119877119911 = 119902119906119911 times119897

2= 6 times

6

2= 18 119896119873

119877119910 = 119902119906119910 times119897

2= 054 119896119873


119877119911 = 18 times 2 = 36 119896119873

119877119910 = 054 times 2 = 108 119896119873


119872119877 = 119877119911 times 119905 + 119877119910 timesℎ

2= 36 times 10 + 108 times 10 = 3708 119896119873 119888119898 = 37119896119873119898


119872119890119897119877119889 =119908119890119897 times 119891119910

1205741198720 119912119955119957 120787 120786 120787 120783 (120784)119914119914119924120791120789

119872119890119897119877119889 =119908119890119897 times 1198911199101205741198720

=gt 119908119890119897 ge119872119890119897119877119889 times 1205741198720

119891119910=gt 119908119890119897 ge

00037 times 11

235

= 173 times 10minus51198983

119908119890119897 = 17321198881198983




119908119890119897 =119887 1198902


6 times 1732

119887= radic

6 times 1732

180

119890 ge 076


Donc on prend e=1cm

51





















52












qsy =(133 + 5) times 125=2288daNml

qsy = 0228 kN

quy=135G=03kN



W += 1541 daN m2


quz=15W

quz=288kN

53



qsz=19262daN=192kN


119891119911 =5 times 119902119904119911 times 119897

4

384 times 119864119910 times 119868le 119891119886119889119873 =

119897

200=600

200= 3 119888119898

119868119910 ge5 times 192 times 6004



Profileacute


UPN 140 A Cm2

h mm

b mm

119905f mm

119905w mm

Iy

Cm4

Iz

Cm4

119908pSy

cm3

119908pSz

cm3

MATERIAU ACIER S235

20 140 60 10 7 605 627 103 283







qsy =(133 + 5) times 125 +1568 = 3856daNml

qsy = 038 kN

quy=135G

quy =053kN


qsz=192kN

quz=15W

quz=288kN

54




119888

119905119891=60

10= 6 lt 10휀 =gt 119888119897119886119904119904119890 1


119889

119905119908=98

7= 14 lt 72휀 =gt 119888119897119886119904119904119890 1


(119872119910119904119889

119872119890119897119910119877119889)

1

+ (119872119911119904119889

119872119890119897119911119877119889)1

le 1


119872119910 =119902119906119911 times 119897

2

8=288 times 62

8= 1296 119896119873119898


119872119911 =119902119906119910 times 119897

2

8=058 times 62

8= 261119896119873119898

119872119890119897119910119877119889 =119908119890119897119910 times 119891119910

1205741198720=864 times 103 times 235

11= 1845 119896119873119898

119872119890119897119911119877119889 =119908119890119897119911 times 119891119910

1205741198720=148 times 103 times 235

11= 316 119896119873119898

Donc

(1296

1845)1+ (

261



55

Nouveau 119872119911

119872119911 =119902119906119910 times 119897

2

8=058 times 32

8= 065119896119873119898

(1296

1845)1+ (

065




119881119911119904119889 =15119882119871

2= 1296 119896119873

119881119901119897119877119889 =119860119907119911 times 119891119910

radic3times 1205741198720= 12855 119896119873





1205741198721gt 119872119910119904119889 119912119955119957 120787 120787 120784 (120787 120786120790)119914119914119924120791120789

Avec

119872119888119903 = 11986211205872 119864 1198681199111198712

radic119868119908119868119911+1198712 119866 1198681199051205872 119864 119868119911

119912119925119925119916119935119916 119913 (119913 120783 120785) minus 119914119914119924120791120789

119872119888119903=311713762 Ncm


119872119888119903


119882119901119897119910 (upn140) =103 cm3

56

λ119897119905 = 0881


2 ]


empty119897119905 = 0959

ꭕ119897119905=

1


2 )

le 1

ꭕ119897119905= 075

119872119887119903119889 = 1652 119896119873119898

119872119887119903119889 = 1652 119896119873119898 gt 119872119910119904119889 = 1296 119896119873119898 119862119900119899119889119894119905119894119900119899 119907eacute119903119894119891119894eacute119890







57

119877 = 125119902119910 times 119897

2

Avec 119902119910 = [135(119866119880119875119873140 + 119866119888119900119906119907119890119903119905119906119903119890)]

119902119910 = 0837119896119873

119897 = 6 119898

119877 = 125119902119910 times 119897

2= 125 times 0837 times 3 = 32119896119873


1198791 =119877

2= 16119896119873

1198792 = 1198791 + 119877=48 kN

1198793 =1198792

2 sin 120579= 374 119896119873 119860119907119890119888 120579 = 119886119903119888 119905119892

25 119898

3 119898= 398deg



119873119905119904119889 =119860 times 119891119910

1205741198720= 4800 119873 =gt 119860 ge

11 times 4800

235 =gt 119860 ge 22461198981198982

119860 =120587empty2

4=gt empty ge radic

4119860

120587= radic

4 times 2246

314= 534 119898119898



Introduction



58



119878ge

63

radic119904

119889times119875

Avec








Srsquo=273

4=6825 m2








59



















96=8989 daNm2





60

119891119910 =5 times119882 times 1198974

384 times 119864 times 119868119910le 119891119886119889119898 =

119897

200


384 times E= 59136 1198881198984


Profileacute


IPE300 A Cm2

h mm

b mm

tf mm

tw

mm 119868y

Cm4

119868z Cm4

Wply

cm3

Wplz

cm3

MATERIAU ACIER S235

538 300 150 107 71 8356 746 628 125





119888

119905119891=

75

107= 7 lt 10 = 10 119878119890119898119890119897119897119890 119889119890 119888119897119886119904119904119890 1


119889

119905119908=2486

71= 35 lt 38 = 38 Acirc119898119890 119889119890 119888119897119886119904119904119890 1



Si 119881119904119889 le 05 119881119901119897119903119889 ⟹119872119904119889 le 119872119888119903119889 119912119955119957120787 120786 120789 119914119914119924 120791120789

61

119881119904119889 =15 times119882 times 119897


2= 388 119896119873 lt 05 119881119901119897119903119889 = 05 (

2570 times 235

radic3 times 11) = 1585 119896119873





Si

119873119904119889 le 119872119894119899 (025119873119901119897119903119889 05119860119908 119891119910

1205741198980)


025119873119901119897119903119889 = 025119860 times 119891119910

1205741198720= 025

5380 times 235

11= 28734 119896119873

05119860119908 times 119891119910

1205741198720= 05

2170 times 235

11= 2317 119896119873

119873119904119889 = 135119866 = 1337 119896119873 lt 119898119894119899 (025119873119901119897119903119889 05119860119908 times 119891119910

1205741198720)





119872119910119904119889 =15119882 times 1198972

8= 9313119896119873119898 119872119911119904119889 = 0 119872119901119897119910119903119889 = 13416 119896119873119898

λ119897119905 =

119871119911119894119911

119888105

[

1 +120(

119871119911119894119911ℎ119905119891

)

2

] 025


62

119871119911 = 1250 119898119898 119894119911 = 335 119898119898 ℎ = 300 119898119898 119905119891 = 107 119898119898




119873119904119889ꭕ119898119894119899

119873119901119897119903119889+119870119910 119872119910119904119889

119872119901119897119910119903119889+119870119911 119872119911119904119889119872119901119897119911119903119889


Avec

λ119910 =119871119910

119894119910=960

125= 768 rarr λ119910 =

768

939= 081

=gt 120583119910 = λ119910(2119861119898119910 minus 4) +119882119901119897119910 minus119882119890119897119910

119882119890119897119910= minus1134 + 0127 = minus1007 lt 09

120572 = 021 λ119910 = 081

empty119910 = 05 [1 + 120572119910(λ119910 minus 02) + λ1199102]

empty119910 = 05[1 + 021(081 minus 02) + 0812] = 089

ꭕ119910=

1


ꭕ119910= 0794 rarr 119870119910 = 1 minus


0794 times 538 times 2350= 101

120582119911 =125

335= 3731 =gt 120582119911 = 0397 rarr empty119911 = 0611 =gt ꭕ

119911= 092

ꭕ119898119894119899

= ꭕ119910= 0794

119873119901119897119903119889 =119860119891119910

1205741198980=5380 times 235

11= 114936 119896119873

119872119910119904119889 =151198821198712

8= 9313 119896119873119898

119872119901119897119910119903119889 = 13416 119896119873119898

119873119904119889 = 135119866 = 1337 119896119873

119896119910 = 101

119872119911119904119889 = 0

63

119873119904119889120594119898119894119899 119873119901119897119903119889

+119896119910 119872119910119904119889

119872119901119897119910119903119889+119896119911 119872119911119904119889119872119901119897119911119903119889

le 10

1337

0794 times 114836+101 times 9313

13416= 071 lt 1 119862119900119899119889119894119905119894119900119899 119907eacute119903119894119891119894eacute119890




64

Chapitre 4


41 Introduction




- Le pont roulant










poteaux de la halle

65





Puissances

N (t)

Porteacutee

L(m)



B

Chariot

K

Total

B+K

Rmax Rmin

125 18 085 520 1040 6809 1151 796 814 194


66


1 035 06 2 36



I 02 11 11 A-2















Groupes II






67
















119877119898119886119909 = 814 119870119873 119877119898119894119899 = 194 119870119873

Charges verticales

119877119881119898119886119909 = Ψ1 119877119898119886119909 = 115 times 814 = 8954 119870119873

119877119881119898119894119899 = Ψ2 119877119898119894119899 = 11 times 194 = 2134 119870119873


68

119877119871119898119886119909 = 119862 119877119898119886119909 = 02 times 814 = 1628 119870119873

119877119871119898119894119899 = 119862 119877119898119894119899 = 02 times 194 = 388 119870119873



1198771198671119898119886119909 = plusmn [0024(119870 + 119873 + 119861)119871

119890+ 0021(119873 + 119870)]

= plusmn [0024(1151 + 125 + 6809)18

36+ 0021(125 + 1151)]

1198771198671119898119886119909 = plusmn274 119905

1198771198671119898119894119899 = plusmn [0024(119870 + 119873 + 119861)119871

119890minus 0021(119873 + 119870)]

= plusmn [0024(1151 + 125 + 6809)18

36minus 0021(125 + 1151)]

1198771198671119898119894119899 = plusmn2168 119905


1198771198672119898119886119909 = plusmn [00052(119870 + 119873 + 5119861)119871

119890+ 0021(119873 + 119870)]

= plusmn [00052(1151 + 125 + 5 times 6809)18

36+ 0021(125 + 1151)]

1198771198672119898119886119909 = plusmn1526 119905

1198771198672119898119894119899 = plusmn [00052(119870 + 119873 + 5119861)119871

119890minus 0021(119873 + 119870)]

= plusmn [00052(1151 + 125 + 5 times 6809)18

36minus 0021(125 + 1151)]

1198771198672119898119894119899 = plusmn0953 119905




69





Rail

Poids

(Kgm)

B

(mm)

H

(mm)

P

(mm)

Section

A (cm2)

I x

(cm4)

I y

(cm4)

A55

318

55

65

150

407

178

337



70



119891119911 le 119891119886119889119898 =119897

750= 08 119888119898



119886 = (119897

2minus119890

4) = (

6

2minus36

4) = 21 119898



119891119911 =119901 119886 1198972

24119864119868(3 minus

4 1198862

1198972)

Avec

L= 6000 mm

a= 2100 mm

P=89540 N

E=21104 Nmm2

71

119868119910 ge119901 119886 1198972(31198972 minus 41198862)



119868119910 ge 421397625 1198981198984






119902 = 119866119901119900119906119905119903119890 + 119866119903119886119894119897 = 142 + 031 = 173 119896119899119898119897

119891119911 =119901 119886 1198972

24119864119868(3 minus

4 1198862

1198972) +

5 119902 1198974

384119864119868

119891119911 =89540 times 2100 times 60002


4 times 21002

60002) +




profileacute


G

Kgm

A cm2 h

mm

b

mm

tf

mm

tw

mm

Iy

cm4

Iz

cm4

Wply

cm3

Wplz

cm 3

HEB360 142 1806 360 300 225 125 43190 10140 2683 1032

72


119902 = 119866119901119900119906119905119903119890 + 119866119903119886119894119897 = 155 + 031 = 186 119870119873119898119897

119891119911 =119901 119886 1198972

24119864119868(3 minus

4 1198862

1198972) +

5 119902 1198974

384119864119868

119891119911 =89540 times 2100 times 60002


4 times 21002

60002) +






119905119908le 72휀

Avec

휀 = radic235

119891119910

298

135le 72radic

235

235 ⟹ 2207 le 72


119888

119905119891=1198872

119905119891le 10휀 ⟹

150

24= 625 le 10




profileacute


G

Kgm

A

cm2

h

mm

b

mm

tf

mm

tw

mm

Iy

cm4

Iz

cm4

Wply

cm3

Wplz

cm 3

HEB400 155 1978 400 300 24 135 57680 10820 3232 1104

73

119881119910119904119889 le 119881119901119897119903119889 119912119955119957 120787 120786 120788 (120787 120784120782)119914119914119924120791120789

119881119901119897119903119889 =119860119907119911 119891119910

radic3 1205741198980=6998 times 235

radic3 times 11= 863154 119873 = 86315 119870119873


119881119881 = 119877119881119898119886119909 times4119886

119897=8954 times 4 times 21

6= 12535 119870119873


119881119875119875 =119866 119897

2=186 times 6

2= 558 119870119873

Drsquoougrave 119881119910119904119889 = 135119881119875119875 + 15119881119881 = 19556 119870119873

119881119910119904119889 le 119881119901119897119903119889



Suivant (z-z)


119872119881 = 119877119881119898119886119909 times(6 minus

1198902)2

4119897= 8954 times

(6 minus362 )

2

4 times 6= 6581 119870119873119898


119872119875119875 =119866 1198972

8= 837 119870119873119898


119872119910119904119889 = 135119872119875119875 + 15119872119881 = 110 119870119873119898



119872119911119904119889 = 119872119867 =21198771198671119871

(119871

2minus119890

4)2

74

119872119911119904119889 = 119872119867 =2 times 274

6times (

6

2minus36

4)2

= 4028 119870119873119898




119873119904119889119873119901119897119903119889

+119872119910119904119889

119872119890119897119910+119872119911119904119889119872119890119897119911

le 1 120787 120785120790 ndash 119810119810119820120791120789

119873119904119889 = 15119877119871119898119886119909 = 15 times 1628 = 2442 119870119873

119872119890119897119910 =119908119890119897119910 119891119910

1205741198720= 61613 119872119890119897119911 =

119908119890119897119911 119891119910

1205741198720= 1541 119873119901119897119903119889 =

119860 119891119910

1205741198720= 422573

2442

422573+

110

61613+4028

1541= 044 le 1



Si 119889


Avec

휀 = radic235

119891119910= 1

119889

119905119908=298

135= 2207 lt 69





1205741198721


75



λ119897119905 =

119871119894119911

119888105

[

1 +120(

119871119894119911ℎ119905119891

)

2

] 025 = 6522 119808119821119821119812119831119812119809 119810119810119820120791120789

Avec 119871 = 600119888119898


λ119871119879 = [λ119897119905λ1] [120573119908]

05 휀 = radic235

119891119910= 1

λ119871119879 =6522

939= 0694

On calcule

ꭕ119871119879=

1


2 )le 1




ꭕ119871119879=

1

(079 + radic0792 minus 06942)= 0856


11= 59104 119870119873119898

119872119910119904119889 = 110 119870119873119898




76



119891119904119889 le 119877119910119877119889

Avec




120590119891119864119889 =119872119910119904119889

119882119890119897119910= 381 1198701198731198881198982

119878119910 = 2(ℎ119877 + 119905119891)radic[1 minus (1205741198720120590119891119864119889

119891119910119891)

2

] = 1751 119888119898

119877119910119877119889 =119878119910 times 119905119908 times 119891119910119908

1205741198720= 505 119870119873 gt 119891119904119889 = 119877119907119898119886119909 = 8954 119870119873




119891119904119889 le 119877119886119877119889

119891119904119889119877119886119877119889

+119872119878119889119872119888119877119889

le 1 119808119825119827 120787 120789120790 minus 119810119810119820120791120789

Avec

77

119877119886119877119889 =

051199051199082 (119864 119891119910119908)

05[(119905119891119905119908)05

+ 3(119905119908119905119891) (119878119904119889 )]

1205741198720 119808119825119827 120787 120789120789 minus 119810119810119820120791120789

119877119886119877119889 = 108284 119870119873

119891119904119889 = 15119877119871119898119886119909 = 15 times 1628 = 2442 119870119873

119872119888119877119889 =3232 times 103 times 235

11= 69047 119870119873119898

119891119904119889119877119886119877119889

+119872119878119889119872119888119877119889

=2442

108284+

110

69047 = 018 le 15




119887119890119891119891 le 119887 119808119825119827 120787 120789120791 minus 119810119810119820120791120789

119887119890119891119891 = radicℎ2 + 1198781199042 = 410 119898119898 gt 119887 = 300 119898119898




efforts suivants




Charge verticale


119901prime = 119876 119871 + 119877119898119886119909 (2 minus119890

119871) ψ


36

6) times 11

119901prime = 13651 119870119873


119901 = 135119876 119871 + 15119877119898119886119909 (2 minus119890

119871) ψ


36

6) times 11

119901 = 2031 119870119873

78

Charge horizontale

119875119867 = 15119877119867119898119886119909 (1 minus119890

119897)ψ


36

6) times 11 = 1808 119870119873




119891119911 le 119891119886119889119898 =119897

500


119891119911 =119901prime 1198893

3119864119868le 119891119886119889119898

119868119910 =500 119901prime 1198892

3119864ge 782667 1198881198984


79




119905119908le 72휀

Avec

휀 = radic235

119891119910

2486

71le 72radic

235

235 ⟹ 3501 le 72


119888

119905119891=1198872

119905119891le 10휀 ⟹

75

102= 735 le 10





119881119910119904119889 le 119881119901119897119903119889

Avec 119860119907119911 = 257 cm2

119881119901119897119903119889 =119860119907119911 119891119910

radic3 1205741198980=257 times 235

radic3 times 11= 317 119870119873

119881119904119889 = 119901 = 2031 lt 05119881119901119897119877119889


profileacute


G

Kgm

A

cm2

h

mm

b

mm

tf

mm

tw

mm

Iy

cm4

Iz

cm4

Wply

cm3

Wplz

cm 3

IPE 300 422 5380 300 150 107 71 8353 604 628 125

80


119872119888119903119889 =119908119901119897119910 119891119910

1205741198720=628 times 235

11= 13416 119870119873119898

119872119910119904119889 = 119901 119889 = 2031 times 085 = 172635 119870119873119898

119872119910119904119889 lt 119872119888119903119889




119872119888119903119889 =119908119901119897119910 119891119910

1205741198720=1019 times 235

11= 2177 119870119873119898

119872119910119904119889 = 119901 119889 = 2031 times 085 = 172635 119870119873119898

119872119910119904119889 lt 119872119888119903119889


17263


profileacute


G

Kgm

A

cm2

h

mm

b

mm

tf

mm

tw

mm

Iy

cm4

Iz

cm4

Wply

cm3

Wplz

cm3

IPE 360 571 727 360 170 127 8 16270 1043 1019 191

81



chemin de roulement

119891119911 le 119891119886119889119898 =119889

500= 017

119902 = 119902119868119875119864 360 = 571 119889119886119873119898119897

119891119911 =119901prime 1198893

3119864119868+119902 1198974

8119864119868= 0082 + 0021 = 0103 119888119898 lt 017 119888119898


82

Chapitre-5








dynamiques


83




119881 =119860119863 119876

119877119882



119863 =

25120578 0 le 119879 le 1198792

25120578(1198792119879)23 1198792 le 119879 le 3119904

25120578 (11987923)

23 (3119879)

53 119879 gt 3119904


84

120578 = radic7

(2 + 120585)ge 07



119879 = 119862119879 ℎ11987334 119917119926119929119924119932119923119916 (120786 120788)119929119927119912 119933120784120782120782120785




119876 = 1 +sum119875119902

6

1


85


119876 = 1 +sum119875119902

6

1

= 1 + 02 = 12


119899119894=1

Avec 119882119894 = 119882119866119894 + 120573119882119876119894




119881 =119860119863 119876

119877119882

119860 = 005 119863 = 25 119876 = 12 119877 = 4 119882 = 189475119896119873

119881119909 = 119881119910 =005 times 25 times 12

4times 189475 = 7105119896119873


119904119886119892=

125119860 (119860 +

119879

1198791(25120578

119876

119877minus 1)) 0 le 119879 le 1198791

25120578(125119860) (119876

119877) 1198791 le 119879 le 1198792

25120578(125119860) (119876

119877)(1198792119879)23

1198792 le 119879 le 30119904

25120578(125119860) (11987923)

23(3

119879)

53(119876

119877) 119879 gt 30119904

86



η = 100 A=005 1198791=015 1198792=050


87













88










89

ℎ

150=890

150= 594119888119898 sans vent

ℎ

125=890

125= 712119888119898 avec vent






Toiture 029 076 116 304


ℎ

100=1025

100= 1025 119888119898



90

Chapitre-6


61 Introduction





119872119910119904119889 = 21902 kNm

119881119904119889 =7249 kN

119873119904119889 =2018 kN

91

Profileacute


IPE 400 A cm2

hmm

b mm

119905f

mm

119905w mm

119868y

cm4

119868z Cm4

119908ply

cm3

119908plz

cm3

MATERIAU ACIER S235

8446 400 180 14 90 231284 131782 123832 2256




119888

119905119891=60

14= 59 lt 10휀 =gt 119888119897119886119904119904119890 1


119889

119905119908=98

9= 11 lt 72휀 =gt 119888119897119886119904119904119890 1





Si 119881119904119889 le 05119881119901119897119903119889 ⟹ 119872119904119889 le 119872119888119903119889 119912119955119957120787 120786 120789 119914119914119924 120791120789


119881119898119886119909 = 119881119904119889 =7248kN

119881119901119897119911119903119889 =

119860119907119911 (119891119910

radic3)

1205741198980=

4270235

radic311

= 526674119896119873

119881119904119889 = 7247 le 05119881119901119897119911119903119889 = 52667119896119873


92



119873119904119889 le 119872119894119899(025119873119901119897119903119889 05119860119908119891119910

1205741198720)


119873119904119889 = 2018119896119873

119873119901119897119903119889 le119860 119891

119910

1205741198720=8446 235

11= 180437119896119873

025119873119901119897119903119889 =451 119896119873

119860119908 = 119860 minus 2119887 119905119891 = 34061198981198982

05119860119908119891119910

1205741198720= 36382119896119873

119873119904119889 = 2018 le 36382119896119873



119872119888119903119889 = 119872119901119897119910119903119889 =119908119901119897119910 119891119910

1205741198720=1238320 235

11= 26455119896119873119898




120594119898119894119899 119873119901119897119903119889+119896119910 119872119910119904119889

119872119901119897119910119903119889+119896119911 119872119911119904119889119872119901119897119911119903119889



120594119911 119873119901119897119903119889+119896119871119879 119872119910119904119889

120594119871119879119872119901119897119910119903119889+119896119911 119872119911119904119889119872119901119897119911119903119889



120594119898119894119899 = 119872119894119899(120594119910 120594119911)


93

120594119910 =1

(120601119910 +radic1206011199102 minus 1205821199102 )

120601119910 = 05[1 + 120572119910(120582119910 minus 02) + 1205821199102]

120582119910= (120582119910

1205821)radic120573119860 =

120582119910

1205821

Avec 120573119860 = 1 Classe 1

1205821 = 939

120582119910 =05119868119910

119894119910=455

166= 274

120582119910=274

939= 029


ℎ

119887=400

180= 222 gt 12 119894119898119901119897119894119902119906119890 120572 = 021

120601 = 05[1 + 120572119910(120582119910 minus 02) + 1205821199102 ] = 055

120594119910 =1

(055 + radic0552 minus 0292)= 098


120594119911 =1

(120601119911 +radic1206011199112 minus 120582119911

2)

120601119911 = 05[1 + 120572119911(120582119911 minus 02) + 1205821199112]

120582119911 = (1205821199111205821)radic120573119860 =

1205821199111205821

Avec 120573119860 = 1 Classe 1

120582119911 =119868119911119894119911=200

395= 5063

120582119911 =5063

939= 054


94

ℎ

119887= 222 gt 12 (119911 minus 119911)119894119898119901119897119894119902119906119890 120572 = 034

120601 = 05[1 + 034(054 minus 02) + 0542 ] = 07

120594119911 =1

(07 + radic072 minus 0542)= 087

120594119898119894119899 = 119872119894119899(120594119910 120594119911) = 087




λ119897119905 =

119871119894119911

119888105

[

1 +120(

119871119894119911ℎ119905119891

)

2

] 025 = 4367 119808119821119821119812119831119812119809 119810119810119820120791120789

Avec

IPE400 119905119891 = 14119898119898 119894119911 = 395119888119898 ℎ = 400119898119898

119870 = 1 1198881=1134 Tableau B11 CCM97


1205821 = 939휀

휀 = radic235

119891119910= 1

120582119871119879 = [1205821198971199051205821] [120573119908]

05

120582119897119905 = 4367

120582119871119879 =4367

939= 046 gt 04



119873119904119889120594119911 119873119901119897119903119889

+119896119871119879 119872119910119904119889

120594119871119879119872119901119897119910119903119889+119896119911 119872119911119904119889119872119901119897119911119903119889


Calcul de 120594119871119879


95

implique 120594119871119879 = 094

Calcul de 119896119871119879


119870119871119879 = 1 minusμLT N119904119889

120594119911 119860 119891119910= 099 lt 15


Donc

119873119904119889=7249 kN 119872119910119904119889=219 kNm 119872119901119897119910119903119889=26455 kNm 120594119911=087 119872119901119897119911119903119889=4819kNm


119873119904119889120594119911 119873119901119897119903119889

+119896119871119879 119872119910119904119889

120594119871119879119872119901119897119910119903119889+119896119911 119872119911119904119889

119872119901119897119911119903119889


7249

087 180437+

099 219

094 26455= 055










96

119872119910119904119889 = 32083 119896119873119898

119881119904119889 = 120 119896119873

119873119904119889 = 602 119896119873

Profileacute


HEA320

A cm2

hmm

b mm

119905f

mm

119905w mm

119868y

cm4

119868z cm4

119908 ply

cm3

119908 plz

cm3

MATERIAU ACIER S235

12437 310 300 16 9 229286 698524 162823 70975




119888

119905119891=60

16= 375 lt 10휀 =gt 119888119897119886119904119904119890 1


119889

119905119908=98

9= 109 lt 72휀 =gt 119888119897119886119904119904119890 1





Si 119881119904119889 le 05119881119901119897119903119889 ⟹ 119872119904119889 le 119872119888119903119889 119912119955119957120787 120786 120789 119914119914119924 120791120789


119881119898119886119909 = 119881119904119889 =120kN

119881119901119897119911119903119889 =

119860119907119911 (119891119910

radic3)

1205741198980=4113 235radic3

11= 50731119896119873

97

119881119904119889 le 05119881119901119897119911119903119889




119873119904119889 le 119872119894119899(025119873119901119897119903119889 05119860119908119891119910

1205741198720)


119873119904119889 =602kN

119873119901119897119903119889 le119860 119891

119910

1205741198720=12437 235

11= 2656995 119896119873

025119873119901119897119903119889 = 664248119896119873

119860119908 = 119860 minus 2119887 119905119891 = 2837 1198981198982

05119860119908119891119910

1205741198720= 30304119896119873

119873119904119889 = 602119896119873 le 30304119896119873



119872119888119903119889 = 119872119901119897119910119903119889 =119908119901119897119910 119891119910

1205741198720=1628000 times 235

11= 3478119896119873119898




120594119898119894119899 119873119901119897119903119889+119896119910 119872119910119904119889

119872119901119897119910119903119889+119896119911 119872119911119904119889119872119901119897119911119903119889



120594119911 119873119901119897119903119889+119896119871119879 119872119910119904119889

120594119871119879119872119901119897119910119903119889+119896119911 119872119911119904119889119872119901119897119911119903119889



120594119898119894119899 = 119872119894119899(120594119910 120594119911)


98

120594119910 =1

(120601119910 +radic1206011199102 minus 1205821199102 )

120601119910 = 05[1 + 120572119910(120582119910 minus 02) + 1205821199102]

120582119910= (120582119910

1205821)radic120573119860 =

120582119910

1205821

Avec 120573119860 = 1 Classe 1

1205821 = 939

120582119910 =05119868119910

119894119910=05 890

1358= 3276

120582119910=3276

939= 034


ℎ

119887=310

300= 1 lt 12 (119910 minus 119910)119894119898119901119897119894119902119906119890 120572 = 034

120601 = 05[1 + 120572119910(120582119910 minus 02) + 1205821199102 ] = 058

120594119910 =1

058 + radic058 minus 034= 095


120594119911 =1

(120601119911 +radic1206011199112 minus 1205821199112)

120601119911 = 05[1 + 120572119911(120582119911 minus 02) + 1205821199112]

120582119911 = (1205821199111205821)radic120573119860 =

1205821199111205821

Avec 120573119860 = 1 Classe 1

1205821 = 939

120582119911 =119868119911119894119911=07 59

749= 055


ℎ

119887= 1 lt 12 (119911 minus 119911) 119894119898119901119897119894119902119906119890 120572 = 049

120601 = 05[1 + 049(055 minus 02) + 0552] = 073

99

120594119911 =1

073 + radic073 minus 055= 082

120594119898119894119899 = 119872119894119899(120594119910 120594119911) = 082


λ119897119905 =

119871119894119911

119888105

[

1 +120(

119871119894119911ℎ119905119891

)

2

] 025 = 3536

HEA320 119905119891 = 16119898119898 119894119911 = 749119888119898 ℎ = 310119898119898

119870 = 07 1198881 = 1134 Tableau B11 CCM97


1205821 = 939휀

휀 = radic235

119891119910= 1

120582119871119879 = [1205821198971199051205821] [120573119908]

05

120582119897119905 = 3536

120582119871119879 =3536

939= 037 lt 04 119901119886119904 119889119890 119903119894119904119902119906119890 119889119890 119889119890119907119890119903119904119890119898119890119899119905


119873119904119889120594119898119894119899 119873119901119897119903119889

+119896119910 119872119910119904119889

119872119901119897119910119903119889+119896119911 119872119911119904119889119872119901119897119911119903119889


Avec

119873119904119889 =602kN 119872119910119904119889=32083kNm 119872119911119904119889=049kNm 119872119901119897119910119903119889=3478kNm

119872119901119897119911119903119889=1516kNm 120594119898119894119899= 082 119873119901119897119903119889=26570kN 119896119910= 05 119896119911= 07

602

082 26570+05 32083

3478+07 049







100





(135G+15V1)


119873119904119889 =69837kN


Profileacute


2CAE (120x12)

A Cm2

hmm

b mm

Anet

Cm2

d

mm

MATERIAU ACIER S235

5508 120 248 4658 8



119873119904119889 le 119873119905119903119889 = 119872119894119899[119873119901119897119903119889 119873119906119903119889 119873119899119890119905119903119889]

101

119873119901119897119903119889 =119860 119891119910

1205741198720= 117671119896119873

119873119906119903119889 = 09119860119899119890119905 1198911199061205741198722

= 13719119896119873

119873119899119890119905119903119889 =119860119899119890119905 119891119910

1205741198720= 995118119896119873








102


119872119910119904119889 = 02 119896119873119898

119881119904119889 = 0048 119896119873

119873119904119889 = 5628 119896119873

Profileacute


IPE300

A cm2

hmm

b mm

119905f

mm

119905w mm

119868y

cm4

119868z cm4

119908ply

cm3

119908plz

cm3

MATERIAU ACIER S235

538 300 150 107 71 8356 746 628 125







Si 119881119904119889 le 05119881119901119897119903119889 ⟹ 119872119904119889 le 119872119888119903119889 119912119955119957120787 120786 120789 119914119914119924 120791120789


119881119898119886119909 = 119881119904119889 =0048kN

119881119901119897119911119903119889 =

119860119907119911 (119891119910

radic3)

1205741198980=2570 235radic3

11= 3169119896119873

119881119904119889 le 05119881119901119897119911119903119889




119873119904119889 le 119872119894119899(025119873119901119897119903119889 05119860119908119891119910

1205741198720)

103


119873119904119889 =5628kN

119873119901119897119903119889 le119860 119891

119910

1205741198720=5380 235

11= 114936 119896119873

025119873119901119897119903119889 = 28734 119896119873

119860119908 = 119860 minus 2119887 119905119891 = 2170 1198981198982

05119860119908119891119910

1205741198720= 23179119896119873

119873119904119889 = 5628119896119873 le 23179119896119873



119872119888119903119889 = 119872119901119897119910119903119889 =119908119901119897119910 119891119910

1205741198720=628000 times 235

11= 134163 119896119873119898




120594119898119894119899 119873119901119897119903119889+119896119910 119872119910119904119889

119872119901119897119910119903119889+119896119911 119872119911119904119889119872119901119897119911119903119889



120594119911 119873119901119897119903119889+119896119871119879 119872119910119904119889

120594119871119879119872119901119897119910119903119889+119896119911 119872119911119904119889119872119901119897119911119903119889



120594119898119894119899 = 119872119894119899(120594119910 120594119911)


120594119910 =1

(120601119910 +radic1206011199102 minus 1205821199102 )

120601119910 = 05[1 + 120572119910(120582119910 minus 02) + 1205821199102]

120582119910= (120582119910

1205821)radic120573119860 =

120582119910

1205821

104

Avec 120573119860 = 1 Classe 1

1205821 = 939

120582119910 =119871119910

119894119910= 960

125= 768

120582119910=768

939= 081


ℎ

119887=300

150= 05 lt 12 (119910 minus 119910)119894119898119901119897119894119902119906119890 120572 = 021

120601 = 05[1 + 120572119910(120582119910 minus 02) + 1205821199102 ] = 089

120594119910 =1

058 + radic058 minus 034= 079


120594119911 =1

(120601119911 +radic1206011199112 minus 1205821199112)

120601119911 = 05[1 + 120572119911(120582119911 minus 02) + 1205821199112]

120582119911 = (1205821199111205821)radic120573119860 =

1205821199111205821

Avec 120573119860 = 1 Classe 1

1205821 = 939

120582119911 =119868119911119894119911=125

335= 3731 120582119911 = 039


ℎ

119887= 1 lt 12 (119911 minus 119911) 119894119898119901119897119894119902119906119890 120572 = 021

120601 = 05[1 + 021(039 minus 02) + 0392] = 061

120594119911 =1

061 + radic061 minus 039= 092

120594119898119894119899 = 119872119894119899(120594119910 120594119911) = 079


105

λ119897119905 =

119871119894119911

119888105

[

1 +120(

119871119894119911ℎ119905119891

)

2

] 025 = 3433

IPE300 119905119891 = 107119898119898 119894119911 = 335119888119898 ℎ = 300119898119898

119870 = 1 1198881 = 1134 Tableau B11 CCM97


1205821 = 939휀

휀 = radic235

119891119910= 1

120582119871119879 = [1205821198971199051205821] [120573119908]

05

120582119897119905 = 3433

120582119871119879 =3433

939= 036 lt 04 119901119886119904 119889119890 119903119894119904119902119906119890 119889119890 119889119890119907119890119903119904119890119898119890119899119905


119873119904119889120594119898119894119899 119873119901119897119903119889

+119896119910 119872119910119904119889

119872119901119897119910119903119889+119896119911 119872119911119904119889119872119901119897119911119903119889


Avec

119873119904119889 =5628kN 119872119910119904119889=02kNm 119872119911119904119889=018kNm 119872119901119897119910119903119889=134163kNm

119872119901119897119911119903119889=267kNm 120594119898119894119899= 079 119873119901119897119903119889=1149kN 119896119910= 1 119896119911= 1

5628

079 1149+

02

134163+018



106

Chapitre-7


71 Introduction










au poteau

107




119872119904119889 = 28961119896119873119898 119873119904119889 = 17878119896119873 119881119904119889 = 8941119896119873




119905 = 119872119894119899(119905119891 119905119901119897119886119905119894119899119890) = 135119898119898

Avec





12119889O = 24 119898119898 le 1198901 le 12119905 =186 119898119898 ⟹ 1198901 = 110 119898119898

15119889O = 30 119898119898 le 1198902 le 12119905 = 186 119898119898 ⟹ 1198902 = 105 119898119898

22119889O = 44 119898119898 le 1199011 le 14119905 =217 119898119898 ⟹ 1199011 = 100 119898119898


108






IPE 400 119905f = 135 119898119898 119905w = 86 119898119898

119886min= 26 le twle119886max= 8

119886min =35 le tf le119886max= 8







sum119897 = 2119887 + 4(119887 minus 119905119908) = 2180 + 4(180 minus 86) = 1045119898119898

119865119908119903119889 =7times 1045 times 360

radic2= 1862119896119873

119873119904119889 =119872119904119889

ℎ=120784120790120791 120788120783

120782 120791= 120785120784120783 120789120790





Avec 120573119908 = 125 120574119872119882 = 08


109

i

sum119897 = 4ℎ119894 = 4 times 373 = 1492119898119898

119865119907119903119889 =7 times 1492 times 360

radic3= 217074119896119873



119873119894 =119872119904119889 119889119894sum119889119894

2


119909 = 119905119891radic119887

119905119908= 135radic

180

86= 6176



- 1198891 = 712 119898119898

- 1198892 = 612 119898119898

- 1198893 = 512 119898119898 ⟹ Σ 1198892 = 129 119898sup2

- 1198894 = 312 119898119898

- 1198895 = 212 119898119898

- 1198896 = 112 119898119898


1198731 =28961 times 0712

129= 15984119896119873



1198731 = 119899119865119907119903119889 ⟹ 119860119904 ge119873119904119889

06 times 119891119906119887 times 119899=

15984

06 times 800 times 2= 16651198981198982



M18 18 20 254 192 800 291



110




119865119901 = 07 times 119891119906119887 times 119860119904 = 06 x 800 x 192 = 10752kN

119872119903119889 =119899 119865119901 sum119889119894

2

119889119894=2 times 10752 times 129

0712= 3896 gt 119872119904119889 = 28961 119896119873119898




119865119907119904119889 le 119865119904119903119889 =119870119904 119898 120583

1205741198722(119865119901119888119889 minus 08119873119904119889) 119917119926119929119924119932119923119916 120788 120789 minus 119914119914119924120791120789

Avec

119870119904 = 10 ∶ Trous normaux



119865119904119903119889 = 024 (10752 minus 08 times15984

2) = 1046119896119873

119865119907119904119889 =8941

12= 745119896119873 lt 1046119896119873




1205741198722 119813119822119825119820119828119819119812 120788 120784 minus 119810119810119820120791120789



125= 213157 119896119873

119865119905119904119889 =119865119901

2=10752

2= 5376119896119873 lt 119861119901 119903119889 = 213157 119896119873


111



1205741198722 119827119808119809119819119812119808119828 120788 120787 120785 ndash 119810119810119820120791120789

Avec 119870119904 = 25

120572119887 = min (119890131198890

(119901131198890

minus 025) 119891119906119887119891119906 1) = 1



125= 46008119896119873 gt

11986511990711990411988912

= 745119896119873



119865119907 le 119865119905119903119889 = 119905119908119888 1198871198901198911198911198911199101205741198720

Avec




⟹ 119865119905119903119889 = 9 times 90times23511

= 173045 119896119873


119865119907 =119872119904119889

ℎ minus 119905119891=28961

029= 99865 gt 119865119905119903119889 = 173045119896119873




119873119904119889 le 119865119888119903119889 =119896119888 120588 119887119890119891119891 119905119908119888 119891119910

1205741198721radic1 + 13 (119887119890119891119891ℎ)2

119887119890119891119891 = 119905119891119887 + 2119886119901radic2 + 5(119905119891119888 + 119903119888) + 2119905119901

Avec

112






119887119890119891119891 =25014mm



120590119888119904119889 =119881119904119889119860+119872119904119889

119882119890119897119910=8941 times 103

1244+28961 times 106

1479= 196533119872119875119886

120590119888119904119889 = 19653119872119875119886 lt 119891119910 = 235119872119875119886 ⟹ 119896119888 = 1


119901 = 0932radic119887119890119891119891 119889119908119888 119891119910

119864 1199051199081198882= 0932radic


21 times 104 times 092= 254

119901 gt 072⟹ 120588 =119901 minus 02

1199012=254 minus 02

2542= 036


11 radic1 + 13 (250131

)2

= 12741119896119873

119873119904119889 = 1119873119894 =119872119904119889 sum119889119894sum119889119894

2 =29861 times 247

129= 57175119896119873





119865119907 le 119881119903119889 = 058119891119910 ℎ1199051199081205741198720


11= 3457119896119873


119865119907 =119872119904119889ℎ minus 119905119891

= 46216 119896119873 gt 119881119903119889 = 3457119896119873 119888119900119899119889119894119905119894119900119899 119899119900119899 119907eacute119903119894119891119894eacute119890


113

119865119907 = 46216119896119873 le 119881119903119889 = 058119891119910 ℎ119905119908 + 04

1205741198720= 058 235 31

(09 + 04)

11= 49935119896119873







logiciel robot

119872119904119889 = 15135119896119873119898 119873119904119889 = 1324119896119873 119881119904119889 = 273119896119873






119905 = min(119905119891 119905119901119897119886119905119894119899119890) = 135119898119898


114









IPE400

tf = 135 mm tw = 86 mm






radic2 times 119861119908 120574119898119908


Donc

119865119908119903119889 =119860 times sum119871 times 119891119906


radic2 times 1= 133083119896119873

119873119904119889 =119872119904119889ℎ

=7283

08= 9103119896119873

115

119873119904119889 = 9103 le 119865119908119903119889 = 1330119896119873






Donc

119865119907119903119889 =119886 times sum119871 times 119891119906


radic3 times 1= 155053119896119873



119873119894 =119872119904119889 119889119894sum119889119894

2


119909 = 119905119891radic119887

119905119908= 135radic

180

86= 6176119898119898


- 1198891 = 700 119898119898

- 1198892 = 600 119898119898

- 1198893 = 500 119898119898 ⟹ Σ1198891198942

= 124 119898sup2

- 1198894 = 300 119898119898

- 1198895 = 200 119898119898

- 1198896 = 100 119898119898


1198731 =119872119904119889 times 119889119894Σ119889119894

2 =15135 times 070

124= 4111119896119873



116


1198731 = 119899 119865119907 ⟹ 119860119904 ge119873119904119889

05 times 119891119906119887 times 119899=

13240

05 times 800 times 2= 16551198981198982



M18 18 20 254 192 800 291




119865119901 = 07 times 119891119906119887 times 119860119904 = 10752 119896119873

119872119903119889 =119899 119865119901sum119889119894

2

119889119894=2 times 10752 times 124

07= 38092 gt 119872119904119889 = 15135119896119873119898




119865119907119904119889 le 119865119904119903119889 =119870119904 119898 120583

1205741198722(119865119901119888119889 minus 08119873119904119889) 119813119822119825119820119828119819119812 120788120789 ndash 119810119810119820120791120789

Avec




119865119904119903119889 = 024 ( 10752 minus 08 times 1324) = 2326119896119873

119865119907119904119889 =273

12= 023 lt 119865119904 119903119889 = 2326119896119873




1205741198722 119813119822119825119820119828119819119812 120788 120784 ndash 119810119810119820120791120789

Avec


117


125= 31578119896119873

119865119905119904119889 =119865119901

2= 5376 lt 31578119896119873




1205741198722 119827119808119809119819119812119808119828 120788 120787 120785 ndash 119810119810119820120791120789

Avec Ks = 25

120572119887 = min (119890131198890

(119901131198890

minus 025) 119891119906119887119891119906 1) = 1


11986511990711990411988912


125= 5184 119896119873







119865119907119904119889 =119873119904119889

119899119887119903 119889119890 119887119900119906119897119900119899=131

3= 4366 le 119865119907119903119889

118


1205741198722⟹ 119860119904 ge

1205741198722 times 119865119907119903119889

06 times 119891119906119887119909 119898=125 times 43666

06 times 800 times 2= 56851198981198982


















119873119898119886119909 le 119865119908119903119889 =119886 sum119897 119891119906

119861119908 120574119898119908 radic(3 minus 1199041198941198991205722)


120572= 30gtgtgt 11990411989411989930o = 05

119865119908119903119889 =5 times 700 times 360



119



1205741198722 119827119808119809119819119812119808119828 120788 120787 120785 minus 119810119810119820120791120789


120572119907= 06



125= 12057119896119873

119865119907119904119889 =119873119904119889

3=3124

3= 10413 le 119865119907119903119889 = 12057119896119873




1205741198722 119827119808119809119819119812119808119828 120788 120787 120785 minus 119810119810119820120791120789

Avec

Ks = 25

120572119887 = min (119890131198890

(119901131198890

minus 025) 119891119906119887119891119906 1) = 092



125= 33914119896119873 gt 119865119907119904119889 = 4366119896119873




119873119898119886119909 le 119881119890119891119891119903119889 =119860119899119905 119891119910

1205741198722+119860119899119907 119891119910

radic3 1205741198722 119812119810120785 119849119834119851119853119842119838120783 minus 120790sect120785120783120782 120784

Avec


119860119899119890119905 = (119897

2minus11988902) 119905 = (60 minus 9)12 = 6121198981198982


120

119860119899119907 = (1198901 + 21199011 minus 251198890)119905 = (50 + 140 minus 45)12 = 17401198981198982

⟹ 119881119890119891119891119903119889 =612 times 235

125+1740 times 235

radic3 times 125= 303918119896119873 gt

119873119904119889

2= 655119896119873








119865119907119904119889 =119877119907119911

119899119887119900119906119897119900119899119904=36

2= 18 119896119873

119865119907119903119889 =06 times 119860119904 times 119891119906119887

120574119872119887⟹119860119904 ge

120574119872119887 times 11986511990711990311988906 times 119891119906119887

=11 times 18000

06 times 800= 41251198981198982



119865119907119903119889 =06 times 119860119904 times 119891119906119887

120574119872119887=06 times 58 times 800

11= 253119896119873 gt 119865119907119904119889 = 18119896119873


119865119905119903119889 =09 times 119860119904 times 119891119906119887

120574119872119887=09 times 58 times 800

11= 379119896119873

121

119865119907119903119889 =06 times 119860119904 times 119891119906119887

120574119872119887= 253119896119873

119865119907119904119889119865119907119903119889

+119865119905119904119889

14 119865119905119903119889= 052 lt 1 119862119900119899119889119894119905119894119900119899 119907119890119903119894119891119894eacute119890


122

Chapitre-8




123








119865119888119896=30 MPa

119891119888119889 =085 times 119865119888119896125

= 204 MPa


119865119895119889 = 120572120573119895 119891119888119889



119865119895119889 = 120572 120573119895 119891119888119889 = 15 times2

3times 17 = 204 119872119875119886


1198601198620 ge119873119904119889119891119888119889

=148960

204

1198601198620 ge 7266341198981198982


bp ge b+2tf = 190+2times155 = 221 mm

hp ge h+2tf = 310+2times155 = 341 mm

On prend

bp =600 hp=620



124


119862 = 119905 (119891119910119901

3119891119895119889 1205741198720)

05

= 30(235


= 5605 119898119898

119862 = 5605 lt(ℎ minus 2119905119891)

2= 1395 119898119898




gorge (a) Annexe H







119890 =119872119904119889119873119904119889

= 041 119898 gt 119885119879 = 0195 119898







125


Ougrave

119871119890119891119891 = min(119887119901 119887119891119888 + 2119888) = min(600 300 + 2 times 4671) = 39342 119898119898

119887119890119891119891 = min (119888ℎ1198882minus 119905119891119888) + 119905119891119888 +min (119888

ℎ119901 minus ℎ119888

2)

119887119890119891119891 = min (4671310

2minus 155) + 155 + min (4671

620 minus 310

2) = 10892 119898119898

⟹ 119865119888119903119889 = 204 times 10892 times 39342 = 874166 119896119873


119865119907119903119889 = 119865119891119903119889 + 119899119887 119865119907119887119903119889


119865119891119903119889 = 02119873119904119889 = 1214 119896119873





119865119907119887119903119889 =120572119888119887 119891119906119887 119860119904

1205741198722

Avec 120572119888119887 = 044 minus 00003119891119910119887 = 0248


126

119865119907119887119903119889 =0248 times 800 times 561

125= 8904 119896119873

⟹ 119865119907119903119889 = 1214 + 8 times 8904 119896119873 = 72446 119896119873




Avec 120573119908 =08 120574119898119908 = 125 119886 = 6 mm


sum119897 = 470 119898119898

119865119908119903119889 =6 times 470 times 360

radic3= 58612 119896119873

119881119904119889 = 9773 119896119873 lt min(119865119907119903119889 119865119908119903119889) = 58612 119896119873





W= 150 mm e = 55 mm ex = 40 mm mx = 40 mm


119897119890119891119891119888119901 = 119898119894119899 2120587119898119909 = 25132 119898119898

120587119898119909 +119882 = 27566 119898119898120587119898119909 + 2119890 = 23566 119898119898

⟹ 119897119890119891119891119888119901 = 23566 119898119898

127


119897119890119891119891119899119888 = 119898119894119899

4119898119909 + 125119890119909 = 210 119898119898

2119898119909 + 0625119890119909 +119882

2= 180 119898119898

2119898119909 + 0625119890119909 + 119890 = 160 119898119898119887119901

2= 150 119898119898

⟹ 119897119890119891119891119899119888 = 150 119898119898


119865119905119886119899119888119903119889 = min[119865119905119887119900119899119889119903119889 119865119905119903119889]


119865119905119903119889 = 09 times119860119904 times 119891119906119887120574119898119887


125= 32314 119896119873



119865119887119889 =036radic119891119888119896

120574119888=036 times 547

15= 1313 119872119875119886


119865119905119887119900119899119889119903119889 =120587 119889 119897119887 119891119887119889

120572

Avec

1198971 = 20119889 = 600 119898119898

119903 = 3119889 = 90 119898119898

1198972 = 20119889 = 600 119898119898






07= 52929 119896119873

119865119905119886119899119888119903119889 = 119898119894119899[52929 32314] = 32314 kN

128




Lb = 8d + em +tp + twa + 05k

Avec







119871119887lowast =

881198981199093 119860119904

1198971198901198911198911 1199051199013 =


150 times 253= 13480 119898119898 lt 119871119887 = 312 119898119898




119898119901119897119903119889 =1199051199012 119891119910119901

41205741198720=252 times 235

4 times 11= 3338119896119873


Mode 1 1198721199011198971119903119889 = 119898119901119897119903119889 times 1198971198901198911198911 = 3338 times 015 = 5007119896119873119898

1198971198901198911198911 = min(119897119890119891119891119888119901 119897119890119891119891119899119888) = 150 119898119898


129




Mode 1-2

1198651199051minus2119903119889 =21198721199011198971119903119889

119898119909=2 times 5

004= 250 119896119873

Mode 3

1198651199053119903119889 = 2119865119905119903119889119886119899119888ℎ119900119903 = 2 times 32314 = 646280 119896119873

Mode 4

1198651199054119903119889 =119887119890119891119891119905 119905119908 119891119910

1205741198720=150 times 9 times 235

11= 288409119896119873

Drsquoougrave

119865119905119903119889 = min(1198651199051minus2119903119889 1198651199053119903119889 1198651199054119903119889) = 250 119896119873




119885119879119890119873minus 1

119865119879119903119889 times 119885

119885119862119890119873+ 1

) 119812119810120785 ndash 120783 120790 119827119808119809119819119812119808119828 120788 120789

119885 = 119885119879+119885119862 = 195 + 155 = 350119898119898

⟹119872119903119889 = 5646 119896119873119898 lt 6207119896119873119898



821 Introduction




- Le site (S3)



130




ELU 119872119880 = 6207119896119873119898 119873119880 = 9773119896119873

ELS 119872119878 = 4136119896119873119898 119873119878 = 7960119896119873




119886 = 119886119901 + 119888 = 062 + 02 = 082 119898


119860

119861=119886

119887= 1025 ⟹ 119860 = 1025119861



119890 =119872119904

119873119904= 052119898



120590119898119886119909 =119873

119860119861(1 +

6119890

119861) le 120590119904119900119897


368B2 - B - 312 ge 0 ⟹ B ge0765m



131

119889 = max (119861 minus 119887

4119860 minus 119886

4) = max (005 0295)

On prend d= 45 cm



On a

119890 = 052 gt119860

6= 041


3120590119898119886119909 1205901198981198941198994

lt 120590119904119900119897

Avec

120590119898119894119899 =119873

119860119861(1 minus

6119890

119860) =

14896

2(1 minus

041

2 ) = 62191198961198731198982

120590119898119894119899 =119873

119860119861(1 +

6119890

119860) =

14896

2(1 +

041

2 ) = 86771198961198731198982

3120590119898119886119909 120590119898119894119899

4= 6835 1198961198731198982 lt 120590119904119900119897 = 180 119896119873119898

2



119890 =119872

119873= 052 119898 lt

119860

4= 062 119898




119890 gt119886

6 119890 gt

119860

24


119860119886 =1198721119911 119904119905

132

1198721 = (119860

2minus 035119886)

2

(1 +119890

119860+14 times 119890 times 119886

1198602)1198731199042119860

1198721 = 2788119896119873119898

Avec 119911 = 09d =40cm

119904119905 = min (2

3119891119890 110radic12057811989111990528) =20163 MPa

11989111990528 = 00611989111988828 + 06 = 24 119872119875119886 120578 = 16 119867 119860 Donc

119860119886 =2788 times 106

400 times 20163= 345 1198881198982


119860119887 =119873prime(119861 minus 119887)

8119889 119904119905

Avec

119873prime = 119873119904 (1 +3119890

119860) = 796 (1 +

3 times 052

25) = 2993119896119873

119904119905 = min (2

3119891119890 110radic12057811989111990528) = 20163119872119875119886

11989111990528 = 00611989111988828 + 06 = 24119896119873 120578 = 16 119867 119860

Donc 119860119887 = 071198881198982


119860119886 =1198721119911 120590119904119905

1198721 = (119860

2minus 035119886)

2

(1 +119890

119860+14 times 119890 times 119886

1198602)1198731199062119860

1198721 = 349119896119873119898

Avec 119911 =09d = 40 cm

120590119904119905 =119891119890120574119904=400

115= 3478119872119875119886

Donc

133

119860119886 =349 times 106

400 times 3478= 251198881198982


119860119886 =119873119906(119861 minus 119887)

8119889 120590119904119905

Avec

119873prime = 119873119906 (1 +3119890

119860) = 23833119896119873

Donc 119860119887 = 1621198881198982


119860119898119894119899 = 023 times11989111990528119891119890

times 119860 times ℎ119905 = 17251198881198982

Sens B

119860119898119894119899 = 023 times11989111990528119891119890

times 119861 times ℎ119905 = 691198881198982



A (cm2) St (cm)

A 345 1725 10T16 201 25 B 07 69 7T16 1407 25



134



119873119905 = (119873

120572) ge 20 119896119873 [119825119823119808120791120791 119855 120784120782120782120785 119808119851119853 120783120782 120783 120783 119835]


119873119905 =14896

12= 1241119896119873

ELS

119873119905 =796

12= 663119896119873


119860119904119905 =119873119905120590119904119905

ELS

119860119904119905 =663

348= 0191198881198982

ELU

119860119904119905 =1241

348= 0351198881198982





119860119904119905 = 0905 le 119860119904 = 6791198881198982


135


120601119898119894119899 le 119898119894119899 (ℎ

35120601119897119898119894119899

119887

10) = 08 119888119898

On prend 120601119905 =8mm


On prend St=10cm


136


137

ANNEXE - 1

138

139

140

ANNEXE - 2

141

ANNEXE - 3

142

143

ANNEXE ndash 4

144

145

ANNEXE ndash 5

Reacutesumeacute


ملخص







Abstract































































































































Liste des tableaux

















LISTE DES NOTATIONS

Majuscules latines








16

Chapitre-1


11 Introduction


17



18

Action

permanente (γG)




Effet favorable

γGinf

10 1 0


γGsup

135 15 15




135119866119896119895 + 15119876119896119898119886119909





1 119866119896119895 + 150119882minus


sum119866119896119895119895

+ 119876119896119898119886119909

119866119896119895 + 119876119896119898119886119909


sum119866119896119895119895

+ 09sum119876119896119894119894gt1

119866119896119895 + 09119876119896119898119886119909 + 09119878 119866119896119895 + 09119876119896119898119886119909 + 09119882


19










20




21






22




23

Chapitre-2


21 Introduction










24

- Effet du site








Ouargla (Zone 4)




Kt=017 Z0=001m Zmin=1m ξ=044






Avec




119902119901(119885) = 119902119903119890119891 times 119862119890

Avec

- 119902ref = 575 119889119886119873119898sup2


2(119885) times [1 + 7119868119907] 119825119821119829120784120782120783120785 119836119841119834119849119842119853119851119838 120784 120786 sect120784 120786 120784 119834


25


119862119903(119911)

119870119905 119871119899 (1199111198981198941198991199110

) 119901119900119906119903 119911 lt 119911119898119894119899

119870119905 119871119899 (119911

1199110) 119901119900119906119903 119911119898119894119899 le 119911 le 200119898


)=0783


Zo)=1178

On retient 119862119903= 1178


119868119907(119911)

1

119862119905(119911) 119871119899 (119911

1199110) 119901119900119906119903 119911 gt 119911119898119894119899

1

119862119905(119911) 119871119899 (1199111198981198941198991199110) 119901119900119906119903 119911 le 119911119898119894119899

Pour z gt zmin 119868119907(119911) =1

1Ln(1

001)= 0217

Pour z lt zmin 119868119907(119911) =1

1Ln(1025

001)= 0144



119862119890(119911119895) = 119862119903(119911119895)2[1 + 7 119868119881]

Pour z gt zmin

119862119890(119911) = 11782 times 12 times [1 + 7(0144)] = 2786

Pour z lt zmin

119862119890(119911) = 07832 times 12 times [1 + 7(0217)] = 154


Avec

26

- 119902119903119890119891 = 575 119889119886119873119898sup2



qp = 160195Nm2 = 16 kNm2





- b=30 m

- d=36 m

- h=89 m


e = min (d 2h)


Donc e = 2x1025 = 205m



27



119862119901119890 = 1198621199011198901 119878119894 119878 le 11198982

119862119901119890 = 1198621199011198901 + (11986211990111989010 minus 1198621199011198901) times 11989711990011989210(119878) 119878119894 11198982 lt 119878 lt 101198982

119862119901119890 = 11986211990111989010 119878119894 119878 ge 101198982



Zone


Parois sous le vent


Cpe10 -10 -08 -05 +08 -03


Versant de Toiture




28







le tableau suivant


853deg F G H

-237 -123 -083



- Parois verticales


-b=36 m

29

-d=30 m

-h=1025


e=Min (b 2h) = Min (36 205) = 205 m





30

Zone


Parois sous le vent








31




853deg -22 -192 -183 -067 -057






2(5 times 4)

30 times 89= 014 = 14


μ119901 =120

160= 075



Pour μ119901=075 on lit 119862119901119894 =-016

32




2 times (5 times 4)

36 times 9575= 0116 = 116


Pour μ119901=075 rarr 119862119901119894 =-02

33





Direction V1 V3


A 1602 -10 -0154 -0846 -135529

B 1602 -08 -0154 -0646 -103489

C 1602 -05 -0154 -0346 -55429

D 1602 +08 -0154 +0954 +152831

E 1602 -03 -0154 -0146 -23389


34

Toiture


F 1602 -237 -0154 -2276 -355003

G 1602 -123 -0154 -1076 -172375

H 1602 -084 -0154 -0676 -108295

Z1 1602 -1 -0154 -0846 -135529

Z2 1602 -06 -0154 -0446 -71449


Direction V2 et V4

Parois verticales


A 1602 -10 -0162 -0838 -134247

B 1602 -08 -0162 -0638 -102207

C 1602 -05 -0162 -0338 -54147

D 1602 +08 -0162 +0962 +154112

E 1602 -03 -0162 -0138 -22107


35

Toiture


Finf 1602 -12 -0162 -1038 -1662876

Fsup 1602 -22 -0162 -2038 -3264876

G 1602 -183 -0162 -1668 -2672136

H 1602 -067 -0162 -0508 -813816

I 1602 -057 -0162 -0408 -653616









9= 015




q1= 300 Nml

q2= 500 Nml



36











- Epaisseur 50 mm

- Largeur 1000 mm





Selon le DTR BC22




37

119902 =8119875

3119871= 044 119896119873119898

119902 = 444 119889119886119873119898













38

Chapitre-3





deacutefavorable

39

(minus354 times5125


0875

6) = minus32754 1198891198861198731198982

Qeq (vent) = 3276 daN1198982















40



41


Vzsd =119902119906119911 times 119897

2=1878 kN

Mysd=119902119906119911 times 119897

2

8=2817 kNm

Mzsd=119902119906119910 times 119897

2

8=081 kNm



IPE 180 A Cm2

h mm

b mm

119905f

mm 119905w

mm 119868y

Cm4

119868z

Cm4

119908ply cm3

119908plz cm3

MATERIAU ACIER S235

239 180 91 8 53 1317 101 146 346




4

384 times 119864 119868119910lt

119897

200=



119897

200= 3 119862119900119899119889119894119905119894119900119899 119907eacute119903119894119891119894eacute119890

Plan z-z

5 times 119902119904119910 times 1198974

384 times 119864 119868119911lt

119897

200=



119897

200= 3 119862119900119899119889119894119905119894119900119899 119907eacute119903119894119891119894eacute119890

42




1205741198721 gt 119872119910119904119889 = 2817 119896119873119898

Calcul de 119872119887119903119889




λ119871119879 =

119871119894119911

119888105

[

1 +120(

119871119894119911ℎ119905119891

)

2

] 025

Avec


(Tableau B12 CCM97)

iz =224mm tf =85mm

L=Lz=3000mm h=200mm

λ119871119879 =

119871119894119911

119888105

[

1 +120(

119871119894119911ℎ119905119891

)

2

] 025 = 9457 rarr λ119871119879 =

989

939= 1007

rarr =1092

43


rarr ꭕ119871119879=

1


2)= 066 le 1

rarr 119872119887119903119889 =ꭕ119871119879times 120573

119908times 119882119901119897119910 times 119891119910

1205741198721

=066 1 166 235

11= 234 119896119873 119898








119872119872119860119883 =119901prime 119897

3=119901 1198972

8⟹ 119901 =

8 119901prime

3119897=800

18= 4444 119889119886119873119898119897

44


(ANNEXE ndash 1)

Soit

119876119890119902 =327 + 1082

2= 2176 1198891198861198731198982









45



Vzsd =119902119906119911 times 119897

2=186 kN

Mysd=119902119906119911 times 119897

2

8=279 kNm

Mzsd=119902119906119910 times 119897

2

8=0855 kNm

46



IPE 200 A Cm2

h mm

b mm

119905f

mm 119905w

mm 119868y

Cm4

119868z

Cm4

119908ply cm3

119908plz cm3

MATERIAU ACIER S235

285 200 100 85 56 1943 142 221 446




4

384 times 119864 119868119910lt

119897

200=



119897

200= 3 119862119900119899119889119894119905119894119900119899 119907eacute119903119894119891119894eacute119890

Plan z-z

5 times 119902119904119910 times 1198974

384 times 119864 119868119911lt

119897

200=



119897

200= 3 119862119900119899119889119894119905119894119900119899 119907eacute119903119894119891119894eacute119890




1205741198721 gt 119872119910119904119889 = 279 119896119873119898

Calcul de 119872119887119903119889

47




λ119871119879 =

119871119894119911

119888105

[

1 +120(

119871119894119911ℎ119905119891

)

2

] 025

Avec


(Tableau B12 CCM97)


-L=Lz=6000mm -h=200mm

λ119871119879 =

119871119894119911

119888105

[

1 +120(

119871119894119911ℎ119905119891

)

2

] 025 = 989 ⟶ λ119871119879 =

989

939= 105

rarr =114


rarr ꭕ119897119905=

1


2)= 063 le 1

rarr 119872119887119903119889 =ꭕ119897119905times 120573

119908times 119882119901119897119910 times 119891119910

1205741198721


11= 2974119896119873119898



48


Avec

119881119901119897119911119903119889 =

119860119907119911 (119891119910

radic3)

11 119890119905 119860119907119911 = 1400 1198981198982

Donc

05119881119901119897119911119903119889 = 05

1400 (235

radic3)

11= 8634 119896119873



Si 119889


CCM97 art 561(1)

119889

119905119908 =

159





(119872119910119904119889

119872119901119897119910119903119889)

120572

+ (119872119911119904119889119872119901119897119911119903119889

)

120573

le 1 119912119955119957 120787 120786 120790 (120783120783)119914119914119924 120791120789


119872119901119897119910119903119889 =119882119901119897119910 times 119891119910

11=221 times 235

11= 4721 119896119873119898

119872119901119897119911119903119889 =119882119901119897119911 times 119891119910

11=446 times 235

11= 952 119896119873119898

119872119910119904119889 = 279 119896119873119898

119872119911119904119889 = 0855 119896119873119898

(279

4721)2

+ (0855

952) = 044 lt 1 119888119900119899119889119894119905119894119900119899 119907eacute119903119894119891119894eacute119890

49











Effort rampant


Lrsquoexcentrement


2 (119887

2) le 119905 le 3(

119887

2)


50

2 (10

2) = 10 le 119905 le 3(

10

2) = 15

On prend t=10 cm


119877119911 = 119902119906119911 times119897

2= 6 times

6

2= 18 119896119873

119877119910 = 119902119906119910 times119897

2= 054 119896119873


119877119911 = 18 times 2 = 36 119896119873

119877119910 = 054 times 2 = 108 119896119873


119872119877 = 119877119911 times 119905 + 119877119910 timesℎ

2= 36 times 10 + 108 times 10 = 3708 119896119873 119888119898 = 37119896119873119898


119872119890119897119877119889 =119908119890119897 times 119891119910

1205741198720 119912119955119957 120787 120786 120787 120783 (120784)119914119914119924120791120789

119872119890119897119877119889 =119908119890119897 times 1198911199101205741198720

=gt 119908119890119897 ge119872119890119897119877119889 times 1205741198720

119891119910=gt 119908119890119897 ge

00037 times 11

235

= 173 times 10minus51198983

119908119890119897 = 17321198881198983




119908119890119897 =119887 1198902


6 times 1732

119887= radic

6 times 1732

180

119890 ge 076


Donc on prend e=1cm

51





















52












qsy =(133 + 5) times 125=2288daNml

qsy = 0228 kN

quy=135G=03kN



W += 1541 daN m2


quz=15W

quz=288kN

53



qsz=19262daN=192kN


119891119911 =5 times 119902119904119911 times 119897

4

384 times 119864119910 times 119868le 119891119886119889119873 =

119897

200=600

200= 3 119888119898

119868119910 ge5 times 192 times 6004



Profileacute


UPN 140 A Cm2

h mm

b mm

119905f mm

119905w mm

Iy

Cm4

Iz

Cm4

119908pSy

cm3

119908pSz

cm3

MATERIAU ACIER S235

20 140 60 10 7 605 627 103 283







qsy =(133 + 5) times 125 +1568 = 3856daNml

qsy = 038 kN

quy=135G

quy =053kN


qsz=192kN

quz=15W

quz=288kN

54




119888

119905119891=60

10= 6 lt 10휀 =gt 119888119897119886119904119904119890 1


119889

119905119908=98

7= 14 lt 72휀 =gt 119888119897119886119904119904119890 1


(119872119910119904119889

119872119890119897119910119877119889)

1

+ (119872119911119904119889

119872119890119897119911119877119889)1

le 1


119872119910 =119902119906119911 times 119897

2

8=288 times 62

8= 1296 119896119873119898


119872119911 =119902119906119910 times 119897

2

8=058 times 62

8= 261119896119873119898

119872119890119897119910119877119889 =119908119890119897119910 times 119891119910

1205741198720=864 times 103 times 235

11= 1845 119896119873119898

119872119890119897119911119877119889 =119908119890119897119911 times 119891119910

1205741198720=148 times 103 times 235

11= 316 119896119873119898

Donc

(1296

1845)1+ (

261



55

Nouveau 119872119911

119872119911 =119902119906119910 times 119897

2

8=058 times 32

8= 065119896119873119898

(1296

1845)1+ (

065




119881119911119904119889 =15119882119871

2= 1296 119896119873

119881119901119897119877119889 =119860119907119911 times 119891119910

radic3times 1205741198720= 12855 119896119873





1205741198721gt 119872119910119904119889 119912119955119957 120787 120787 120784 (120787 120786120790)119914119914119924120791120789

Avec

119872119888119903 = 11986211205872 119864 1198681199111198712

radic119868119908119868119911+1198712 119866 1198681199051205872 119864 119868119911

119912119925119925119916119935119916 119913 (119913 120783 120785) minus 119914119914119924120791120789

119872119888119903=311713762 Ncm


119872119888119903


119882119901119897119910 (upn140) =103 cm3

56

λ119897119905 = 0881


2 ]


empty119897119905 = 0959

ꭕ119897119905=

1


2 )

le 1

ꭕ119897119905= 075

119872119887119903119889 = 1652 119896119873119898

119872119887119903119889 = 1652 119896119873119898 gt 119872119910119904119889 = 1296 119896119873119898 119862119900119899119889119894119905119894119900119899 119907eacute119903119894119891119894eacute119890







57

119877 = 125119902119910 times 119897

2

Avec 119902119910 = [135(119866119880119875119873140 + 119866119888119900119906119907119890119903119905119906119903119890)]

119902119910 = 0837119896119873

119897 = 6 119898

119877 = 125119902119910 times 119897

2= 125 times 0837 times 3 = 32119896119873


1198791 =119877

2= 16119896119873

1198792 = 1198791 + 119877=48 kN

1198793 =1198792

2 sin 120579= 374 119896119873 119860119907119890119888 120579 = 119886119903119888 119905119892

25 119898

3 119898= 398deg



119873119905119904119889 =119860 times 119891119910

1205741198720= 4800 119873 =gt 119860 ge

11 times 4800

235 =gt 119860 ge 22461198981198982

119860 =120587empty2

4=gt empty ge radic

4119860

120587= radic

4 times 2246

314= 534 119898119898



Introduction



58



119878ge

63

radic119904

119889times119875

Avec








Srsquo=273

4=6825 m2








59



















96=8989 daNm2





60

119891119910 =5 times119882 times 1198974

384 times 119864 times 119868119910le 119891119886119889119898 =

119897

200


384 times E= 59136 1198881198984


Profileacute


IPE300 A Cm2

h mm

b mm

tf mm

tw

mm 119868y

Cm4

119868z Cm4

Wply

cm3

Wplz

cm3

MATERIAU ACIER S235

538 300 150 107 71 8356 746 628 125





119888

119905119891=

75

107= 7 lt 10 = 10 119878119890119898119890119897119897119890 119889119890 119888119897119886119904119904119890 1


119889

119905119908=2486

71= 35 lt 38 = 38 Acirc119898119890 119889119890 119888119897119886119904119904119890 1



Si 119881119904119889 le 05 119881119901119897119903119889 ⟹119872119904119889 le 119872119888119903119889 119912119955119957120787 120786 120789 119914119914119924 120791120789

61

119881119904119889 =15 times119882 times 119897


2= 388 119896119873 lt 05 119881119901119897119903119889 = 05 (

2570 times 235

radic3 times 11) = 1585 119896119873





Si

119873119904119889 le 119872119894119899 (025119873119901119897119903119889 05119860119908 119891119910

1205741198980)


025119873119901119897119903119889 = 025119860 times 119891119910

1205741198720= 025

5380 times 235

11= 28734 119896119873

05119860119908 times 119891119910

1205741198720= 05

2170 times 235

11= 2317 119896119873

119873119904119889 = 135119866 = 1337 119896119873 lt 119898119894119899 (025119873119901119897119903119889 05119860119908 times 119891119910

1205741198720)





119872119910119904119889 =15119882 times 1198972

8= 9313119896119873119898 119872119911119904119889 = 0 119872119901119897119910119903119889 = 13416 119896119873119898

λ119897119905 =

119871119911119894119911

119888105

[

1 +120(

119871119911119894119911ℎ119905119891

)

2

] 025


62

119871119911 = 1250 119898119898 119894119911 = 335 119898119898 ℎ = 300 119898119898 119905119891 = 107 119898119898




119873119904119889ꭕ119898119894119899

119873119901119897119903119889+119870119910 119872119910119904119889

119872119901119897119910119903119889+119870119911 119872119911119904119889119872119901119897119911119903119889


Avec

λ119910 =119871119910

119894119910=960

125= 768 rarr λ119910 =

768

939= 081

=gt 120583119910 = λ119910(2119861119898119910 minus 4) +119882119901119897119910 minus119882119890119897119910

119882119890119897119910= minus1134 + 0127 = minus1007 lt 09

120572 = 021 λ119910 = 081

empty119910 = 05 [1 + 120572119910(λ119910 minus 02) + λ1199102]

empty119910 = 05[1 + 021(081 minus 02) + 0812] = 089

ꭕ119910=

1


ꭕ119910= 0794 rarr 119870119910 = 1 minus


0794 times 538 times 2350= 101

120582119911 =125

335= 3731 =gt 120582119911 = 0397 rarr empty119911 = 0611 =gt ꭕ

119911= 092

ꭕ119898119894119899

= ꭕ119910= 0794

119873119901119897119903119889 =119860119891119910

1205741198980=5380 times 235

11= 114936 119896119873

119872119910119904119889 =151198821198712

8= 9313 119896119873119898

119872119901119897119910119903119889 = 13416 119896119873119898

119873119904119889 = 135119866 = 1337 119896119873

119896119910 = 101

119872119911119904119889 = 0

63

119873119904119889120594119898119894119899 119873119901119897119903119889

+119896119910 119872119910119904119889

119872119901119897119910119903119889+119896119911 119872119911119904119889119872119901119897119911119903119889

le 10

1337

0794 times 114836+101 times 9313

13416= 071 lt 1 119862119900119899119889119894119905119894119900119899 119907eacute119903119894119891119894eacute119890




64

Chapitre 4


41 Introduction




- Le pont roulant










poteaux de la halle

65





Puissances

N (t)

Porteacutee

L(m)



B

Chariot

K

Total

B+K

Rmax Rmin

125 18 085 520 1040 6809 1151 796 814 194


66


1 035 06 2 36



I 02 11 11 A-2















Groupes II






67
















119877119898119886119909 = 814 119870119873 119877119898119894119899 = 194 119870119873

Charges verticales

119877119881119898119886119909 = Ψ1 119877119898119886119909 = 115 times 814 = 8954 119870119873

119877119881119898119894119899 = Ψ2 119877119898119894119899 = 11 times 194 = 2134 119870119873


68

119877119871119898119886119909 = 119862 119877119898119886119909 = 02 times 814 = 1628 119870119873

119877119871119898119894119899 = 119862 119877119898119894119899 = 02 times 194 = 388 119870119873



1198771198671119898119886119909 = plusmn [0024(119870 + 119873 + 119861)119871

119890+ 0021(119873 + 119870)]

= plusmn [0024(1151 + 125 + 6809)18

36+ 0021(125 + 1151)]

1198771198671119898119886119909 = plusmn274 119905

1198771198671119898119894119899 = plusmn [0024(119870 + 119873 + 119861)119871

119890minus 0021(119873 + 119870)]

= plusmn [0024(1151 + 125 + 6809)18

36minus 0021(125 + 1151)]

1198771198671119898119894119899 = plusmn2168 119905


1198771198672119898119886119909 = plusmn [00052(119870 + 119873 + 5119861)119871

119890+ 0021(119873 + 119870)]

= plusmn [00052(1151 + 125 + 5 times 6809)18

36+ 0021(125 + 1151)]

1198771198672119898119886119909 = plusmn1526 119905

1198771198672119898119894119899 = plusmn [00052(119870 + 119873 + 5119861)119871

119890minus 0021(119873 + 119870)]

= plusmn [00052(1151 + 125 + 5 times 6809)18

36minus 0021(125 + 1151)]

1198771198672119898119894119899 = plusmn0953 119905




69





Rail

Poids

(Kgm)

B

(mm)

H

(mm)

P

(mm)

Section

A (cm2)

I x

(cm4)

I y

(cm4)

A55

318

55

65

150

407

178

337



70



119891119911 le 119891119886119889119898 =119897

750= 08 119888119898



119886 = (119897

2minus119890

4) = (

6

2minus36

4) = 21 119898



119891119911 =119901 119886 1198972

24119864119868(3 minus

4 1198862

1198972)

Avec

L= 6000 mm

a= 2100 mm

P=89540 N

E=21104 Nmm2

71

119868119910 ge119901 119886 1198972(31198972 minus 41198862)



119868119910 ge 421397625 1198981198984






119902 = 119866119901119900119906119905119903119890 + 119866119903119886119894119897 = 142 + 031 = 173 119896119899119898119897

119891119911 =119901 119886 1198972

24119864119868(3 minus

4 1198862

1198972) +

5 119902 1198974

384119864119868

119891119911 =89540 times 2100 times 60002


4 times 21002

60002) +




profileacute


G

Kgm

A cm2 h

mm

b

mm

tf

mm

tw

mm

Iy

cm4

Iz

cm4

Wply

cm3

Wplz

cm 3

HEB360 142 1806 360 300 225 125 43190 10140 2683 1032

72


119902 = 119866119901119900119906119905119903119890 + 119866119903119886119894119897 = 155 + 031 = 186 119870119873119898119897

119891119911 =119901 119886 1198972

24119864119868(3 minus

4 1198862

1198972) +

5 119902 1198974

384119864119868

119891119911 =89540 times 2100 times 60002


4 times 21002

60002) +






119905119908le 72휀

Avec

휀 = radic235

119891119910

298

135le 72radic

235

235 ⟹ 2207 le 72


119888

119905119891=1198872

119905119891le 10휀 ⟹

150

24= 625 le 10




profileacute


G

Kgm

A

cm2

h

mm

b

mm

tf

mm

tw

mm

Iy

cm4

Iz

cm4

Wply

cm3

Wplz

cm 3

HEB400 155 1978 400 300 24 135 57680 10820 3232 1104

73

119881119910119904119889 le 119881119901119897119903119889 119912119955119957 120787 120786 120788 (120787 120784120782)119914119914119924120791120789

119881119901119897119903119889 =119860119907119911 119891119910

radic3 1205741198980=6998 times 235

radic3 times 11= 863154 119873 = 86315 119870119873


119881119881 = 119877119881119898119886119909 times4119886

119897=8954 times 4 times 21

6= 12535 119870119873


119881119875119875 =119866 119897

2=186 times 6

2= 558 119870119873

Drsquoougrave 119881119910119904119889 = 135119881119875119875 + 15119881119881 = 19556 119870119873

119881119910119904119889 le 119881119901119897119903119889



Suivant (z-z)


119872119881 = 119877119881119898119886119909 times(6 minus

1198902)2

4119897= 8954 times

(6 minus362 )

2

4 times 6= 6581 119870119873119898


119872119875119875 =119866 1198972

8= 837 119870119873119898


119872119910119904119889 = 135119872119875119875 + 15119872119881 = 110 119870119873119898



119872119911119904119889 = 119872119867 =21198771198671119871

(119871

2minus119890

4)2

74

119872119911119904119889 = 119872119867 =2 times 274

6times (

6

2minus36

4)2

= 4028 119870119873119898




119873119904119889119873119901119897119903119889

+119872119910119904119889

119872119890119897119910+119872119911119904119889119872119890119897119911

le 1 120787 120785120790 ndash 119810119810119820120791120789

119873119904119889 = 15119877119871119898119886119909 = 15 times 1628 = 2442 119870119873

119872119890119897119910 =119908119890119897119910 119891119910

1205741198720= 61613 119872119890119897119911 =

119908119890119897119911 119891119910

1205741198720= 1541 119873119901119897119903119889 =

119860 119891119910

1205741198720= 422573

2442

422573+

110

61613+4028

1541= 044 le 1



Si 119889


Avec

휀 = radic235

119891119910= 1

119889

119905119908=298

135= 2207 lt 69





1205741198721


75



λ119897119905 =

119871119894119911

119888105

[

1 +120(

119871119894119911ℎ119905119891

)

2

] 025 = 6522 119808119821119821119812119831119812119809 119810119810119820120791120789

Avec 119871 = 600119888119898


λ119871119879 = [λ119897119905λ1] [120573119908]

05 휀 = radic235

119891119910= 1

λ119871119879 =6522

939= 0694

On calcule

ꭕ119871119879=

1


2 )le 1




ꭕ119871119879=

1

(079 + radic0792 minus 06942)= 0856


11= 59104 119870119873119898

119872119910119904119889 = 110 119870119873119898




76



119891119904119889 le 119877119910119877119889

Avec




120590119891119864119889 =119872119910119904119889

119882119890119897119910= 381 1198701198731198881198982

119878119910 = 2(ℎ119877 + 119905119891)radic[1 minus (1205741198720120590119891119864119889

119891119910119891)

2

] = 1751 119888119898

119877119910119877119889 =119878119910 times 119905119908 times 119891119910119908

1205741198720= 505 119870119873 gt 119891119904119889 = 119877119907119898119886119909 = 8954 119870119873




119891119904119889 le 119877119886119877119889

119891119904119889119877119886119877119889

+119872119878119889119872119888119877119889

le 1 119808119825119827 120787 120789120790 minus 119810119810119820120791120789

Avec

77

119877119886119877119889 =

051199051199082 (119864 119891119910119908)

05[(119905119891119905119908)05

+ 3(119905119908119905119891) (119878119904119889 )]

1205741198720 119808119825119827 120787 120789120789 minus 119810119810119820120791120789

119877119886119877119889 = 108284 119870119873

119891119904119889 = 15119877119871119898119886119909 = 15 times 1628 = 2442 119870119873

119872119888119877119889 =3232 times 103 times 235

11= 69047 119870119873119898

119891119904119889119877119886119877119889

+119872119878119889119872119888119877119889

=2442

108284+

110

69047 = 018 le 15




119887119890119891119891 le 119887 119808119825119827 120787 120789120791 minus 119810119810119820120791120789

119887119890119891119891 = radicℎ2 + 1198781199042 = 410 119898119898 gt 119887 = 300 119898119898




efforts suivants




Charge verticale


119901prime = 119876 119871 + 119877119898119886119909 (2 minus119890

119871) ψ


36

6) times 11

119901prime = 13651 119870119873


119901 = 135119876 119871 + 15119877119898119886119909 (2 minus119890

119871) ψ


36

6) times 11

119901 = 2031 119870119873

78

Charge horizontale

119875119867 = 15119877119867119898119886119909 (1 minus119890

119897)ψ


36

6) times 11 = 1808 119870119873




119891119911 le 119891119886119889119898 =119897

500


119891119911 =119901prime 1198893

3119864119868le 119891119886119889119898

119868119910 =500 119901prime 1198892

3119864ge 782667 1198881198984


79




119905119908le 72휀

Avec

휀 = radic235

119891119910

2486

71le 72radic

235

235 ⟹ 3501 le 72


119888

119905119891=1198872

119905119891le 10휀 ⟹

75

102= 735 le 10





119881119910119904119889 le 119881119901119897119903119889

Avec 119860119907119911 = 257 cm2

119881119901119897119903119889 =119860119907119911 119891119910

radic3 1205741198980=257 times 235

radic3 times 11= 317 119870119873

119881119904119889 = 119901 = 2031 lt 05119881119901119897119877119889


profileacute


G

Kgm

A

cm2

h

mm

b

mm

tf

mm

tw

mm

Iy

cm4

Iz

cm4

Wply

cm3

Wplz

cm 3

IPE 300 422 5380 300 150 107 71 8353 604 628 125

80


119872119888119903119889 =119908119901119897119910 119891119910

1205741198720=628 times 235

11= 13416 119870119873119898

119872119910119904119889 = 119901 119889 = 2031 times 085 = 172635 119870119873119898

119872119910119904119889 lt 119872119888119903119889




119872119888119903119889 =119908119901119897119910 119891119910

1205741198720=1019 times 235

11= 2177 119870119873119898

119872119910119904119889 = 119901 119889 = 2031 times 085 = 172635 119870119873119898

119872119910119904119889 lt 119872119888119903119889


17263


profileacute


G

Kgm

A

cm2

h

mm

b

mm

tf

mm

tw

mm

Iy

cm4

Iz

cm4

Wply

cm3

Wplz

cm3

IPE 360 571 727 360 170 127 8 16270 1043 1019 191

81



chemin de roulement

119891119911 le 119891119886119889119898 =119889

500= 017

119902 = 119902119868119875119864 360 = 571 119889119886119873119898119897

119891119911 =119901prime 1198893

3119864119868+119902 1198974

8119864119868= 0082 + 0021 = 0103 119888119898 lt 017 119888119898


82

Chapitre-5








dynamiques


83




119881 =119860119863 119876

119877119882



119863 =

25120578 0 le 119879 le 1198792

25120578(1198792119879)23 1198792 le 119879 le 3119904

25120578 (11987923)

23 (3119879)

53 119879 gt 3119904


84

120578 = radic7

(2 + 120585)ge 07



119879 = 119862119879 ℎ11987334 119917119926119929119924119932119923119916 (120786 120788)119929119927119912 119933120784120782120782120785




119876 = 1 +sum119875119902

6

1


85


119876 = 1 +sum119875119902

6

1

= 1 + 02 = 12


119899119894=1

Avec 119882119894 = 119882119866119894 + 120573119882119876119894




119881 =119860119863 119876

119877119882

119860 = 005 119863 = 25 119876 = 12 119877 = 4 119882 = 189475119896119873

119881119909 = 119881119910 =005 times 25 times 12

4times 189475 = 7105119896119873


119904119886119892=

125119860 (119860 +

119879

1198791(25120578

119876

119877minus 1)) 0 le 119879 le 1198791

25120578(125119860) (119876

119877) 1198791 le 119879 le 1198792

25120578(125119860) (119876

119877)(1198792119879)23

1198792 le 119879 le 30119904

25120578(125119860) (11987923)

23(3

119879)

53(119876

119877) 119879 gt 30119904

86



η = 100 A=005 1198791=015 1198792=050


87













88










89

ℎ

150=890

150= 594119888119898 sans vent

ℎ

125=890

125= 712119888119898 avec vent






Toiture 029 076 116 304


ℎ

100=1025

100= 1025 119888119898



90

Chapitre-6


61 Introduction





119872119910119904119889 = 21902 kNm

119881119904119889 =7249 kN

119873119904119889 =2018 kN

91

Profileacute


IPE 400 A cm2

hmm

b mm

119905f

mm

119905w mm

119868y

cm4

119868z Cm4

119908ply

cm3

119908plz

cm3

MATERIAU ACIER S235

8446 400 180 14 90 231284 131782 123832 2256




119888

119905119891=60

14= 59 lt 10휀 =gt 119888119897119886119904119904119890 1


119889

119905119908=98

9= 11 lt 72휀 =gt 119888119897119886119904119904119890 1





Si 119881119904119889 le 05119881119901119897119903119889 ⟹ 119872119904119889 le 119872119888119903119889 119912119955119957120787 120786 120789 119914119914119924 120791120789


119881119898119886119909 = 119881119904119889 =7248kN

119881119901119897119911119903119889 =

119860119907119911 (119891119910

radic3)

1205741198980=

4270235

radic311

= 526674119896119873

119881119904119889 = 7247 le 05119881119901119897119911119903119889 = 52667119896119873


92



119873119904119889 le 119872119894119899(025119873119901119897119903119889 05119860119908119891119910

1205741198720)


119873119904119889 = 2018119896119873

119873119901119897119903119889 le119860 119891

119910

1205741198720=8446 235

11= 180437119896119873

025119873119901119897119903119889 =451 119896119873

119860119908 = 119860 minus 2119887 119905119891 = 34061198981198982

05119860119908119891119910

1205741198720= 36382119896119873

119873119904119889 = 2018 le 36382119896119873



119872119888119903119889 = 119872119901119897119910119903119889 =119908119901119897119910 119891119910

1205741198720=1238320 235

11= 26455119896119873119898




120594119898119894119899 119873119901119897119903119889+119896119910 119872119910119904119889

119872119901119897119910119903119889+119896119911 119872119911119904119889119872119901119897119911119903119889



120594119911 119873119901119897119903119889+119896119871119879 119872119910119904119889

120594119871119879119872119901119897119910119903119889+119896119911 119872119911119904119889119872119901119897119911119903119889



120594119898119894119899 = 119872119894119899(120594119910 120594119911)


93

120594119910 =1

(120601119910 +radic1206011199102 minus 1205821199102 )

120601119910 = 05[1 + 120572119910(120582119910 minus 02) + 1205821199102]

120582119910= (120582119910

1205821)radic120573119860 =

120582119910

1205821

Avec 120573119860 = 1 Classe 1

1205821 = 939

120582119910 =05119868119910

119894119910=455

166= 274

120582119910=274

939= 029


ℎ

119887=400

180= 222 gt 12 119894119898119901119897119894119902119906119890 120572 = 021

120601 = 05[1 + 120572119910(120582119910 minus 02) + 1205821199102 ] = 055

120594119910 =1

(055 + radic0552 minus 0292)= 098


120594119911 =1

(120601119911 +radic1206011199112 minus 120582119911

2)

120601119911 = 05[1 + 120572119911(120582119911 minus 02) + 1205821199112]

120582119911 = (1205821199111205821)radic120573119860 =

1205821199111205821

Avec 120573119860 = 1 Classe 1

120582119911 =119868119911119894119911=200

395= 5063

120582119911 =5063

939= 054


94

ℎ

119887= 222 gt 12 (119911 minus 119911)119894119898119901119897119894119902119906119890 120572 = 034

120601 = 05[1 + 034(054 minus 02) + 0542 ] = 07

120594119911 =1

(07 + radic072 minus 0542)= 087

120594119898119894119899 = 119872119894119899(120594119910 120594119911) = 087




λ119897119905 =

119871119894119911

119888105

[

1 +120(

119871119894119911ℎ119905119891

)

2

] 025 = 4367 119808119821119821119812119831119812119809 119810119810119820120791120789

Avec

IPE400 119905119891 = 14119898119898 119894119911 = 395119888119898 ℎ = 400119898119898

119870 = 1 1198881=1134 Tableau B11 CCM97


1205821 = 939휀

휀 = radic235

119891119910= 1

120582119871119879 = [1205821198971199051205821] [120573119908]

05

120582119897119905 = 4367

120582119871119879 =4367

939= 046 gt 04



119873119904119889120594119911 119873119901119897119903119889

+119896119871119879 119872119910119904119889

120594119871119879119872119901119897119910119903119889+119896119911 119872119911119904119889119872119901119897119911119903119889


Calcul de 120594119871119879


95

implique 120594119871119879 = 094

Calcul de 119896119871119879


119870119871119879 = 1 minusμLT N119904119889

120594119911 119860 119891119910= 099 lt 15


Donc

119873119904119889=7249 kN 119872119910119904119889=219 kNm 119872119901119897119910119903119889=26455 kNm 120594119911=087 119872119901119897119911119903119889=4819kNm


119873119904119889120594119911 119873119901119897119903119889

+119896119871119879 119872119910119904119889

120594119871119879119872119901119897119910119903119889+119896119911 119872119911119904119889

119872119901119897119911119903119889


7249

087 180437+

099 219

094 26455= 055










96

119872119910119904119889 = 32083 119896119873119898

119881119904119889 = 120 119896119873

119873119904119889 = 602 119896119873

Profileacute


HEA320

A cm2

hmm

b mm

119905f

mm

119905w mm

119868y

cm4

119868z cm4

119908 ply

cm3

119908 plz

cm3

MATERIAU ACIER S235

12437 310 300 16 9 229286 698524 162823 70975




119888

119905119891=60

16= 375 lt 10휀 =gt 119888119897119886119904119904119890 1


119889

119905119908=98

9= 109 lt 72휀 =gt 119888119897119886119904119904119890 1





Si 119881119904119889 le 05119881119901119897119903119889 ⟹ 119872119904119889 le 119872119888119903119889 119912119955119957120787 120786 120789 119914119914119924 120791120789


119881119898119886119909 = 119881119904119889 =120kN

119881119901119897119911119903119889 =

119860119907119911 (119891119910

radic3)

1205741198980=4113 235radic3

11= 50731119896119873

97

119881119904119889 le 05119881119901119897119911119903119889




119873119904119889 le 119872119894119899(025119873119901119897119903119889 05119860119908119891119910

1205741198720)


119873119904119889 =602kN

119873119901119897119903119889 le119860 119891

119910

1205741198720=12437 235

11= 2656995 119896119873

025119873119901119897119903119889 = 664248119896119873

119860119908 = 119860 minus 2119887 119905119891 = 2837 1198981198982

05119860119908119891119910

1205741198720= 30304119896119873

119873119904119889 = 602119896119873 le 30304119896119873



119872119888119903119889 = 119872119901119897119910119903119889 =119908119901119897119910 119891119910

1205741198720=1628000 times 235

11= 3478119896119873119898




120594119898119894119899 119873119901119897119903119889+119896119910 119872119910119904119889

119872119901119897119910119903119889+119896119911 119872119911119904119889119872119901119897119911119903119889



120594119911 119873119901119897119903119889+119896119871119879 119872119910119904119889

120594119871119879119872119901119897119910119903119889+119896119911 119872119911119904119889119872119901119897119911119903119889



120594119898119894119899 = 119872119894119899(120594119910 120594119911)


98

120594119910 =1

(120601119910 +radic1206011199102 minus 1205821199102 )

120601119910 = 05[1 + 120572119910(120582119910 minus 02) + 1205821199102]

120582119910= (120582119910

1205821)radic120573119860 =

120582119910

1205821

Avec 120573119860 = 1 Classe 1

1205821 = 939

120582119910 =05119868119910

119894119910=05 890

1358= 3276

120582119910=3276

939= 034


ℎ

119887=310

300= 1 lt 12 (119910 minus 119910)119894119898119901119897119894119902119906119890 120572 = 034

120601 = 05[1 + 120572119910(120582119910 minus 02) + 1205821199102 ] = 058

120594119910 =1

058 + radic058 minus 034= 095


120594119911 =1

(120601119911 +radic1206011199112 minus 1205821199112)

120601119911 = 05[1 + 120572119911(120582119911 minus 02) + 1205821199112]

120582119911 = (1205821199111205821)radic120573119860 =

1205821199111205821

Avec 120573119860 = 1 Classe 1

1205821 = 939

120582119911 =119868119911119894119911=07 59

749= 055


ℎ

119887= 1 lt 12 (119911 minus 119911) 119894119898119901119897119894119902119906119890 120572 = 049

120601 = 05[1 + 049(055 minus 02) + 0552] = 073

99

120594119911 =1

073 + radic073 minus 055= 082

120594119898119894119899 = 119872119894119899(120594119910 120594119911) = 082


λ119897119905 =

119871119894119911

119888105

[

1 +120(

119871119894119911ℎ119905119891

)

2

] 025 = 3536

HEA320 119905119891 = 16119898119898 119894119911 = 749119888119898 ℎ = 310119898119898

119870 = 07 1198881 = 1134 Tableau B11 CCM97


1205821 = 939휀

휀 = radic235

119891119910= 1

120582119871119879 = [1205821198971199051205821] [120573119908]

05

120582119897119905 = 3536

120582119871119879 =3536

939= 037 lt 04 119901119886119904 119889119890 119903119894119904119902119906119890 119889119890 119889119890119907119890119903119904119890119898119890119899119905


119873119904119889120594119898119894119899 119873119901119897119903119889

+119896119910 119872119910119904119889

119872119901119897119910119903119889+119896119911 119872119911119904119889119872119901119897119911119903119889


Avec

119873119904119889 =602kN 119872119910119904119889=32083kNm 119872119911119904119889=049kNm 119872119901119897119910119903119889=3478kNm

119872119901119897119911119903119889=1516kNm 120594119898119894119899= 082 119873119901119897119903119889=26570kN 119896119910= 05 119896119911= 07

602

082 26570+05 32083

3478+07 049







100





(135G+15V1)


119873119904119889 =69837kN


Profileacute


2CAE (120x12)

A Cm2

hmm

b mm

Anet

Cm2

d

mm

MATERIAU ACIER S235

5508 120 248 4658 8



119873119904119889 le 119873119905119903119889 = 119872119894119899[119873119901119897119903119889 119873119906119903119889 119873119899119890119905119903119889]

101

119873119901119897119903119889 =119860 119891119910

1205741198720= 117671119896119873

119873119906119903119889 = 09119860119899119890119905 1198911199061205741198722

= 13719119896119873

119873119899119890119905119903119889 =119860119899119890119905 119891119910

1205741198720= 995118119896119873








102


119872119910119904119889 = 02 119896119873119898

119881119904119889 = 0048 119896119873

119873119904119889 = 5628 119896119873

Profileacute


IPE300

A cm2

hmm

b mm

119905f

mm

119905w mm

119868y

cm4

119868z cm4

119908ply

cm3

119908plz

cm3

MATERIAU ACIER S235

538 300 150 107 71 8356 746 628 125







Si 119881119904119889 le 05119881119901119897119903119889 ⟹ 119872119904119889 le 119872119888119903119889 119912119955119957120787 120786 120789 119914119914119924 120791120789


119881119898119886119909 = 119881119904119889 =0048kN

119881119901119897119911119903119889 =

119860119907119911 (119891119910

radic3)

1205741198980=2570 235radic3

11= 3169119896119873

119881119904119889 le 05119881119901119897119911119903119889




119873119904119889 le 119872119894119899(025119873119901119897119903119889 05119860119908119891119910

1205741198720)

103


119873119904119889 =5628kN

119873119901119897119903119889 le119860 119891

119910

1205741198720=5380 235

11= 114936 119896119873

025119873119901119897119903119889 = 28734 119896119873

119860119908 = 119860 minus 2119887 119905119891 = 2170 1198981198982

05119860119908119891119910

1205741198720= 23179119896119873

119873119904119889 = 5628119896119873 le 23179119896119873



119872119888119903119889 = 119872119901119897119910119903119889 =119908119901119897119910 119891119910

1205741198720=628000 times 235

11= 134163 119896119873119898




120594119898119894119899 119873119901119897119903119889+119896119910 119872119910119904119889

119872119901119897119910119903119889+119896119911 119872119911119904119889119872119901119897119911119903119889



120594119911 119873119901119897119903119889+119896119871119879 119872119910119904119889

120594119871119879119872119901119897119910119903119889+119896119911 119872119911119904119889119872119901119897119911119903119889



120594119898119894119899 = 119872119894119899(120594119910 120594119911)


120594119910 =1

(120601119910 +radic1206011199102 minus 1205821199102 )

120601119910 = 05[1 + 120572119910(120582119910 minus 02) + 1205821199102]

120582119910= (120582119910

1205821)radic120573119860 =

120582119910

1205821

104

Avec 120573119860 = 1 Classe 1

1205821 = 939

120582119910 =119871119910

119894119910= 960

125= 768

120582119910=768

939= 081


ℎ

119887=300

150= 05 lt 12 (119910 minus 119910)119894119898119901119897119894119902119906119890 120572 = 021

120601 = 05[1 + 120572119910(120582119910 minus 02) + 1205821199102 ] = 089

120594119910 =1

058 + radic058 minus 034= 079


120594119911 =1

(120601119911 +radic1206011199112 minus 1205821199112)

120601119911 = 05[1 + 120572119911(120582119911 minus 02) + 1205821199112]

120582119911 = (1205821199111205821)radic120573119860 =

1205821199111205821

Avec 120573119860 = 1 Classe 1

1205821 = 939

120582119911 =119868119911119894119911=125

335= 3731 120582119911 = 039


ℎ

119887= 1 lt 12 (119911 minus 119911) 119894119898119901119897119894119902119906119890 120572 = 021

120601 = 05[1 + 021(039 minus 02) + 0392] = 061

120594119911 =1

061 + radic061 minus 039= 092

120594119898119894119899 = 119872119894119899(120594119910 120594119911) = 079


105

λ119897119905 =

119871119894119911

119888105

[

1 +120(

119871119894119911ℎ119905119891

)

2

] 025 = 3433

IPE300 119905119891 = 107119898119898 119894119911 = 335119888119898 ℎ = 300119898119898

119870 = 1 1198881 = 1134 Tableau B11 CCM97


1205821 = 939휀

휀 = radic235

119891119910= 1

120582119871119879 = [1205821198971199051205821] [120573119908]

05

120582119897119905 = 3433

120582119871119879 =3433

939= 036 lt 04 119901119886119904 119889119890 119903119894119904119902119906119890 119889119890 119889119890119907119890119903119904119890119898119890119899119905


119873119904119889120594119898119894119899 119873119901119897119903119889

+119896119910 119872119910119904119889

119872119901119897119910119903119889+119896119911 119872119911119904119889119872119901119897119911119903119889


Avec

119873119904119889 =5628kN 119872119910119904119889=02kNm 119872119911119904119889=018kNm 119872119901119897119910119903119889=134163kNm

119872119901119897119911119903119889=267kNm 120594119898119894119899= 079 119873119901119897119903119889=1149kN 119896119910= 1 119896119911= 1

5628

079 1149+

02

134163+018



106

Chapitre-7


71 Introduction










au poteau

107




119872119904119889 = 28961119896119873119898 119873119904119889 = 17878119896119873 119881119904119889 = 8941119896119873




119905 = 119872119894119899(119905119891 119905119901119897119886119905119894119899119890) = 135119898119898

Avec





12119889O = 24 119898119898 le 1198901 le 12119905 =186 119898119898 ⟹ 1198901 = 110 119898119898

15119889O = 30 119898119898 le 1198902 le 12119905 = 186 119898119898 ⟹ 1198902 = 105 119898119898

22119889O = 44 119898119898 le 1199011 le 14119905 =217 119898119898 ⟹ 1199011 = 100 119898119898


108






IPE 400 119905f = 135 119898119898 119905w = 86 119898119898

119886min= 26 le twle119886max= 8

119886min =35 le tf le119886max= 8







sum119897 = 2119887 + 4(119887 minus 119905119908) = 2180 + 4(180 minus 86) = 1045119898119898

119865119908119903119889 =7times 1045 times 360

radic2= 1862119896119873

119873119904119889 =119872119904119889

ℎ=120784120790120791 120788120783

120782 120791= 120785120784120783 120789120790





Avec 120573119908 = 125 120574119872119882 = 08


109

i

sum119897 = 4ℎ119894 = 4 times 373 = 1492119898119898

119865119907119903119889 =7 times 1492 times 360

radic3= 217074119896119873



119873119894 =119872119904119889 119889119894sum119889119894

2


119909 = 119905119891radic119887

119905119908= 135radic

180

86= 6176



- 1198891 = 712 119898119898

- 1198892 = 612 119898119898

- 1198893 = 512 119898119898 ⟹ Σ 1198892 = 129 119898sup2

- 1198894 = 312 119898119898

- 1198895 = 212 119898119898

- 1198896 = 112 119898119898


1198731 =28961 times 0712

129= 15984119896119873



1198731 = 119899119865119907119903119889 ⟹ 119860119904 ge119873119904119889

06 times 119891119906119887 times 119899=

15984

06 times 800 times 2= 16651198981198982



M18 18 20 254 192 800 291



110




119865119901 = 07 times 119891119906119887 times 119860119904 = 06 x 800 x 192 = 10752kN

119872119903119889 =119899 119865119901 sum119889119894

2

119889119894=2 times 10752 times 129

0712= 3896 gt 119872119904119889 = 28961 119896119873119898




119865119907119904119889 le 119865119904119903119889 =119870119904 119898 120583

1205741198722(119865119901119888119889 minus 08119873119904119889) 119917119926119929119924119932119923119916 120788 120789 minus 119914119914119924120791120789

Avec

119870119904 = 10 ∶ Trous normaux



119865119904119903119889 = 024 (10752 minus 08 times15984

2) = 1046119896119873

119865119907119904119889 =8941

12= 745119896119873 lt 1046119896119873




1205741198722 119813119822119825119820119828119819119812 120788 120784 minus 119810119810119820120791120789



125= 213157 119896119873

119865119905119904119889 =119865119901

2=10752

2= 5376119896119873 lt 119861119901 119903119889 = 213157 119896119873


111



1205741198722 119827119808119809119819119812119808119828 120788 120787 120785 ndash 119810119810119820120791120789

Avec 119870119904 = 25

120572119887 = min (119890131198890

(119901131198890

minus 025) 119891119906119887119891119906 1) = 1



125= 46008119896119873 gt

11986511990711990411988912

= 745119896119873



119865119907 le 119865119905119903119889 = 119905119908119888 1198871198901198911198911198911199101205741198720

Avec




⟹ 119865119905119903119889 = 9 times 90times23511

= 173045 119896119873


119865119907 =119872119904119889

ℎ minus 119905119891=28961

029= 99865 gt 119865119905119903119889 = 173045119896119873




119873119904119889 le 119865119888119903119889 =119896119888 120588 119887119890119891119891 119905119908119888 119891119910

1205741198721radic1 + 13 (119887119890119891119891ℎ)2

119887119890119891119891 = 119905119891119887 + 2119886119901radic2 + 5(119905119891119888 + 119903119888) + 2119905119901

Avec

112






119887119890119891119891 =25014mm



120590119888119904119889 =119881119904119889119860+119872119904119889

119882119890119897119910=8941 times 103

1244+28961 times 106

1479= 196533119872119875119886

120590119888119904119889 = 19653119872119875119886 lt 119891119910 = 235119872119875119886 ⟹ 119896119888 = 1


119901 = 0932radic119887119890119891119891 119889119908119888 119891119910

119864 1199051199081198882= 0932radic


21 times 104 times 092= 254

119901 gt 072⟹ 120588 =119901 minus 02

1199012=254 minus 02

2542= 036


11 radic1 + 13 (250131

)2

= 12741119896119873

119873119904119889 = 1119873119894 =119872119904119889 sum119889119894sum119889119894

2 =29861 times 247

129= 57175119896119873





119865119907 le 119881119903119889 = 058119891119910 ℎ1199051199081205741198720


11= 3457119896119873


119865119907 =119872119904119889ℎ minus 119905119891

= 46216 119896119873 gt 119881119903119889 = 3457119896119873 119888119900119899119889119894119905119894119900119899 119899119900119899 119907eacute119903119894119891119894eacute119890


113

119865119907 = 46216119896119873 le 119881119903119889 = 058119891119910 ℎ119905119908 + 04

1205741198720= 058 235 31

(09 + 04)

11= 49935119896119873







logiciel robot

119872119904119889 = 15135119896119873119898 119873119904119889 = 1324119896119873 119881119904119889 = 273119896119873






119905 = min(119905119891 119905119901119897119886119905119894119899119890) = 135119898119898


114









IPE400

tf = 135 mm tw = 86 mm






radic2 times 119861119908 120574119898119908


Donc

119865119908119903119889 =119860 times sum119871 times 119891119906


radic2 times 1= 133083119896119873

119873119904119889 =119872119904119889ℎ

=7283

08= 9103119896119873

115

119873119904119889 = 9103 le 119865119908119903119889 = 1330119896119873






Donc

119865119907119903119889 =119886 times sum119871 times 119891119906


radic3 times 1= 155053119896119873



119873119894 =119872119904119889 119889119894sum119889119894

2


119909 = 119905119891radic119887

119905119908= 135radic

180

86= 6176119898119898


- 1198891 = 700 119898119898

- 1198892 = 600 119898119898

- 1198893 = 500 119898119898 ⟹ Σ1198891198942

= 124 119898sup2

- 1198894 = 300 119898119898

- 1198895 = 200 119898119898

- 1198896 = 100 119898119898


1198731 =119872119904119889 times 119889119894Σ119889119894

2 =15135 times 070

124= 4111119896119873



116


1198731 = 119899 119865119907 ⟹ 119860119904 ge119873119904119889

05 times 119891119906119887 times 119899=

13240

05 times 800 times 2= 16551198981198982



M18 18 20 254 192 800 291




119865119901 = 07 times 119891119906119887 times 119860119904 = 10752 119896119873

119872119903119889 =119899 119865119901sum119889119894

2

119889119894=2 times 10752 times 124

07= 38092 gt 119872119904119889 = 15135119896119873119898




119865119907119904119889 le 119865119904119903119889 =119870119904 119898 120583

1205741198722(119865119901119888119889 minus 08119873119904119889) 119813119822119825119820119828119819119812 120788120789 ndash 119810119810119820120791120789

Avec




119865119904119903119889 = 024 ( 10752 minus 08 times 1324) = 2326119896119873

119865119907119904119889 =273

12= 023 lt 119865119904 119903119889 = 2326119896119873




1205741198722 119813119822119825119820119828119819119812 120788 120784 ndash 119810119810119820120791120789

Avec


117


125= 31578119896119873

119865119905119904119889 =119865119901

2= 5376 lt 31578119896119873




1205741198722 119827119808119809119819119812119808119828 120788 120787 120785 ndash 119810119810119820120791120789

Avec Ks = 25

120572119887 = min (119890131198890

(119901131198890

minus 025) 119891119906119887119891119906 1) = 1


11986511990711990411988912


125= 5184 119896119873







119865119907119904119889 =119873119904119889

119899119887119903 119889119890 119887119900119906119897119900119899=131

3= 4366 le 119865119907119903119889

118


1205741198722⟹ 119860119904 ge

1205741198722 times 119865119907119903119889

06 times 119891119906119887119909 119898=125 times 43666

06 times 800 times 2= 56851198981198982


















119873119898119886119909 le 119865119908119903119889 =119886 sum119897 119891119906

119861119908 120574119898119908 radic(3 minus 1199041198941198991205722)


120572= 30gtgtgt 11990411989411989930o = 05

119865119908119903119889 =5 times 700 times 360



119



1205741198722 119827119808119809119819119812119808119828 120788 120787 120785 minus 119810119810119820120791120789


120572119907= 06



125= 12057119896119873

119865119907119904119889 =119873119904119889

3=3124

3= 10413 le 119865119907119903119889 = 12057119896119873




1205741198722 119827119808119809119819119812119808119828 120788 120787 120785 minus 119810119810119820120791120789

Avec

Ks = 25

120572119887 = min (119890131198890

(119901131198890

minus 025) 119891119906119887119891119906 1) = 092



125= 33914119896119873 gt 119865119907119904119889 = 4366119896119873




119873119898119886119909 le 119881119890119891119891119903119889 =119860119899119905 119891119910

1205741198722+119860119899119907 119891119910

radic3 1205741198722 119812119810120785 119849119834119851119853119842119838120783 minus 120790sect120785120783120782 120784

Avec


119860119899119890119905 = (119897

2minus11988902) 119905 = (60 minus 9)12 = 6121198981198982


120

119860119899119907 = (1198901 + 21199011 minus 251198890)119905 = (50 + 140 minus 45)12 = 17401198981198982

⟹ 119881119890119891119891119903119889 =612 times 235

125+1740 times 235

radic3 times 125= 303918119896119873 gt

119873119904119889

2= 655119896119873








119865119907119904119889 =119877119907119911

119899119887119900119906119897119900119899119904=36

2= 18 119896119873

119865119907119903119889 =06 times 119860119904 times 119891119906119887

120574119872119887⟹119860119904 ge

120574119872119887 times 11986511990711990311988906 times 119891119906119887

=11 times 18000

06 times 800= 41251198981198982



119865119907119903119889 =06 times 119860119904 times 119891119906119887

120574119872119887=06 times 58 times 800

11= 253119896119873 gt 119865119907119904119889 = 18119896119873


119865119905119903119889 =09 times 119860119904 times 119891119906119887

120574119872119887=09 times 58 times 800

11= 379119896119873

121

119865119907119903119889 =06 times 119860119904 times 119891119906119887

120574119872119887= 253119896119873

119865119907119904119889119865119907119903119889

+119865119905119904119889

14 119865119905119903119889= 052 lt 1 119862119900119899119889119894119905119894119900119899 119907119890119903119894119891119894eacute119890


122

Chapitre-8




123








119865119888119896=30 MPa

119891119888119889 =085 times 119865119888119896125

= 204 MPa


119865119895119889 = 120572120573119895 119891119888119889



119865119895119889 = 120572 120573119895 119891119888119889 = 15 times2

3times 17 = 204 119872119875119886


1198601198620 ge119873119904119889119891119888119889

=148960

204

1198601198620 ge 7266341198981198982


bp ge b+2tf = 190+2times155 = 221 mm

hp ge h+2tf = 310+2times155 = 341 mm

On prend

bp =600 hp=620



124


119862 = 119905 (119891119910119901

3119891119895119889 1205741198720)

05

= 30(235


= 5605 119898119898

119862 = 5605 lt(ℎ minus 2119905119891)

2= 1395 119898119898




gorge (a) Annexe H







119890 =119872119904119889119873119904119889

= 041 119898 gt 119885119879 = 0195 119898







125


Ougrave

119871119890119891119891 = min(119887119901 119887119891119888 + 2119888) = min(600 300 + 2 times 4671) = 39342 119898119898

119887119890119891119891 = min (119888ℎ1198882minus 119905119891119888) + 119905119891119888 +min (119888

ℎ119901 minus ℎ119888

2)

119887119890119891119891 = min (4671310

2minus 155) + 155 + min (4671

620 minus 310

2) = 10892 119898119898

⟹ 119865119888119903119889 = 204 times 10892 times 39342 = 874166 119896119873


119865119907119903119889 = 119865119891119903119889 + 119899119887 119865119907119887119903119889


119865119891119903119889 = 02119873119904119889 = 1214 119896119873





119865119907119887119903119889 =120572119888119887 119891119906119887 119860119904

1205741198722

Avec 120572119888119887 = 044 minus 00003119891119910119887 = 0248


126

119865119907119887119903119889 =0248 times 800 times 561

125= 8904 119896119873

⟹ 119865119907119903119889 = 1214 + 8 times 8904 119896119873 = 72446 119896119873




Avec 120573119908 =08 120574119898119908 = 125 119886 = 6 mm


sum119897 = 470 119898119898

119865119908119903119889 =6 times 470 times 360

radic3= 58612 119896119873

119881119904119889 = 9773 119896119873 lt min(119865119907119903119889 119865119908119903119889) = 58612 119896119873





W= 150 mm e = 55 mm ex = 40 mm mx = 40 mm


119897119890119891119891119888119901 = 119898119894119899 2120587119898119909 = 25132 119898119898

120587119898119909 +119882 = 27566 119898119898120587119898119909 + 2119890 = 23566 119898119898

⟹ 119897119890119891119891119888119901 = 23566 119898119898

127


119897119890119891119891119899119888 = 119898119894119899

4119898119909 + 125119890119909 = 210 119898119898

2119898119909 + 0625119890119909 +119882

2= 180 119898119898

2119898119909 + 0625119890119909 + 119890 = 160 119898119898119887119901

2= 150 119898119898

⟹ 119897119890119891119891119899119888 = 150 119898119898


119865119905119886119899119888119903119889 = min[119865119905119887119900119899119889119903119889 119865119905119903119889]


119865119905119903119889 = 09 times119860119904 times 119891119906119887120574119898119887


125= 32314 119896119873



119865119887119889 =036radic119891119888119896

120574119888=036 times 547

15= 1313 119872119875119886


119865119905119887119900119899119889119903119889 =120587 119889 119897119887 119891119887119889

120572

Avec

1198971 = 20119889 = 600 119898119898

119903 = 3119889 = 90 119898119898

1198972 = 20119889 = 600 119898119898






07= 52929 119896119873

119865119905119886119899119888119903119889 = 119898119894119899[52929 32314] = 32314 kN

128




Lb = 8d + em +tp + twa + 05k

Avec







119871119887lowast =

881198981199093 119860119904

1198971198901198911198911 1199051199013 =


150 times 253= 13480 119898119898 lt 119871119887 = 312 119898119898




119898119901119897119903119889 =1199051199012 119891119910119901

41205741198720=252 times 235

4 times 11= 3338119896119873


Mode 1 1198721199011198971119903119889 = 119898119901119897119903119889 times 1198971198901198911198911 = 3338 times 015 = 5007119896119873119898

1198971198901198911198911 = min(119897119890119891119891119888119901 119897119890119891119891119899119888) = 150 119898119898


129




Mode 1-2

1198651199051minus2119903119889 =21198721199011198971119903119889

119898119909=2 times 5

004= 250 119896119873

Mode 3

1198651199053119903119889 = 2119865119905119903119889119886119899119888ℎ119900119903 = 2 times 32314 = 646280 119896119873

Mode 4

1198651199054119903119889 =119887119890119891119891119905 119905119908 119891119910

1205741198720=150 times 9 times 235

11= 288409119896119873

Drsquoougrave

119865119905119903119889 = min(1198651199051minus2119903119889 1198651199053119903119889 1198651199054119903119889) = 250 119896119873




119885119879119890119873minus 1

119865119879119903119889 times 119885

119885119862119890119873+ 1

) 119812119810120785 ndash 120783 120790 119827119808119809119819119812119808119828 120788 120789

119885 = 119885119879+119885119862 = 195 + 155 = 350119898119898

⟹119872119903119889 = 5646 119896119873119898 lt 6207119896119873119898



821 Introduction




- Le site (S3)



130




ELU 119872119880 = 6207119896119873119898 119873119880 = 9773119896119873

ELS 119872119878 = 4136119896119873119898 119873119878 = 7960119896119873




119886 = 119886119901 + 119888 = 062 + 02 = 082 119898


119860

119861=119886

119887= 1025 ⟹ 119860 = 1025119861



119890 =119872119904

119873119904= 052119898



120590119898119886119909 =119873

119860119861(1 +

6119890

119861) le 120590119904119900119897


368B2 - B - 312 ge 0 ⟹ B ge0765m



131

119889 = max (119861 minus 119887

4119860 minus 119886

4) = max (005 0295)

On prend d= 45 cm



On a

119890 = 052 gt119860

6= 041


3120590119898119886119909 1205901198981198941198994

lt 120590119904119900119897

Avec

120590119898119894119899 =119873

119860119861(1 minus

6119890

119860) =

14896

2(1 minus

041

2 ) = 62191198961198731198982

120590119898119894119899 =119873

119860119861(1 +

6119890

119860) =

14896

2(1 +

041

2 ) = 86771198961198731198982

3120590119898119886119909 120590119898119894119899

4= 6835 1198961198731198982 lt 120590119904119900119897 = 180 119896119873119898

2



119890 =119872

119873= 052 119898 lt

119860

4= 062 119898




119890 gt119886

6 119890 gt

119860

24


119860119886 =1198721119911 119904119905

132

1198721 = (119860

2minus 035119886)

2

(1 +119890

119860+14 times 119890 times 119886

1198602)1198731199042119860

1198721 = 2788119896119873119898

Avec 119911 = 09d =40cm

119904119905 = min (2

3119891119890 110radic12057811989111990528) =20163 MPa

11989111990528 = 00611989111988828 + 06 = 24 119872119875119886 120578 = 16 119867 119860 Donc

119860119886 =2788 times 106

400 times 20163= 345 1198881198982


119860119887 =119873prime(119861 minus 119887)

8119889 119904119905

Avec

119873prime = 119873119904 (1 +3119890

119860) = 796 (1 +

3 times 052

25) = 2993119896119873

119904119905 = min (2

3119891119890 110radic12057811989111990528) = 20163119872119875119886

11989111990528 = 00611989111988828 + 06 = 24119896119873 120578 = 16 119867 119860

Donc 119860119887 = 071198881198982


119860119886 =1198721119911 120590119904119905

1198721 = (119860

2minus 035119886)

2

(1 +119890

119860+14 times 119890 times 119886

1198602)1198731199062119860

1198721 = 349119896119873119898

Avec 119911 =09d = 40 cm

120590119904119905 =119891119890120574119904=400

115= 3478119872119875119886

Donc

133

119860119886 =349 times 106

400 times 3478= 251198881198982


119860119886 =119873119906(119861 minus 119887)

8119889 120590119904119905

Avec

119873prime = 119873119906 (1 +3119890

119860) = 23833119896119873

Donc 119860119887 = 1621198881198982


119860119898119894119899 = 023 times11989111990528119891119890

times 119860 times ℎ119905 = 17251198881198982

Sens B

119860119898119894119899 = 023 times11989111990528119891119890

times 119861 times ℎ119905 = 691198881198982



A (cm2) St (cm)

A 345 1725 10T16 201 25 B 07 69 7T16 1407 25



134



119873119905 = (119873

120572) ge 20 119896119873 [119825119823119808120791120791 119855 120784120782120782120785 119808119851119853 120783120782 120783 120783 119835]


119873119905 =14896

12= 1241119896119873

ELS

119873119905 =796

12= 663119896119873


119860119904119905 =119873119905120590119904119905

ELS

119860119904119905 =663

348= 0191198881198982

ELU

119860119904119905 =1241

348= 0351198881198982





119860119904119905 = 0905 le 119860119904 = 6791198881198982


135


120601119898119894119899 le 119898119894119899 (ℎ

35120601119897119898119894119899

119887

10) = 08 119888119898

On prend 120601119905 =8mm


On prend St=10cm


136


137

ANNEXE - 1

138

139

140

ANNEXE - 2

141

ANNEXE - 3

142

143

ANNEXE ndash 4

144

145

ANNEXE ndash 5






























































































































Liste des tableaux

















LISTE DES NOTATIONS

Majuscules latines








16

Chapitre-1


11 Introduction


17



18

Action

permanente (γG)




Effet favorable

γGinf

10 1 0


γGsup

135 15 15




135119866119896119895 + 15119876119896119898119886119909





1 119866119896119895 + 150119882minus


sum119866119896119895119895

+ 119876119896119898119886119909

119866119896119895 + 119876119896119898119886119909


sum119866119896119895119895

+ 09sum119876119896119894119894gt1

119866119896119895 + 09119876119896119898119886119909 + 09119878 119866119896119895 + 09119876119896119898119886119909 + 09119882


19










20




21






22




23

Chapitre-2


21 Introduction










24

- Effet du site








Ouargla (Zone 4)




Kt=017 Z0=001m Zmin=1m ξ=044






Avec




119902119901(119885) = 119902119903119890119891 times 119862119890

Avec

- 119902ref = 575 119889119886119873119898sup2


2(119885) times [1 + 7119868119907] 119825119821119829120784120782120783120785 119836119841119834119849119842119853119851119838 120784 120786 sect120784 120786 120784 119834


25


119862119903(119911)

119870119905 119871119899 (1199111198981198941198991199110

) 119901119900119906119903 119911 lt 119911119898119894119899

119870119905 119871119899 (119911

1199110) 119901119900119906119903 119911119898119894119899 le 119911 le 200119898


)=0783


Zo)=1178

On retient 119862119903= 1178


119868119907(119911)

1

119862119905(119911) 119871119899 (119911

1199110) 119901119900119906119903 119911 gt 119911119898119894119899

1

119862119905(119911) 119871119899 (1199111198981198941198991199110) 119901119900119906119903 119911 le 119911119898119894119899

Pour z gt zmin 119868119907(119911) =1

1Ln(1

001)= 0217

Pour z lt zmin 119868119907(119911) =1

1Ln(1025

001)= 0144



119862119890(119911119895) = 119862119903(119911119895)2[1 + 7 119868119881]

Pour z gt zmin

119862119890(119911) = 11782 times 12 times [1 + 7(0144)] = 2786

Pour z lt zmin

119862119890(119911) = 07832 times 12 times [1 + 7(0217)] = 154


Avec

26

- 119902119903119890119891 = 575 119889119886119873119898sup2



qp = 160195Nm2 = 16 kNm2





- b=30 m

- d=36 m

- h=89 m


e = min (d 2h)


Donc e = 2x1025 = 205m



27



119862119901119890 = 1198621199011198901 119878119894 119878 le 11198982

119862119901119890 = 1198621199011198901 + (11986211990111989010 minus 1198621199011198901) times 11989711990011989210(119878) 119878119894 11198982 lt 119878 lt 101198982

119862119901119890 = 11986211990111989010 119878119894 119878 ge 101198982



Zone


Parois sous le vent


Cpe10 -10 -08 -05 +08 -03


Versant de Toiture




28







le tableau suivant


853deg F G H

-237 -123 -083



- Parois verticales


-b=36 m

29

-d=30 m

-h=1025


e=Min (b 2h) = Min (36 205) = 205 m





30

Zone


Parois sous le vent








31




853deg -22 -192 -183 -067 -057






2(5 times 4)

30 times 89= 014 = 14


μ119901 =120

160= 075



Pour μ119901=075 on lit 119862119901119894 =-016

32




2 times (5 times 4)

36 times 9575= 0116 = 116


Pour μ119901=075 rarr 119862119901119894 =-02

33





Direction V1 V3


A 1602 -10 -0154 -0846 -135529

B 1602 -08 -0154 -0646 -103489

C 1602 -05 -0154 -0346 -55429

D 1602 +08 -0154 +0954 +152831

E 1602 -03 -0154 -0146 -23389


34

Toiture


F 1602 -237 -0154 -2276 -355003

G 1602 -123 -0154 -1076 -172375

H 1602 -084 -0154 -0676 -108295

Z1 1602 -1 -0154 -0846 -135529

Z2 1602 -06 -0154 -0446 -71449


Direction V2 et V4

Parois verticales


A 1602 -10 -0162 -0838 -134247

B 1602 -08 -0162 -0638 -102207

C 1602 -05 -0162 -0338 -54147

D 1602 +08 -0162 +0962 +154112

E 1602 -03 -0162 -0138 -22107


35

Toiture


Finf 1602 -12 -0162 -1038 -1662876

Fsup 1602 -22 -0162 -2038 -3264876

G 1602 -183 -0162 -1668 -2672136

H 1602 -067 -0162 -0508 -813816

I 1602 -057 -0162 -0408 -653616









9= 015




q1= 300 Nml

q2= 500 Nml



36











- Epaisseur 50 mm

- Largeur 1000 mm





Selon le DTR BC22




37

119902 =8119875

3119871= 044 119896119873119898

119902 = 444 119889119886119873119898













38

Chapitre-3





deacutefavorable

39

(minus354 times5125


0875

6) = minus32754 1198891198861198731198982

Qeq (vent) = 3276 daN1198982















40



41


Vzsd =119902119906119911 times 119897

2=1878 kN

Mysd=119902119906119911 times 119897

2

8=2817 kNm

Mzsd=119902119906119910 times 119897

2

8=081 kNm



IPE 180 A Cm2

h mm

b mm

119905f

mm 119905w

mm 119868y

Cm4

119868z

Cm4

119908ply cm3

119908plz cm3

MATERIAU ACIER S235

239 180 91 8 53 1317 101 146 346




4

384 times 119864 119868119910lt

119897

200=



119897

200= 3 119862119900119899119889119894119905119894119900119899 119907eacute119903119894119891119894eacute119890

Plan z-z

5 times 119902119904119910 times 1198974

384 times 119864 119868119911lt

119897

200=



119897

200= 3 119862119900119899119889119894119905119894119900119899 119907eacute119903119894119891119894eacute119890

42




1205741198721 gt 119872119910119904119889 = 2817 119896119873119898

Calcul de 119872119887119903119889




λ119871119879 =

119871119894119911

119888105

[

1 +120(

119871119894119911ℎ119905119891

)

2

] 025

Avec


(Tableau B12 CCM97)

iz =224mm tf =85mm

L=Lz=3000mm h=200mm

λ119871119879 =

119871119894119911

119888105

[

1 +120(

119871119894119911ℎ119905119891

)

2

] 025 = 9457 rarr λ119871119879 =

989

939= 1007

rarr =1092

43


rarr ꭕ119871119879=

1


2)= 066 le 1

rarr 119872119887119903119889 =ꭕ119871119879times 120573

119908times 119882119901119897119910 times 119891119910

1205741198721

=066 1 166 235

11= 234 119896119873 119898








119872119872119860119883 =119901prime 119897

3=119901 1198972

8⟹ 119901 =

8 119901prime

3119897=800

18= 4444 119889119886119873119898119897

44


(ANNEXE ndash 1)

Soit

119876119890119902 =327 + 1082

2= 2176 1198891198861198731198982









45



Vzsd =119902119906119911 times 119897

2=186 kN

Mysd=119902119906119911 times 119897

2

8=279 kNm

Mzsd=119902119906119910 times 119897

2

8=0855 kNm

46



IPE 200 A Cm2

h mm

b mm

119905f

mm 119905w

mm 119868y

Cm4

119868z

Cm4

119908ply cm3

119908plz cm3

MATERIAU ACIER S235

285 200 100 85 56 1943 142 221 446




4

384 times 119864 119868119910lt

119897

200=



119897

200= 3 119862119900119899119889119894119905119894119900119899 119907eacute119903119894119891119894eacute119890

Plan z-z

5 times 119902119904119910 times 1198974

384 times 119864 119868119911lt

119897

200=



119897

200= 3 119862119900119899119889119894119905119894119900119899 119907eacute119903119894119891119894eacute119890




1205741198721 gt 119872119910119904119889 = 279 119896119873119898

Calcul de 119872119887119903119889

47




λ119871119879 =

119871119894119911

119888105

[

1 +120(

119871119894119911ℎ119905119891

)

2

] 025

Avec


(Tableau B12 CCM97)


-L=Lz=6000mm -h=200mm

λ119871119879 =

119871119894119911

119888105

[

1 +120(

119871119894119911ℎ119905119891

)

2

] 025 = 989 ⟶ λ119871119879 =

989

939= 105

rarr =114


rarr ꭕ119897119905=

1


2)= 063 le 1

rarr 119872119887119903119889 =ꭕ119897119905times 120573

119908times 119882119901119897119910 times 119891119910

1205741198721


11= 2974119896119873119898



48


Avec

119881119901119897119911119903119889 =

119860119907119911 (119891119910

radic3)

11 119890119905 119860119907119911 = 1400 1198981198982

Donc

05119881119901119897119911119903119889 = 05

1400 (235

radic3)

11= 8634 119896119873



Si 119889


CCM97 art 561(1)

119889

119905119908 =

159





(119872119910119904119889

119872119901119897119910119903119889)

120572

+ (119872119911119904119889119872119901119897119911119903119889

)

120573

le 1 119912119955119957 120787 120786 120790 (120783120783)119914119914119924 120791120789


119872119901119897119910119903119889 =119882119901119897119910 times 119891119910

11=221 times 235

11= 4721 119896119873119898

119872119901119897119911119903119889 =119882119901119897119911 times 119891119910

11=446 times 235

11= 952 119896119873119898

119872119910119904119889 = 279 119896119873119898

119872119911119904119889 = 0855 119896119873119898

(279

4721)2

+ (0855

952) = 044 lt 1 119888119900119899119889119894119905119894119900119899 119907eacute119903119894119891119894eacute119890

49











Effort rampant


Lrsquoexcentrement


2 (119887

2) le 119905 le 3(

119887

2)


50

2 (10

2) = 10 le 119905 le 3(

10

2) = 15

On prend t=10 cm


119877119911 = 119902119906119911 times119897

2= 6 times

6

2= 18 119896119873

119877119910 = 119902119906119910 times119897

2= 054 119896119873


119877119911 = 18 times 2 = 36 119896119873

119877119910 = 054 times 2 = 108 119896119873


119872119877 = 119877119911 times 119905 + 119877119910 timesℎ

2= 36 times 10 + 108 times 10 = 3708 119896119873 119888119898 = 37119896119873119898


119872119890119897119877119889 =119908119890119897 times 119891119910

1205741198720 119912119955119957 120787 120786 120787 120783 (120784)119914119914119924120791120789

119872119890119897119877119889 =119908119890119897 times 1198911199101205741198720

=gt 119908119890119897 ge119872119890119897119877119889 times 1205741198720

119891119910=gt 119908119890119897 ge

00037 times 11

235

= 173 times 10minus51198983

119908119890119897 = 17321198881198983




119908119890119897 =119887 1198902


6 times 1732

119887= radic

6 times 1732

180

119890 ge 076


Donc on prend e=1cm

51





















52












qsy =(133 + 5) times 125=2288daNml

qsy = 0228 kN

quy=135G=03kN



W += 1541 daN m2


quz=15W

quz=288kN

53



qsz=19262daN=192kN


119891119911 =5 times 119902119904119911 times 119897

4

384 times 119864119910 times 119868le 119891119886119889119873 =

119897

200=600

200= 3 119888119898

119868119910 ge5 times 192 times 6004



Profileacute


UPN 140 A Cm2

h mm

b mm

119905f mm

119905w mm

Iy

Cm4

Iz

Cm4

119908pSy

cm3

119908pSz

cm3

MATERIAU ACIER S235

20 140 60 10 7 605 627 103 283







qsy =(133 + 5) times 125 +1568 = 3856daNml

qsy = 038 kN

quy=135G

quy =053kN


qsz=192kN

quz=15W

quz=288kN

54




119888

119905119891=60

10= 6 lt 10휀 =gt 119888119897119886119904119904119890 1


119889

119905119908=98

7= 14 lt 72휀 =gt 119888119897119886119904119904119890 1


(119872119910119904119889

119872119890119897119910119877119889)

1

+ (119872119911119904119889

119872119890119897119911119877119889)1

le 1


119872119910 =119902119906119911 times 119897

2

8=288 times 62

8= 1296 119896119873119898


119872119911 =119902119906119910 times 119897

2

8=058 times 62

8= 261119896119873119898

119872119890119897119910119877119889 =119908119890119897119910 times 119891119910

1205741198720=864 times 103 times 235

11= 1845 119896119873119898

119872119890119897119911119877119889 =119908119890119897119911 times 119891119910

1205741198720=148 times 103 times 235

11= 316 119896119873119898

Donc

(1296

1845)1+ (

261



55

Nouveau 119872119911

119872119911 =119902119906119910 times 119897

2

8=058 times 32

8= 065119896119873119898

(1296

1845)1+ (

065




119881119911119904119889 =15119882119871

2= 1296 119896119873

119881119901119897119877119889 =119860119907119911 times 119891119910

radic3times 1205741198720= 12855 119896119873





1205741198721gt 119872119910119904119889 119912119955119957 120787 120787 120784 (120787 120786120790)119914119914119924120791120789

Avec

119872119888119903 = 11986211205872 119864 1198681199111198712

radic119868119908119868119911+1198712 119866 1198681199051205872 119864 119868119911

119912119925119925119916119935119916 119913 (119913 120783 120785) minus 119914119914119924120791120789

119872119888119903=311713762 Ncm


119872119888119903


119882119901119897119910 (upn140) =103 cm3

56

λ119897119905 = 0881


2 ]


empty119897119905 = 0959

ꭕ119897119905=

1


2 )

le 1

ꭕ119897119905= 075

119872119887119903119889 = 1652 119896119873119898

119872119887119903119889 = 1652 119896119873119898 gt 119872119910119904119889 = 1296 119896119873119898 119862119900119899119889119894119905119894119900119899 119907eacute119903119894119891119894eacute119890







57

119877 = 125119902119910 times 119897

2

Avec 119902119910 = [135(119866119880119875119873140 + 119866119888119900119906119907119890119903119905119906119903119890)]

119902119910 = 0837119896119873

119897 = 6 119898

119877 = 125119902119910 times 119897

2= 125 times 0837 times 3 = 32119896119873


1198791 =119877

2= 16119896119873

1198792 = 1198791 + 119877=48 kN

1198793 =1198792

2 sin 120579= 374 119896119873 119860119907119890119888 120579 = 119886119903119888 119905119892

25 119898

3 119898= 398deg



119873119905119904119889 =119860 times 119891119910

1205741198720= 4800 119873 =gt 119860 ge

11 times 4800

235 =gt 119860 ge 22461198981198982

119860 =120587empty2

4=gt empty ge radic

4119860

120587= radic

4 times 2246

314= 534 119898119898



Introduction



58



119878ge

63

radic119904

119889times119875

Avec








Srsquo=273

4=6825 m2








59



















96=8989 daNm2





60

119891119910 =5 times119882 times 1198974

384 times 119864 times 119868119910le 119891119886119889119898 =

119897

200


384 times E= 59136 1198881198984


Profileacute


IPE300 A Cm2

h mm

b mm

tf mm

tw

mm 119868y

Cm4

119868z Cm4

Wply

cm3

Wplz

cm3

MATERIAU ACIER S235

538 300 150 107 71 8356 746 628 125





119888

119905119891=

75

107= 7 lt 10 = 10 119878119890119898119890119897119897119890 119889119890 119888119897119886119904119904119890 1


119889

119905119908=2486

71= 35 lt 38 = 38 Acirc119898119890 119889119890 119888119897119886119904119904119890 1



Si 119881119904119889 le 05 119881119901119897119903119889 ⟹119872119904119889 le 119872119888119903119889 119912119955119957120787 120786 120789 119914119914119924 120791120789

61

119881119904119889 =15 times119882 times 119897


2= 388 119896119873 lt 05 119881119901119897119903119889 = 05 (

2570 times 235

radic3 times 11) = 1585 119896119873





Si

119873119904119889 le 119872119894119899 (025119873119901119897119903119889 05119860119908 119891119910

1205741198980)


025119873119901119897119903119889 = 025119860 times 119891119910

1205741198720= 025

5380 times 235

11= 28734 119896119873

05119860119908 times 119891119910

1205741198720= 05

2170 times 235

11= 2317 119896119873

119873119904119889 = 135119866 = 1337 119896119873 lt 119898119894119899 (025119873119901119897119903119889 05119860119908 times 119891119910

1205741198720)





119872119910119904119889 =15119882 times 1198972

8= 9313119896119873119898 119872119911119904119889 = 0 119872119901119897119910119903119889 = 13416 119896119873119898

λ119897119905 =

119871119911119894119911

119888105

[

1 +120(

119871119911119894119911ℎ119905119891

)

2

] 025


62

119871119911 = 1250 119898119898 119894119911 = 335 119898119898 ℎ = 300 119898119898 119905119891 = 107 119898119898




119873119904119889ꭕ119898119894119899

119873119901119897119903119889+119870119910 119872119910119904119889

119872119901119897119910119903119889+119870119911 119872119911119904119889119872119901119897119911119903119889


Avec

λ119910 =119871119910

119894119910=960

125= 768 rarr λ119910 =

768

939= 081

=gt 120583119910 = λ119910(2119861119898119910 minus 4) +119882119901119897119910 minus119882119890119897119910

119882119890119897119910= minus1134 + 0127 = minus1007 lt 09

120572 = 021 λ119910 = 081

empty119910 = 05 [1 + 120572119910(λ119910 minus 02) + λ1199102]

empty119910 = 05[1 + 021(081 minus 02) + 0812] = 089

ꭕ119910=

1


ꭕ119910= 0794 rarr 119870119910 = 1 minus


0794 times 538 times 2350= 101

120582119911 =125

335= 3731 =gt 120582119911 = 0397 rarr empty119911 = 0611 =gt ꭕ

119911= 092

ꭕ119898119894119899

= ꭕ119910= 0794

119873119901119897119903119889 =119860119891119910

1205741198980=5380 times 235

11= 114936 119896119873

119872119910119904119889 =151198821198712

8= 9313 119896119873119898

119872119901119897119910119903119889 = 13416 119896119873119898

119873119904119889 = 135119866 = 1337 119896119873

119896119910 = 101

119872119911119904119889 = 0

63

119873119904119889120594119898119894119899 119873119901119897119903119889

+119896119910 119872119910119904119889

119872119901119897119910119903119889+119896119911 119872119911119904119889119872119901119897119911119903119889

le 10

1337

0794 times 114836+101 times 9313

13416= 071 lt 1 119862119900119899119889119894119905119894119900119899 119907eacute119903119894119891119894eacute119890




64

Chapitre 4


41 Introduction




- Le pont roulant










poteaux de la halle

65





Puissances

N (t)

Porteacutee

L(m)



B

Chariot

K

Total

B+K

Rmax Rmin

125 18 085 520 1040 6809 1151 796 814 194


66


1 035 06 2 36



I 02 11 11 A-2















Groupes II






67
















119877119898119886119909 = 814 119870119873 119877119898119894119899 = 194 119870119873

Charges verticales

119877119881119898119886119909 = Ψ1 119877119898119886119909 = 115 times 814 = 8954 119870119873

119877119881119898119894119899 = Ψ2 119877119898119894119899 = 11 times 194 = 2134 119870119873


68

119877119871119898119886119909 = 119862 119877119898119886119909 = 02 times 814 = 1628 119870119873

119877119871119898119894119899 = 119862 119877119898119894119899 = 02 times 194 = 388 119870119873



1198771198671119898119886119909 = plusmn [0024(119870 + 119873 + 119861)119871

119890+ 0021(119873 + 119870)]

= plusmn [0024(1151 + 125 + 6809)18

36+ 0021(125 + 1151)]

1198771198671119898119886119909 = plusmn274 119905

1198771198671119898119894119899 = plusmn [0024(119870 + 119873 + 119861)119871

119890minus 0021(119873 + 119870)]

= plusmn [0024(1151 + 125 + 6809)18

36minus 0021(125 + 1151)]

1198771198671119898119894119899 = plusmn2168 119905


1198771198672119898119886119909 = plusmn [00052(119870 + 119873 + 5119861)119871

119890+ 0021(119873 + 119870)]

= plusmn [00052(1151 + 125 + 5 times 6809)18

36+ 0021(125 + 1151)]

1198771198672119898119886119909 = plusmn1526 119905

1198771198672119898119894119899 = plusmn [00052(119870 + 119873 + 5119861)119871

119890minus 0021(119873 + 119870)]

= plusmn [00052(1151 + 125 + 5 times 6809)18

36minus 0021(125 + 1151)]

1198771198672119898119894119899 = plusmn0953 119905




69





Rail

Poids

(Kgm)

B

(mm)

H

(mm)

P

(mm)

Section

A (cm2)

I x

(cm4)

I y

(cm4)

A55

318

55

65

150

407

178

337



70



119891119911 le 119891119886119889119898 =119897

750= 08 119888119898



119886 = (119897

2minus119890

4) = (

6

2minus36

4) = 21 119898



119891119911 =119901 119886 1198972

24119864119868(3 minus

4 1198862

1198972)

Avec

L= 6000 mm

a= 2100 mm

P=89540 N

E=21104 Nmm2

71

119868119910 ge119901 119886 1198972(31198972 minus 41198862)



119868119910 ge 421397625 1198981198984






119902 = 119866119901119900119906119905119903119890 + 119866119903119886119894119897 = 142 + 031 = 173 119896119899119898119897

119891119911 =119901 119886 1198972

24119864119868(3 minus

4 1198862

1198972) +

5 119902 1198974

384119864119868

119891119911 =89540 times 2100 times 60002


4 times 21002

60002) +




profileacute


G

Kgm

A cm2 h

mm

b

mm

tf

mm

tw

mm

Iy

cm4

Iz

cm4

Wply

cm3

Wplz

cm 3

HEB360 142 1806 360 300 225 125 43190 10140 2683 1032

72


119902 = 119866119901119900119906119905119903119890 + 119866119903119886119894119897 = 155 + 031 = 186 119870119873119898119897

119891119911 =119901 119886 1198972

24119864119868(3 minus

4 1198862

1198972) +

5 119902 1198974

384119864119868

119891119911 =89540 times 2100 times 60002


4 times 21002

60002) +






119905119908le 72휀

Avec

휀 = radic235

119891119910

298

135le 72radic

235

235 ⟹ 2207 le 72


119888

119905119891=1198872

119905119891le 10휀 ⟹

150

24= 625 le 10




profileacute


G

Kgm

A

cm2

h

mm

b

mm

tf

mm

tw

mm

Iy

cm4

Iz

cm4

Wply

cm3

Wplz

cm 3

HEB400 155 1978 400 300 24 135 57680 10820 3232 1104

73

119881119910119904119889 le 119881119901119897119903119889 119912119955119957 120787 120786 120788 (120787 120784120782)119914119914119924120791120789

119881119901119897119903119889 =119860119907119911 119891119910

radic3 1205741198980=6998 times 235

radic3 times 11= 863154 119873 = 86315 119870119873


119881119881 = 119877119881119898119886119909 times4119886

119897=8954 times 4 times 21

6= 12535 119870119873


119881119875119875 =119866 119897

2=186 times 6

2= 558 119870119873

Drsquoougrave 119881119910119904119889 = 135119881119875119875 + 15119881119881 = 19556 119870119873

119881119910119904119889 le 119881119901119897119903119889



Suivant (z-z)


119872119881 = 119877119881119898119886119909 times(6 minus

1198902)2

4119897= 8954 times

(6 minus362 )

2

4 times 6= 6581 119870119873119898


119872119875119875 =119866 1198972

8= 837 119870119873119898


119872119910119904119889 = 135119872119875119875 + 15119872119881 = 110 119870119873119898



119872119911119904119889 = 119872119867 =21198771198671119871

(119871

2minus119890

4)2

74

119872119911119904119889 = 119872119867 =2 times 274

6times (

6

2minus36

4)2

= 4028 119870119873119898




119873119904119889119873119901119897119903119889

+119872119910119904119889

119872119890119897119910+119872119911119904119889119872119890119897119911

le 1 120787 120785120790 ndash 119810119810119820120791120789

119873119904119889 = 15119877119871119898119886119909 = 15 times 1628 = 2442 119870119873

119872119890119897119910 =119908119890119897119910 119891119910

1205741198720= 61613 119872119890119897119911 =

119908119890119897119911 119891119910

1205741198720= 1541 119873119901119897119903119889 =

119860 119891119910

1205741198720= 422573

2442

422573+

110

61613+4028

1541= 044 le 1



Si 119889


Avec

휀 = radic235

119891119910= 1

119889

119905119908=298

135= 2207 lt 69





1205741198721


75



λ119897119905 =

119871119894119911

119888105

[

1 +120(

119871119894119911ℎ119905119891

)

2

] 025 = 6522 119808119821119821119812119831119812119809 119810119810119820120791120789

Avec 119871 = 600119888119898


λ119871119879 = [λ119897119905λ1] [120573119908]

05 휀 = radic235

119891119910= 1

λ119871119879 =6522

939= 0694

On calcule

ꭕ119871119879=

1


2 )le 1




ꭕ119871119879=

1

(079 + radic0792 minus 06942)= 0856


11= 59104 119870119873119898

119872119910119904119889 = 110 119870119873119898




76



119891119904119889 le 119877119910119877119889

Avec




120590119891119864119889 =119872119910119904119889

119882119890119897119910= 381 1198701198731198881198982

119878119910 = 2(ℎ119877 + 119905119891)radic[1 minus (1205741198720120590119891119864119889

119891119910119891)

2

] = 1751 119888119898

119877119910119877119889 =119878119910 times 119905119908 times 119891119910119908

1205741198720= 505 119870119873 gt 119891119904119889 = 119877119907119898119886119909 = 8954 119870119873




119891119904119889 le 119877119886119877119889

119891119904119889119877119886119877119889

+119872119878119889119872119888119877119889

le 1 119808119825119827 120787 120789120790 minus 119810119810119820120791120789

Avec

77

119877119886119877119889 =

051199051199082 (119864 119891119910119908)

05[(119905119891119905119908)05

+ 3(119905119908119905119891) (119878119904119889 )]

1205741198720 119808119825119827 120787 120789120789 minus 119810119810119820120791120789

119877119886119877119889 = 108284 119870119873

119891119904119889 = 15119877119871119898119886119909 = 15 times 1628 = 2442 119870119873

119872119888119877119889 =3232 times 103 times 235

11= 69047 119870119873119898

119891119904119889119877119886119877119889

+119872119878119889119872119888119877119889

=2442

108284+

110

69047 = 018 le 15




119887119890119891119891 le 119887 119808119825119827 120787 120789120791 minus 119810119810119820120791120789

119887119890119891119891 = radicℎ2 + 1198781199042 = 410 119898119898 gt 119887 = 300 119898119898




efforts suivants




Charge verticale


119901prime = 119876 119871 + 119877119898119886119909 (2 minus119890

119871) ψ


36

6) times 11

119901prime = 13651 119870119873


119901 = 135119876 119871 + 15119877119898119886119909 (2 minus119890

119871) ψ


36

6) times 11

119901 = 2031 119870119873

78

Charge horizontale

119875119867 = 15119877119867119898119886119909 (1 minus119890

119897)ψ


36

6) times 11 = 1808 119870119873




119891119911 le 119891119886119889119898 =119897

500


119891119911 =119901prime 1198893

3119864119868le 119891119886119889119898

119868119910 =500 119901prime 1198892

3119864ge 782667 1198881198984


79




119905119908le 72휀

Avec

휀 = radic235

119891119910

2486

71le 72radic

235

235 ⟹ 3501 le 72


119888

119905119891=1198872

119905119891le 10휀 ⟹

75

102= 735 le 10





119881119910119904119889 le 119881119901119897119903119889

Avec 119860119907119911 = 257 cm2

119881119901119897119903119889 =119860119907119911 119891119910

radic3 1205741198980=257 times 235

radic3 times 11= 317 119870119873

119881119904119889 = 119901 = 2031 lt 05119881119901119897119877119889


profileacute


G

Kgm

A

cm2

h

mm

b

mm

tf

mm

tw

mm

Iy

cm4

Iz

cm4

Wply

cm3

Wplz

cm 3

IPE 300 422 5380 300 150 107 71 8353 604 628 125

80


119872119888119903119889 =119908119901119897119910 119891119910

1205741198720=628 times 235

11= 13416 119870119873119898

119872119910119904119889 = 119901 119889 = 2031 times 085 = 172635 119870119873119898

119872119910119904119889 lt 119872119888119903119889




119872119888119903119889 =119908119901119897119910 119891119910

1205741198720=1019 times 235

11= 2177 119870119873119898

119872119910119904119889 = 119901 119889 = 2031 times 085 = 172635 119870119873119898

119872119910119904119889 lt 119872119888119903119889


17263


profileacute


G

Kgm

A

cm2

h

mm

b

mm

tf

mm

tw

mm

Iy

cm4

Iz

cm4

Wply

cm3

Wplz

cm3

IPE 360 571 727 360 170 127 8 16270 1043 1019 191

81



chemin de roulement

119891119911 le 119891119886119889119898 =119889

500= 017

119902 = 119902119868119875119864 360 = 571 119889119886119873119898119897

119891119911 =119901prime 1198893

3119864119868+119902 1198974

8119864119868= 0082 + 0021 = 0103 119888119898 lt 017 119888119898


82

Chapitre-5








dynamiques


83




119881 =119860119863 119876

119877119882



119863 =

25120578 0 le 119879 le 1198792

25120578(1198792119879)23 1198792 le 119879 le 3119904

25120578 (11987923)

23 (3119879)

53 119879 gt 3119904


84

120578 = radic7

(2 + 120585)ge 07



119879 = 119862119879 ℎ11987334 119917119926119929119924119932119923119916 (120786 120788)119929119927119912 119933120784120782120782120785




119876 = 1 +sum119875119902

6

1


85


119876 = 1 +sum119875119902

6

1

= 1 + 02 = 12


119899119894=1

Avec 119882119894 = 119882119866119894 + 120573119882119876119894




119881 =119860119863 119876

119877119882

119860 = 005 119863 = 25 119876 = 12 119877 = 4 119882 = 189475119896119873

119881119909 = 119881119910 =005 times 25 times 12

4times 189475 = 7105119896119873


119904119886119892=

125119860 (119860 +

119879

1198791(25120578

119876

119877minus 1)) 0 le 119879 le 1198791

25120578(125119860) (119876

119877) 1198791 le 119879 le 1198792

25120578(125119860) (119876

119877)(1198792119879)23

1198792 le 119879 le 30119904

25120578(125119860) (11987923)

23(3

119879)

53(119876

119877) 119879 gt 30119904

86



η = 100 A=005 1198791=015 1198792=050


87













88










89

ℎ

150=890

150= 594119888119898 sans vent

ℎ

125=890

125= 712119888119898 avec vent






Toiture 029 076 116 304


ℎ

100=1025

100= 1025 119888119898



90

Chapitre-6


61 Introduction





119872119910119904119889 = 21902 kNm

119881119904119889 =7249 kN

119873119904119889 =2018 kN

91

Profileacute


IPE 400 A cm2

hmm

b mm

119905f

mm

119905w mm

119868y

cm4

119868z Cm4

119908ply

cm3

119908plz

cm3

MATERIAU ACIER S235

8446 400 180 14 90 231284 131782 123832 2256




119888

119905119891=60

14= 59 lt 10휀 =gt 119888119897119886119904119904119890 1


119889

119905119908=98

9= 11 lt 72휀 =gt 119888119897119886119904119904119890 1





Si 119881119904119889 le 05119881119901119897119903119889 ⟹ 119872119904119889 le 119872119888119903119889 119912119955119957120787 120786 120789 119914119914119924 120791120789


119881119898119886119909 = 119881119904119889 =7248kN

119881119901119897119911119903119889 =

119860119907119911 (119891119910

radic3)

1205741198980=

4270235

radic311

= 526674119896119873

119881119904119889 = 7247 le 05119881119901119897119911119903119889 = 52667119896119873


92



119873119904119889 le 119872119894119899(025119873119901119897119903119889 05119860119908119891119910

1205741198720)


119873119904119889 = 2018119896119873

119873119901119897119903119889 le119860 119891

119910

1205741198720=8446 235

11= 180437119896119873

025119873119901119897119903119889 =451 119896119873

119860119908 = 119860 minus 2119887 119905119891 = 34061198981198982

05119860119908119891119910

1205741198720= 36382119896119873

119873119904119889 = 2018 le 36382119896119873



119872119888119903119889 = 119872119901119897119910119903119889 =119908119901119897119910 119891119910

1205741198720=1238320 235

11= 26455119896119873119898




120594119898119894119899 119873119901119897119903119889+119896119910 119872119910119904119889

119872119901119897119910119903119889+119896119911 119872119911119904119889119872119901119897119911119903119889



120594119911 119873119901119897119903119889+119896119871119879 119872119910119904119889

120594119871119879119872119901119897119910119903119889+119896119911 119872119911119904119889119872119901119897119911119903119889



120594119898119894119899 = 119872119894119899(120594119910 120594119911)


93

120594119910 =1

(120601119910 +radic1206011199102 minus 1205821199102 )

120601119910 = 05[1 + 120572119910(120582119910 minus 02) + 1205821199102]

120582119910= (120582119910

1205821)radic120573119860 =

120582119910

1205821

Avec 120573119860 = 1 Classe 1

1205821 = 939

120582119910 =05119868119910

119894119910=455

166= 274

120582119910=274

939= 029


ℎ

119887=400

180= 222 gt 12 119894119898119901119897119894119902119906119890 120572 = 021

120601 = 05[1 + 120572119910(120582119910 minus 02) + 1205821199102 ] = 055

120594119910 =1

(055 + radic0552 minus 0292)= 098


120594119911 =1

(120601119911 +radic1206011199112 minus 120582119911

2)

120601119911 = 05[1 + 120572119911(120582119911 minus 02) + 1205821199112]

120582119911 = (1205821199111205821)radic120573119860 =

1205821199111205821

Avec 120573119860 = 1 Classe 1

120582119911 =119868119911119894119911=200

395= 5063

120582119911 =5063

939= 054


94

ℎ

119887= 222 gt 12 (119911 minus 119911)119894119898119901119897119894119902119906119890 120572 = 034

120601 = 05[1 + 034(054 minus 02) + 0542 ] = 07

120594119911 =1

(07 + radic072 minus 0542)= 087

120594119898119894119899 = 119872119894119899(120594119910 120594119911) = 087




λ119897119905 =

119871119894119911

119888105

[

1 +120(

119871119894119911ℎ119905119891

)

2

] 025 = 4367 119808119821119821119812119831119812119809 119810119810119820120791120789

Avec

IPE400 119905119891 = 14119898119898 119894119911 = 395119888119898 ℎ = 400119898119898

119870 = 1 1198881=1134 Tableau B11 CCM97


1205821 = 939휀

휀 = radic235

119891119910= 1

120582119871119879 = [1205821198971199051205821] [120573119908]

05

120582119897119905 = 4367

120582119871119879 =4367

939= 046 gt 04



119873119904119889120594119911 119873119901119897119903119889

+119896119871119879 119872119910119904119889

120594119871119879119872119901119897119910119903119889+119896119911 119872119911119904119889119872119901119897119911119903119889


Calcul de 120594119871119879


95

implique 120594119871119879 = 094

Calcul de 119896119871119879


119870119871119879 = 1 minusμLT N119904119889

120594119911 119860 119891119910= 099 lt 15


Donc

119873119904119889=7249 kN 119872119910119904119889=219 kNm 119872119901119897119910119903119889=26455 kNm 120594119911=087 119872119901119897119911119903119889=4819kNm


119873119904119889120594119911 119873119901119897119903119889

+119896119871119879 119872119910119904119889

120594119871119879119872119901119897119910119903119889+119896119911 119872119911119904119889

119872119901119897119911119903119889


7249

087 180437+

099 219

094 26455= 055










96

119872119910119904119889 = 32083 119896119873119898

119881119904119889 = 120 119896119873

119873119904119889 = 602 119896119873

Profileacute


HEA320

A cm2

hmm

b mm

119905f

mm

119905w mm

119868y

cm4

119868z cm4

119908 ply

cm3

119908 plz

cm3

MATERIAU ACIER S235

12437 310 300 16 9 229286 698524 162823 70975




119888

119905119891=60

16= 375 lt 10휀 =gt 119888119897119886119904119904119890 1


119889

119905119908=98

9= 109 lt 72휀 =gt 119888119897119886119904119904119890 1





Si 119881119904119889 le 05119881119901119897119903119889 ⟹ 119872119904119889 le 119872119888119903119889 119912119955119957120787 120786 120789 119914119914119924 120791120789


119881119898119886119909 = 119881119904119889 =120kN

119881119901119897119911119903119889 =

119860119907119911 (119891119910

radic3)

1205741198980=4113 235radic3

11= 50731119896119873

97

119881119904119889 le 05119881119901119897119911119903119889




119873119904119889 le 119872119894119899(025119873119901119897119903119889 05119860119908119891119910

1205741198720)


119873119904119889 =602kN

119873119901119897119903119889 le119860 119891

119910

1205741198720=12437 235

11= 2656995 119896119873

025119873119901119897119903119889 = 664248119896119873

119860119908 = 119860 minus 2119887 119905119891 = 2837 1198981198982

05119860119908119891119910

1205741198720= 30304119896119873

119873119904119889 = 602119896119873 le 30304119896119873



119872119888119903119889 = 119872119901119897119910119903119889 =119908119901119897119910 119891119910

1205741198720=1628000 times 235

11= 3478119896119873119898




120594119898119894119899 119873119901119897119903119889+119896119910 119872119910119904119889

119872119901119897119910119903119889+119896119911 119872119911119904119889119872119901119897119911119903119889



120594119911 119873119901119897119903119889+119896119871119879 119872119910119904119889

120594119871119879119872119901119897119910119903119889+119896119911 119872119911119904119889119872119901119897119911119903119889



120594119898119894119899 = 119872119894119899(120594119910 120594119911)


98

120594119910 =1

(120601119910 +radic1206011199102 minus 1205821199102 )

120601119910 = 05[1 + 120572119910(120582119910 minus 02) + 1205821199102]

120582119910= (120582119910

1205821)radic120573119860 =

120582119910

1205821

Avec 120573119860 = 1 Classe 1

1205821 = 939

120582119910 =05119868119910

119894119910=05 890

1358= 3276

120582119910=3276

939= 034


ℎ

119887=310

300= 1 lt 12 (119910 minus 119910)119894119898119901119897119894119902119906119890 120572 = 034

120601 = 05[1 + 120572119910(120582119910 minus 02) + 1205821199102 ] = 058

120594119910 =1

058 + radic058 minus 034= 095


120594119911 =1

(120601119911 +radic1206011199112 minus 1205821199112)

120601119911 = 05[1 + 120572119911(120582119911 minus 02) + 1205821199112]

120582119911 = (1205821199111205821)radic120573119860 =

1205821199111205821

Avec 120573119860 = 1 Classe 1

1205821 = 939

120582119911 =119868119911119894119911=07 59

749= 055


ℎ

119887= 1 lt 12 (119911 minus 119911) 119894119898119901119897119894119902119906119890 120572 = 049

120601 = 05[1 + 049(055 minus 02) + 0552] = 073

99

120594119911 =1

073 + radic073 minus 055= 082

120594119898119894119899 = 119872119894119899(120594119910 120594119911) = 082


λ119897119905 =

119871119894119911

119888105

[

1 +120(

119871119894119911ℎ119905119891

)

2

] 025 = 3536

HEA320 119905119891 = 16119898119898 119894119911 = 749119888119898 ℎ = 310119898119898

119870 = 07 1198881 = 1134 Tableau B11 CCM97


1205821 = 939휀

휀 = radic235

119891119910= 1

120582119871119879 = [1205821198971199051205821] [120573119908]

05

120582119897119905 = 3536

120582119871119879 =3536

939= 037 lt 04 119901119886119904 119889119890 119903119894119904119902119906119890 119889119890 119889119890119907119890119903119904119890119898119890119899119905


119873119904119889120594119898119894119899 119873119901119897119903119889

+119896119910 119872119910119904119889

119872119901119897119910119903119889+119896119911 119872119911119904119889119872119901119897119911119903119889


Avec

119873119904119889 =602kN 119872119910119904119889=32083kNm 119872119911119904119889=049kNm 119872119901119897119910119903119889=3478kNm

119872119901119897119911119903119889=1516kNm 120594119898119894119899= 082 119873119901119897119903119889=26570kN 119896119910= 05 119896119911= 07

602

082 26570+05 32083

3478+07 049







100





(135G+15V1)


119873119904119889 =69837kN


Profileacute


2CAE (120x12)

A Cm2

hmm

b mm

Anet

Cm2

d

mm

MATERIAU ACIER S235

5508 120 248 4658 8



119873119904119889 le 119873119905119903119889 = 119872119894119899[119873119901119897119903119889 119873119906119903119889 119873119899119890119905119903119889]

101

119873119901119897119903119889 =119860 119891119910

1205741198720= 117671119896119873

119873119906119903119889 = 09119860119899119890119905 1198911199061205741198722

= 13719119896119873

119873119899119890119905119903119889 =119860119899119890119905 119891119910

1205741198720= 995118119896119873








102


119872119910119904119889 = 02 119896119873119898

119881119904119889 = 0048 119896119873

119873119904119889 = 5628 119896119873

Profileacute


IPE300

A cm2

hmm

b mm

119905f

mm

119905w mm

119868y

cm4

119868z cm4

119908ply

cm3

119908plz

cm3

MATERIAU ACIER S235

538 300 150 107 71 8356 746 628 125







Si 119881119904119889 le 05119881119901119897119903119889 ⟹ 119872119904119889 le 119872119888119903119889 119912119955119957120787 120786 120789 119914119914119924 120791120789


119881119898119886119909 = 119881119904119889 =0048kN

119881119901119897119911119903119889 =

119860119907119911 (119891119910

radic3)

1205741198980=2570 235radic3

11= 3169119896119873

119881119904119889 le 05119881119901119897119911119903119889




119873119904119889 le 119872119894119899(025119873119901119897119903119889 05119860119908119891119910

1205741198720)

103


119873119904119889 =5628kN

119873119901119897119903119889 le119860 119891

119910

1205741198720=5380 235

11= 114936 119896119873

025119873119901119897119903119889 = 28734 119896119873

119860119908 = 119860 minus 2119887 119905119891 = 2170 1198981198982

05119860119908119891119910

1205741198720= 23179119896119873

119873119904119889 = 5628119896119873 le 23179119896119873



119872119888119903119889 = 119872119901119897119910119903119889 =119908119901119897119910 119891119910

1205741198720=628000 times 235

11= 134163 119896119873119898




120594119898119894119899 119873119901119897119903119889+119896119910 119872119910119904119889

119872119901119897119910119903119889+119896119911 119872119911119904119889119872119901119897119911119903119889



120594119911 119873119901119897119903119889+119896119871119879 119872119910119904119889

120594119871119879119872119901119897119910119903119889+119896119911 119872119911119904119889119872119901119897119911119903119889



120594119898119894119899 = 119872119894119899(120594119910 120594119911)


120594119910 =1

(120601119910 +radic1206011199102 minus 1205821199102 )

120601119910 = 05[1 + 120572119910(120582119910 minus 02) + 1205821199102]

120582119910= (120582119910

1205821)radic120573119860 =

120582119910

1205821

104

Avec 120573119860 = 1 Classe 1

1205821 = 939

120582119910 =119871119910

119894119910= 960

125= 768

120582119910=768

939= 081


ℎ

119887=300

150= 05 lt 12 (119910 minus 119910)119894119898119901119897119894119902119906119890 120572 = 021

120601 = 05[1 + 120572119910(120582119910 minus 02) + 1205821199102 ] = 089

120594119910 =1

058 + radic058 minus 034= 079


120594119911 =1

(120601119911 +radic1206011199112 minus 1205821199112)

120601119911 = 05[1 + 120572119911(120582119911 minus 02) + 1205821199112]

120582119911 = (1205821199111205821)radic120573119860 =

1205821199111205821

Avec 120573119860 = 1 Classe 1

1205821 = 939

120582119911 =119868119911119894119911=125

335= 3731 120582119911 = 039


ℎ

119887= 1 lt 12 (119911 minus 119911) 119894119898119901119897119894119902119906119890 120572 = 021

120601 = 05[1 + 021(039 minus 02) + 0392] = 061

120594119911 =1

061 + radic061 minus 039= 092

120594119898119894119899 = 119872119894119899(120594119910 120594119911) = 079


105

λ119897119905 =

119871119894119911

119888105

[

1 +120(

119871119894119911ℎ119905119891

)

2

] 025 = 3433

IPE300 119905119891 = 107119898119898 119894119911 = 335119888119898 ℎ = 300119898119898

119870 = 1 1198881 = 1134 Tableau B11 CCM97


1205821 = 939휀

휀 = radic235

119891119910= 1

120582119871119879 = [1205821198971199051205821] [120573119908]

05

120582119897119905 = 3433

120582119871119879 =3433

939= 036 lt 04 119901119886119904 119889119890 119903119894119904119902119906119890 119889119890 119889119890119907119890119903119904119890119898119890119899119905


119873119904119889120594119898119894119899 119873119901119897119903119889

+119896119910 119872119910119904119889

119872119901119897119910119903119889+119896119911 119872119911119904119889119872119901119897119911119903119889


Avec

119873119904119889 =5628kN 119872119910119904119889=02kNm 119872119911119904119889=018kNm 119872119901119897119910119903119889=134163kNm

119872119901119897119911119903119889=267kNm 120594119898119894119899= 079 119873119901119897119903119889=1149kN 119896119910= 1 119896119911= 1

5628

079 1149+

02

134163+018



106

Chapitre-7


71 Introduction










au poteau

107




119872119904119889 = 28961119896119873119898 119873119904119889 = 17878119896119873 119881119904119889 = 8941119896119873




119905 = 119872119894119899(119905119891 119905119901119897119886119905119894119899119890) = 135119898119898

Avec





12119889O = 24 119898119898 le 1198901 le 12119905 =186 119898119898 ⟹ 1198901 = 110 119898119898

15119889O = 30 119898119898 le 1198902 le 12119905 = 186 119898119898 ⟹ 1198902 = 105 119898119898

22119889O = 44 119898119898 le 1199011 le 14119905 =217 119898119898 ⟹ 1199011 = 100 119898119898


108






IPE 400 119905f = 135 119898119898 119905w = 86 119898119898

119886min= 26 le twle119886max= 8

119886min =35 le tf le119886max= 8







sum119897 = 2119887 + 4(119887 minus 119905119908) = 2180 + 4(180 minus 86) = 1045119898119898

119865119908119903119889 =7times 1045 times 360

radic2= 1862119896119873

119873119904119889 =119872119904119889

ℎ=120784120790120791 120788120783

120782 120791= 120785120784120783 120789120790





Avec 120573119908 = 125 120574119872119882 = 08


109

i

sum119897 = 4ℎ119894 = 4 times 373 = 1492119898119898

119865119907119903119889 =7 times 1492 times 360

radic3= 217074119896119873



119873119894 =119872119904119889 119889119894sum119889119894

2


119909 = 119905119891radic119887

119905119908= 135radic

180

86= 6176



- 1198891 = 712 119898119898

- 1198892 = 612 119898119898

- 1198893 = 512 119898119898 ⟹ Σ 1198892 = 129 119898sup2

- 1198894 = 312 119898119898

- 1198895 = 212 119898119898

- 1198896 = 112 119898119898


1198731 =28961 times 0712

129= 15984119896119873



1198731 = 119899119865119907119903119889 ⟹ 119860119904 ge119873119904119889

06 times 119891119906119887 times 119899=

15984

06 times 800 times 2= 16651198981198982



M18 18 20 254 192 800 291



110




119865119901 = 07 times 119891119906119887 times 119860119904 = 06 x 800 x 192 = 10752kN

119872119903119889 =119899 119865119901 sum119889119894

2

119889119894=2 times 10752 times 129

0712= 3896 gt 119872119904119889 = 28961 119896119873119898




119865119907119904119889 le 119865119904119903119889 =119870119904 119898 120583

1205741198722(119865119901119888119889 minus 08119873119904119889) 119917119926119929119924119932119923119916 120788 120789 minus 119914119914119924120791120789

Avec

119870119904 = 10 ∶ Trous normaux



119865119904119903119889 = 024 (10752 minus 08 times15984

2) = 1046119896119873

119865119907119904119889 =8941

12= 745119896119873 lt 1046119896119873




1205741198722 119813119822119825119820119828119819119812 120788 120784 minus 119810119810119820120791120789



125= 213157 119896119873

119865119905119904119889 =119865119901

2=10752

2= 5376119896119873 lt 119861119901 119903119889 = 213157 119896119873


111



1205741198722 119827119808119809119819119812119808119828 120788 120787 120785 ndash 119810119810119820120791120789

Avec 119870119904 = 25

120572119887 = min (119890131198890

(119901131198890

minus 025) 119891119906119887119891119906 1) = 1



125= 46008119896119873 gt

11986511990711990411988912

= 745119896119873



119865119907 le 119865119905119903119889 = 119905119908119888 1198871198901198911198911198911199101205741198720

Avec




⟹ 119865119905119903119889 = 9 times 90times23511

= 173045 119896119873


119865119907 =119872119904119889

ℎ minus 119905119891=28961

029= 99865 gt 119865119905119903119889 = 173045119896119873




119873119904119889 le 119865119888119903119889 =119896119888 120588 119887119890119891119891 119905119908119888 119891119910

1205741198721radic1 + 13 (119887119890119891119891ℎ)2

119887119890119891119891 = 119905119891119887 + 2119886119901radic2 + 5(119905119891119888 + 119903119888) + 2119905119901

Avec

112






119887119890119891119891 =25014mm



120590119888119904119889 =119881119904119889119860+119872119904119889

119882119890119897119910=8941 times 103

1244+28961 times 106

1479= 196533119872119875119886

120590119888119904119889 = 19653119872119875119886 lt 119891119910 = 235119872119875119886 ⟹ 119896119888 = 1


119901 = 0932radic119887119890119891119891 119889119908119888 119891119910

119864 1199051199081198882= 0932radic


21 times 104 times 092= 254

119901 gt 072⟹ 120588 =119901 minus 02

1199012=254 minus 02

2542= 036


11 radic1 + 13 (250131

)2

= 12741119896119873

119873119904119889 = 1119873119894 =119872119904119889 sum119889119894sum119889119894

2 =29861 times 247

129= 57175119896119873





119865119907 le 119881119903119889 = 058119891119910 ℎ1199051199081205741198720


11= 3457119896119873


119865119907 =119872119904119889ℎ minus 119905119891

= 46216 119896119873 gt 119881119903119889 = 3457119896119873 119888119900119899119889119894119905119894119900119899 119899119900119899 119907eacute119903119894119891119894eacute119890


113

119865119907 = 46216119896119873 le 119881119903119889 = 058119891119910 ℎ119905119908 + 04

1205741198720= 058 235 31

(09 + 04)

11= 49935119896119873







logiciel robot

119872119904119889 = 15135119896119873119898 119873119904119889 = 1324119896119873 119881119904119889 = 273119896119873






119905 = min(119905119891 119905119901119897119886119905119894119899119890) = 135119898119898


114









IPE400

tf = 135 mm tw = 86 mm






radic2 times 119861119908 120574119898119908


Donc

119865119908119903119889 =119860 times sum119871 times 119891119906


radic2 times 1= 133083119896119873

119873119904119889 =119872119904119889ℎ

=7283

08= 9103119896119873

115

119873119904119889 = 9103 le 119865119908119903119889 = 1330119896119873






Donc

119865119907119903119889 =119886 times sum119871 times 119891119906


radic3 times 1= 155053119896119873



119873119894 =119872119904119889 119889119894sum119889119894

2


119909 = 119905119891radic119887

119905119908= 135radic

180

86= 6176119898119898


- 1198891 = 700 119898119898

- 1198892 = 600 119898119898

- 1198893 = 500 119898119898 ⟹ Σ1198891198942

= 124 119898sup2

- 1198894 = 300 119898119898

- 1198895 = 200 119898119898

- 1198896 = 100 119898119898


1198731 =119872119904119889 times 119889119894Σ119889119894

2 =15135 times 070

124= 4111119896119873



116


1198731 = 119899 119865119907 ⟹ 119860119904 ge119873119904119889

05 times 119891119906119887 times 119899=

13240

05 times 800 times 2= 16551198981198982



M18 18 20 254 192 800 291




119865119901 = 07 times 119891119906119887 times 119860119904 = 10752 119896119873

119872119903119889 =119899 119865119901sum119889119894

2

119889119894=2 times 10752 times 124

07= 38092 gt 119872119904119889 = 15135119896119873119898




119865119907119904119889 le 119865119904119903119889 =119870119904 119898 120583

1205741198722(119865119901119888119889 minus 08119873119904119889) 119813119822119825119820119828119819119812 120788120789 ndash 119810119810119820120791120789

Avec




119865119904119903119889 = 024 ( 10752 minus 08 times 1324) = 2326119896119873

119865119907119904119889 =273

12= 023 lt 119865119904 119903119889 = 2326119896119873




1205741198722 119813119822119825119820119828119819119812 120788 120784 ndash 119810119810119820120791120789

Avec


117


125= 31578119896119873

119865119905119904119889 =119865119901

2= 5376 lt 31578119896119873




1205741198722 119827119808119809119819119812119808119828 120788 120787 120785 ndash 119810119810119820120791120789

Avec Ks = 25

120572119887 = min (119890131198890

(119901131198890

minus 025) 119891119906119887119891119906 1) = 1


11986511990711990411988912


125= 5184 119896119873







119865119907119904119889 =119873119904119889

119899119887119903 119889119890 119887119900119906119897119900119899=131

3= 4366 le 119865119907119903119889

118


1205741198722⟹ 119860119904 ge

1205741198722 times 119865119907119903119889

06 times 119891119906119887119909 119898=125 times 43666

06 times 800 times 2= 56851198981198982


















119873119898119886119909 le 119865119908119903119889 =119886 sum119897 119891119906

119861119908 120574119898119908 radic(3 minus 1199041198941198991205722)


120572= 30gtgtgt 11990411989411989930o = 05

119865119908119903119889 =5 times 700 times 360



119



1205741198722 119827119808119809119819119812119808119828 120788 120787 120785 minus 119810119810119820120791120789


120572119907= 06



125= 12057119896119873

119865119907119904119889 =119873119904119889

3=3124

3= 10413 le 119865119907119903119889 = 12057119896119873




1205741198722 119827119808119809119819119812119808119828 120788 120787 120785 minus 119810119810119820120791120789

Avec

Ks = 25

120572119887 = min (119890131198890

(119901131198890

minus 025) 119891119906119887119891119906 1) = 092



125= 33914119896119873 gt 119865119907119904119889 = 4366119896119873




119873119898119886119909 le 119881119890119891119891119903119889 =119860119899119905 119891119910

1205741198722+119860119899119907 119891119910

radic3 1205741198722 119812119810120785 119849119834119851119853119842119838120783 minus 120790sect120785120783120782 120784

Avec


119860119899119890119905 = (119897

2minus11988902) 119905 = (60 minus 9)12 = 6121198981198982


120

119860119899119907 = (1198901 + 21199011 minus 251198890)119905 = (50 + 140 minus 45)12 = 17401198981198982

⟹ 119881119890119891119891119903119889 =612 times 235

125+1740 times 235

radic3 times 125= 303918119896119873 gt

119873119904119889

2= 655119896119873








119865119907119904119889 =119877119907119911

119899119887119900119906119897119900119899119904=36

2= 18 119896119873

119865119907119903119889 =06 times 119860119904 times 119891119906119887

120574119872119887⟹119860119904 ge

120574119872119887 times 11986511990711990311988906 times 119891119906119887

=11 times 18000

06 times 800= 41251198981198982



119865119907119903119889 =06 times 119860119904 times 119891119906119887

120574119872119887=06 times 58 times 800

11= 253119896119873 gt 119865119907119904119889 = 18119896119873


119865119905119903119889 =09 times 119860119904 times 119891119906119887

120574119872119887=09 times 58 times 800

11= 379119896119873

121

119865119907119903119889 =06 times 119860119904 times 119891119906119887

120574119872119887= 253119896119873

119865119907119904119889119865119907119903119889

+119865119905119904119889

14 119865119905119903119889= 052 lt 1 119862119900119899119889119894119905119894119900119899 119907119890119903119894119891119894eacute119890


122

Chapitre-8




123








119865119888119896=30 MPa

119891119888119889 =085 times 119865119888119896125

= 204 MPa


119865119895119889 = 120572120573119895 119891119888119889



119865119895119889 = 120572 120573119895 119891119888119889 = 15 times2

3times 17 = 204 119872119875119886


1198601198620 ge119873119904119889119891119888119889

=148960

204

1198601198620 ge 7266341198981198982


bp ge b+2tf = 190+2times155 = 221 mm

hp ge h+2tf = 310+2times155 = 341 mm

On prend

bp =600 hp=620



124


119862 = 119905 (119891119910119901

3119891119895119889 1205741198720)

05

= 30(235


= 5605 119898119898

119862 = 5605 lt(ℎ minus 2119905119891)

2= 1395 119898119898




gorge (a) Annexe H







119890 =119872119904119889119873119904119889

= 041 119898 gt 119885119879 = 0195 119898







125


Ougrave

119871119890119891119891 = min(119887119901 119887119891119888 + 2119888) = min(600 300 + 2 times 4671) = 39342 119898119898

119887119890119891119891 = min (119888ℎ1198882minus 119905119891119888) + 119905119891119888 +min (119888

ℎ119901 minus ℎ119888

2)

119887119890119891119891 = min (4671310

2minus 155) + 155 + min (4671

620 minus 310

2) = 10892 119898119898

⟹ 119865119888119903119889 = 204 times 10892 times 39342 = 874166 119896119873


119865119907119903119889 = 119865119891119903119889 + 119899119887 119865119907119887119903119889


119865119891119903119889 = 02119873119904119889 = 1214 119896119873





119865119907119887119903119889 =120572119888119887 119891119906119887 119860119904

1205741198722

Avec 120572119888119887 = 044 minus 00003119891119910119887 = 0248


126

119865119907119887119903119889 =0248 times 800 times 561

125= 8904 119896119873

⟹ 119865119907119903119889 = 1214 + 8 times 8904 119896119873 = 72446 119896119873




Avec 120573119908 =08 120574119898119908 = 125 119886 = 6 mm


sum119897 = 470 119898119898

119865119908119903119889 =6 times 470 times 360

radic3= 58612 119896119873

119881119904119889 = 9773 119896119873 lt min(119865119907119903119889 119865119908119903119889) = 58612 119896119873





W= 150 mm e = 55 mm ex = 40 mm mx = 40 mm


119897119890119891119891119888119901 = 119898119894119899 2120587119898119909 = 25132 119898119898

120587119898119909 +119882 = 27566 119898119898120587119898119909 + 2119890 = 23566 119898119898

⟹ 119897119890119891119891119888119901 = 23566 119898119898

127


119897119890119891119891119899119888 = 119898119894119899

4119898119909 + 125119890119909 = 210 119898119898

2119898119909 + 0625119890119909 +119882

2= 180 119898119898

2119898119909 + 0625119890119909 + 119890 = 160 119898119898119887119901

2= 150 119898119898

⟹ 119897119890119891119891119899119888 = 150 119898119898


119865119905119886119899119888119903119889 = min[119865119905119887119900119899119889119903119889 119865119905119903119889]


119865119905119903119889 = 09 times119860119904 times 119891119906119887120574119898119887


125= 32314 119896119873



119865119887119889 =036radic119891119888119896

120574119888=036 times 547

15= 1313 119872119875119886


119865119905119887119900119899119889119903119889 =120587 119889 119897119887 119891119887119889

120572

Avec

1198971 = 20119889 = 600 119898119898

119903 = 3119889 = 90 119898119898

1198972 = 20119889 = 600 119898119898






07= 52929 119896119873

119865119905119886119899119888119903119889 = 119898119894119899[52929 32314] = 32314 kN

128




Lb = 8d + em +tp + twa + 05k

Avec







119871119887lowast =

881198981199093 119860119904

1198971198901198911198911 1199051199013 =


150 times 253= 13480 119898119898 lt 119871119887 = 312 119898119898




119898119901119897119903119889 =1199051199012 119891119910119901

41205741198720=252 times 235

4 times 11= 3338119896119873


Mode 1 1198721199011198971119903119889 = 119898119901119897119903119889 times 1198971198901198911198911 = 3338 times 015 = 5007119896119873119898

1198971198901198911198911 = min(119897119890119891119891119888119901 119897119890119891119891119899119888) = 150 119898119898


129




Mode 1-2

1198651199051minus2119903119889 =21198721199011198971119903119889

119898119909=2 times 5

004= 250 119896119873

Mode 3

1198651199053119903119889 = 2119865119905119903119889119886119899119888ℎ119900119903 = 2 times 32314 = 646280 119896119873

Mode 4

1198651199054119903119889 =119887119890119891119891119905 119905119908 119891119910

1205741198720=150 times 9 times 235

11= 288409119896119873

Drsquoougrave

119865119905119903119889 = min(1198651199051minus2119903119889 1198651199053119903119889 1198651199054119903119889) = 250 119896119873




119885119879119890119873minus 1

119865119879119903119889 times 119885

119885119862119890119873+ 1

) 119812119810120785 ndash 120783 120790 119827119808119809119819119812119808119828 120788 120789

119885 = 119885119879+119885119862 = 195 + 155 = 350119898119898

⟹119872119903119889 = 5646 119896119873119898 lt 6207119896119873119898



821 Introduction




- Le site (S3)



130




ELU 119872119880 = 6207119896119873119898 119873119880 = 9773119896119873

ELS 119872119878 = 4136119896119873119898 119873119878 = 7960119896119873




119886 = 119886119901 + 119888 = 062 + 02 = 082 119898


119860

119861=119886

119887= 1025 ⟹ 119860 = 1025119861



119890 =119872119904

119873119904= 052119898



120590119898119886119909 =119873

119860119861(1 +

6119890

119861) le 120590119904119900119897


368B2 - B - 312 ge 0 ⟹ B ge0765m



131

119889 = max (119861 minus 119887

4119860 minus 119886

4) = max (005 0295)

On prend d= 45 cm



On a

119890 = 052 gt119860

6= 041


3120590119898119886119909 1205901198981198941198994

lt 120590119904119900119897

Avec

120590119898119894119899 =119873

119860119861(1 minus

6119890

119860) =

14896

2(1 minus

041

2 ) = 62191198961198731198982

120590119898119894119899 =119873

119860119861(1 +

6119890

119860) =

14896

2(1 +

041

2 ) = 86771198961198731198982

3120590119898119886119909 120590119898119894119899

4= 6835 1198961198731198982 lt 120590119904119900119897 = 180 119896119873119898

2



119890 =119872

119873= 052 119898 lt

119860

4= 062 119898




119890 gt119886

6 119890 gt

119860

24


119860119886 =1198721119911 119904119905

132

1198721 = (119860

2minus 035119886)

2

(1 +119890

119860+14 times 119890 times 119886

1198602)1198731199042119860

1198721 = 2788119896119873119898

Avec 119911 = 09d =40cm

119904119905 = min (2

3119891119890 110radic12057811989111990528) =20163 MPa

11989111990528 = 00611989111988828 + 06 = 24 119872119875119886 120578 = 16 119867 119860 Donc

119860119886 =2788 times 106

400 times 20163= 345 1198881198982


119860119887 =119873prime(119861 minus 119887)

8119889 119904119905

Avec

119873prime = 119873119904 (1 +3119890

119860) = 796 (1 +

3 times 052

25) = 2993119896119873

119904119905 = min (2

3119891119890 110radic12057811989111990528) = 20163119872119875119886

11989111990528 = 00611989111988828 + 06 = 24119896119873 120578 = 16 119867 119860

Donc 119860119887 = 071198881198982


119860119886 =1198721119911 120590119904119905

1198721 = (119860

2minus 035119886)

2

(1 +119890

119860+14 times 119890 times 119886

1198602)1198731199062119860

1198721 = 349119896119873119898

Avec 119911 =09d = 40 cm

120590119904119905 =119891119890120574119904=400

115= 3478119872119875119886

Donc

133

119860119886 =349 times 106

400 times 3478= 251198881198982


119860119886 =119873119906(119861 minus 119887)

8119889 120590119904119905

Avec

119873prime = 119873119906 (1 +3119890

119860) = 23833119896119873

Donc 119860119887 = 1621198881198982


119860119898119894119899 = 023 times11989111990528119891119890

times 119860 times ℎ119905 = 17251198881198982

Sens B

119860119898119894119899 = 023 times11989111990528119891119890

times 119861 times ℎ119905 = 691198881198982



A (cm2) St (cm)

A 345 1725 10T16 201 25 B 07 69 7T16 1407 25



134



119873119905 = (119873

120572) ge 20 119896119873 [119825119823119808120791120791 119855 120784120782120782120785 119808119851119853 120783120782 120783 120783 119835]


119873119905 =14896

12= 1241119896119873

ELS

119873119905 =796

12= 663119896119873


119860119904119905 =119873119905120590119904119905

ELS

119860119904119905 =663

348= 0191198881198982

ELU

119860119904119905 =1241

348= 0351198881198982





119860119904119905 = 0905 le 119860119904 = 6791198881198982


135


120601119898119894119899 le 119898119894119899 (ℎ

35120601119897119898119894119899

119887

10) = 08 119888119898

On prend 120601119905 =8mm


On prend St=10cm


136


137

ANNEXE - 1

138

139

140

ANNEXE - 2

141

ANNEXE - 3

142

143

ANNEXE ndash 4

144

145

ANNEXE ndash 5
























































































Liste des tableaux

















LISTE DES NOTATIONS

Majuscules latines








16

Chapitre-1


11 Introduction


17



18

Action

permanente (γG)




Effet favorable

γGinf

10 1 0


γGsup

135 15 15




135119866119896119895 + 15119876119896119898119886119909





1 119866119896119895 + 150119882minus


sum119866119896119895119895

+ 119876119896119898119886119909

119866119896119895 + 119876119896119898119886119909


sum119866119896119895119895

+ 09sum119876119896119894119894gt1

119866119896119895 + 09119876119896119898119886119909 + 09119878 119866119896119895 + 09119876119896119898119886119909 + 09119882


19










20




21






22




23

Chapitre-2


21 Introduction










24

- Effet du site








Ouargla (Zone 4)




Kt=017 Z0=001m Zmin=1m ξ=044






Avec




119902119901(119885) = 119902119903119890119891 times 119862119890

Avec

- 119902ref = 575 119889119886119873119898sup2


2(119885) times [1 + 7119868119907] 119825119821119829120784120782120783120785 119836119841119834119849119842119853119851119838 120784 120786 sect120784 120786 120784 119834


25


119862119903(119911)

119870119905 119871119899 (1199111198981198941198991199110

) 119901119900119906119903 119911 lt 119911119898119894119899

119870119905 119871119899 (119911

1199110) 119901119900119906119903 119911119898119894119899 le 119911 le 200119898


)=0783


Zo)=1178

On retient 119862119903= 1178


119868119907(119911)

1

119862119905(119911) 119871119899 (119911

1199110) 119901119900119906119903 119911 gt 119911119898119894119899

1

119862119905(119911) 119871119899 (1199111198981198941198991199110) 119901119900119906119903 119911 le 119911119898119894119899

Pour z gt zmin 119868119907(119911) =1

1Ln(1

001)= 0217

Pour z lt zmin 119868119907(119911) =1

1Ln(1025

001)= 0144



119862119890(119911119895) = 119862119903(119911119895)2[1 + 7 119868119881]

Pour z gt zmin

119862119890(119911) = 11782 times 12 times [1 + 7(0144)] = 2786

Pour z lt zmin

119862119890(119911) = 07832 times 12 times [1 + 7(0217)] = 154


Avec

26

- 119902119903119890119891 = 575 119889119886119873119898sup2



qp = 160195Nm2 = 16 kNm2





- b=30 m

- d=36 m

- h=89 m


e = min (d 2h)


Donc e = 2x1025 = 205m



27



119862119901119890 = 1198621199011198901 119878119894 119878 le 11198982

119862119901119890 = 1198621199011198901 + (11986211990111989010 minus 1198621199011198901) times 11989711990011989210(119878) 119878119894 11198982 lt 119878 lt 101198982

119862119901119890 = 11986211990111989010 119878119894 119878 ge 101198982



Zone


Parois sous le vent


Cpe10 -10 -08 -05 +08 -03


Versant de Toiture




28







le tableau suivant


853deg F G H

-237 -123 -083



- Parois verticales


-b=36 m

29

-d=30 m

-h=1025


e=Min (b 2h) = Min (36 205) = 205 m





30

Zone


Parois sous le vent








31




853deg -22 -192 -183 -067 -057






2(5 times 4)

30 times 89= 014 = 14


μ119901 =120

160= 075



Pour μ119901=075 on lit 119862119901119894 =-016

32




2 times (5 times 4)

36 times 9575= 0116 = 116


Pour μ119901=075 rarr 119862119901119894 =-02

33





Direction V1 V3


A 1602 -10 -0154 -0846 -135529

B 1602 -08 -0154 -0646 -103489

C 1602 -05 -0154 -0346 -55429

D 1602 +08 -0154 +0954 +152831

E 1602 -03 -0154 -0146 -23389


34

Toiture


F 1602 -237 -0154 -2276 -355003

G 1602 -123 -0154 -1076 -172375

H 1602 -084 -0154 -0676 -108295

Z1 1602 -1 -0154 -0846 -135529

Z2 1602 -06 -0154 -0446 -71449


Direction V2 et V4

Parois verticales


A 1602 -10 -0162 -0838 -134247

B 1602 -08 -0162 -0638 -102207

C 1602 -05 -0162 -0338 -54147

D 1602 +08 -0162 +0962 +154112

E 1602 -03 -0162 -0138 -22107


35

Toiture


Finf 1602 -12 -0162 -1038 -1662876

Fsup 1602 -22 -0162 -2038 -3264876

G 1602 -183 -0162 -1668 -2672136

H 1602 -067 -0162 -0508 -813816

I 1602 -057 -0162 -0408 -653616









9= 015




q1= 300 Nml

q2= 500 Nml



36











- Epaisseur 50 mm

- Largeur 1000 mm





Selon le DTR BC22




37

119902 =8119875

3119871= 044 119896119873119898

119902 = 444 119889119886119873119898













38

Chapitre-3





deacutefavorable

39

(minus354 times5125


0875

6) = minus32754 1198891198861198731198982

Qeq (vent) = 3276 daN1198982















40



41


Vzsd =119902119906119911 times 119897

2=1878 kN

Mysd=119902119906119911 times 119897

2

8=2817 kNm

Mzsd=119902119906119910 times 119897

2

8=081 kNm



IPE 180 A Cm2

h mm

b mm

119905f

mm 119905w

mm 119868y

Cm4

119868z

Cm4

119908ply cm3

119908plz cm3

MATERIAU ACIER S235

239 180 91 8 53 1317 101 146 346




4

384 times 119864 119868119910lt

119897

200=



119897

200= 3 119862119900119899119889119894119905119894119900119899 119907eacute119903119894119891119894eacute119890

Plan z-z

5 times 119902119904119910 times 1198974

384 times 119864 119868119911lt

119897

200=



119897

200= 3 119862119900119899119889119894119905119894119900119899 119907eacute119903119894119891119894eacute119890

42




1205741198721 gt 119872119910119904119889 = 2817 119896119873119898

Calcul de 119872119887119903119889




λ119871119879 =

119871119894119911

119888105

[

1 +120(

119871119894119911ℎ119905119891

)

2

] 025

Avec


(Tableau B12 CCM97)

iz =224mm tf =85mm

L=Lz=3000mm h=200mm

λ119871119879 =

119871119894119911

119888105

[

1 +120(

119871119894119911ℎ119905119891

)

2

] 025 = 9457 rarr λ119871119879 =

989

939= 1007

rarr =1092

43


rarr ꭕ119871119879=

1


2)= 066 le 1

rarr 119872119887119903119889 =ꭕ119871119879times 120573

119908times 119882119901119897119910 times 119891119910

1205741198721

=066 1 166 235

11= 234 119896119873 119898








119872119872119860119883 =119901prime 119897

3=119901 1198972

8⟹ 119901 =

8 119901prime

3119897=800

18= 4444 119889119886119873119898119897

44


(ANNEXE ndash 1)

Soit

119876119890119902 =327 + 1082

2= 2176 1198891198861198731198982









45



Vzsd =119902119906119911 times 119897

2=186 kN

Mysd=119902119906119911 times 119897

2

8=279 kNm

Mzsd=119902119906119910 times 119897

2

8=0855 kNm

46



IPE 200 A Cm2

h mm

b mm

119905f

mm 119905w

mm 119868y

Cm4

119868z

Cm4

119908ply cm3

119908plz cm3

MATERIAU ACIER S235

285 200 100 85 56 1943 142 221 446




4

384 times 119864 119868119910lt

119897

200=



119897

200= 3 119862119900119899119889119894119905119894119900119899 119907eacute119903119894119891119894eacute119890

Plan z-z

5 times 119902119904119910 times 1198974

384 times 119864 119868119911lt

119897

200=



119897

200= 3 119862119900119899119889119894119905119894119900119899 119907eacute119903119894119891119894eacute119890




1205741198721 gt 119872119910119904119889 = 279 119896119873119898

Calcul de 119872119887119903119889

47




λ119871119879 =

119871119894119911

119888105

[

1 +120(

119871119894119911ℎ119905119891

)

2

] 025

Avec


(Tableau B12 CCM97)


-L=Lz=6000mm -h=200mm

λ119871119879 =

119871119894119911

119888105

[

1 +120(

119871119894119911ℎ119905119891

)

2

] 025 = 989 ⟶ λ119871119879 =

989

939= 105

rarr =114


rarr ꭕ119897119905=

1


2)= 063 le 1

rarr 119872119887119903119889 =ꭕ119897119905times 120573

119908times 119882119901119897119910 times 119891119910

1205741198721


11= 2974119896119873119898



48


Avec

119881119901119897119911119903119889 =

119860119907119911 (119891119910

radic3)

11 119890119905 119860119907119911 = 1400 1198981198982

Donc

05119881119901119897119911119903119889 = 05

1400 (235

radic3)

11= 8634 119896119873



Si 119889


CCM97 art 561(1)

119889

119905119908 =

159





(119872119910119904119889

119872119901119897119910119903119889)

120572

+ (119872119911119904119889119872119901119897119911119903119889

)

120573

le 1 119912119955119957 120787 120786 120790 (120783120783)119914119914119924 120791120789


119872119901119897119910119903119889 =119882119901119897119910 times 119891119910

11=221 times 235

11= 4721 119896119873119898

119872119901119897119911119903119889 =119882119901119897119911 times 119891119910

11=446 times 235

11= 952 119896119873119898

119872119910119904119889 = 279 119896119873119898

119872119911119904119889 = 0855 119896119873119898

(279

4721)2

+ (0855

952) = 044 lt 1 119888119900119899119889119894119905119894119900119899 119907eacute119903119894119891119894eacute119890

49











Effort rampant


Lrsquoexcentrement


2 (119887

2) le 119905 le 3(

119887

2)


50

2 (10

2) = 10 le 119905 le 3(

10

2) = 15

On prend t=10 cm


119877119911 = 119902119906119911 times119897

2= 6 times

6

2= 18 119896119873

119877119910 = 119902119906119910 times119897

2= 054 119896119873


119877119911 = 18 times 2 = 36 119896119873

119877119910 = 054 times 2 = 108 119896119873


119872119877 = 119877119911 times 119905 + 119877119910 timesℎ

2= 36 times 10 + 108 times 10 = 3708 119896119873 119888119898 = 37119896119873119898


119872119890119897119877119889 =119908119890119897 times 119891119910

1205741198720 119912119955119957 120787 120786 120787 120783 (120784)119914119914119924120791120789

119872119890119897119877119889 =119908119890119897 times 1198911199101205741198720

=gt 119908119890119897 ge119872119890119897119877119889 times 1205741198720

119891119910=gt 119908119890119897 ge

00037 times 11

235

= 173 times 10minus51198983

119908119890119897 = 17321198881198983




119908119890119897 =119887 1198902


6 times 1732

119887= radic

6 times 1732

180

119890 ge 076


Donc on prend e=1cm

51





















52












qsy =(133 + 5) times 125=2288daNml

qsy = 0228 kN

quy=135G=03kN



W += 1541 daN m2


quz=15W

quz=288kN

53



qsz=19262daN=192kN


119891119911 =5 times 119902119904119911 times 119897

4

384 times 119864119910 times 119868le 119891119886119889119873 =

119897

200=600

200= 3 119888119898

119868119910 ge5 times 192 times 6004



Profileacute


UPN 140 A Cm2

h mm

b mm

119905f mm

119905w mm

Iy

Cm4

Iz

Cm4

119908pSy

cm3

119908pSz

cm3

MATERIAU ACIER S235

20 140 60 10 7 605 627 103 283







qsy =(133 + 5) times 125 +1568 = 3856daNml

qsy = 038 kN

quy=135G

quy =053kN


qsz=192kN

quz=15W

quz=288kN

54




119888

119905119891=60

10= 6 lt 10휀 =gt 119888119897119886119904119904119890 1


119889

119905119908=98

7= 14 lt 72휀 =gt 119888119897119886119904119904119890 1


(119872119910119904119889

119872119890119897119910119877119889)

1

+ (119872119911119904119889

119872119890119897119911119877119889)1

le 1


119872119910 =119902119906119911 times 119897

2

8=288 times 62

8= 1296 119896119873119898


119872119911 =119902119906119910 times 119897

2

8=058 times 62

8= 261119896119873119898

119872119890119897119910119877119889 =119908119890119897119910 times 119891119910

1205741198720=864 times 103 times 235

11= 1845 119896119873119898

119872119890119897119911119877119889 =119908119890119897119911 times 119891119910

1205741198720=148 times 103 times 235

11= 316 119896119873119898

Donc

(1296

1845)1+ (

261



55

Nouveau 119872119911

119872119911 =119902119906119910 times 119897

2

8=058 times 32

8= 065119896119873119898

(1296

1845)1+ (

065




119881119911119904119889 =15119882119871

2= 1296 119896119873

119881119901119897119877119889 =119860119907119911 times 119891119910

radic3times 1205741198720= 12855 119896119873





1205741198721gt 119872119910119904119889 119912119955119957 120787 120787 120784 (120787 120786120790)119914119914119924120791120789

Avec

119872119888119903 = 11986211205872 119864 1198681199111198712

radic119868119908119868119911+1198712 119866 1198681199051205872 119864 119868119911

119912119925119925119916119935119916 119913 (119913 120783 120785) minus 119914119914119924120791120789

119872119888119903=311713762 Ncm


119872119888119903


119882119901119897119910 (upn140) =103 cm3

56

λ119897119905 = 0881


2 ]


empty119897119905 = 0959

ꭕ119897119905=

1


2 )

le 1

ꭕ119897119905= 075

119872119887119903119889 = 1652 119896119873119898

119872119887119903119889 = 1652 119896119873119898 gt 119872119910119904119889 = 1296 119896119873119898 119862119900119899119889119894119905119894119900119899 119907eacute119903119894119891119894eacute119890







57

119877 = 125119902119910 times 119897

2

Avec 119902119910 = [135(119866119880119875119873140 + 119866119888119900119906119907119890119903119905119906119903119890)]

119902119910 = 0837119896119873

119897 = 6 119898

119877 = 125119902119910 times 119897

2= 125 times 0837 times 3 = 32119896119873


1198791 =119877

2= 16119896119873

1198792 = 1198791 + 119877=48 kN

1198793 =1198792

2 sin 120579= 374 119896119873 119860119907119890119888 120579 = 119886119903119888 119905119892

25 119898

3 119898= 398deg



119873119905119904119889 =119860 times 119891119910

1205741198720= 4800 119873 =gt 119860 ge

11 times 4800

235 =gt 119860 ge 22461198981198982

119860 =120587empty2

4=gt empty ge radic

4119860

120587= radic

4 times 2246

314= 534 119898119898



Introduction



58



119878ge

63

radic119904

119889times119875

Avec








Srsquo=273

4=6825 m2








59



















96=8989 daNm2





60

119891119910 =5 times119882 times 1198974

384 times 119864 times 119868119910le 119891119886119889119898 =

119897

200


384 times E= 59136 1198881198984


Profileacute


IPE300 A Cm2

h mm

b mm

tf mm

tw

mm 119868y

Cm4

119868z Cm4

Wply

cm3

Wplz

cm3

MATERIAU ACIER S235

538 300 150 107 71 8356 746 628 125





119888

119905119891=

75

107= 7 lt 10 = 10 119878119890119898119890119897119897119890 119889119890 119888119897119886119904119904119890 1


119889

119905119908=2486

71= 35 lt 38 = 38 Acirc119898119890 119889119890 119888119897119886119904119904119890 1



Si 119881119904119889 le 05 119881119901119897119903119889 ⟹119872119904119889 le 119872119888119903119889 119912119955119957120787 120786 120789 119914119914119924 120791120789

61

119881119904119889 =15 times119882 times 119897


2= 388 119896119873 lt 05 119881119901119897119903119889 = 05 (

2570 times 235

radic3 times 11) = 1585 119896119873





Si

119873119904119889 le 119872119894119899 (025119873119901119897119903119889 05119860119908 119891119910

1205741198980)


025119873119901119897119903119889 = 025119860 times 119891119910

1205741198720= 025

5380 times 235

11= 28734 119896119873

05119860119908 times 119891119910

1205741198720= 05

2170 times 235

11= 2317 119896119873

119873119904119889 = 135119866 = 1337 119896119873 lt 119898119894119899 (025119873119901119897119903119889 05119860119908 times 119891119910

1205741198720)





119872119910119904119889 =15119882 times 1198972

8= 9313119896119873119898 119872119911119904119889 = 0 119872119901119897119910119903119889 = 13416 119896119873119898

λ119897119905 =

119871119911119894119911

119888105

[

1 +120(

119871119911119894119911ℎ119905119891

)

2

] 025


62

119871119911 = 1250 119898119898 119894119911 = 335 119898119898 ℎ = 300 119898119898 119905119891 = 107 119898119898




119873119904119889ꭕ119898119894119899

119873119901119897119903119889+119870119910 119872119910119904119889

119872119901119897119910119903119889+119870119911 119872119911119904119889119872119901119897119911119903119889


Avec

λ119910 =119871119910

119894119910=960

125= 768 rarr λ119910 =

768

939= 081

=gt 120583119910 = λ119910(2119861119898119910 minus 4) +119882119901119897119910 minus119882119890119897119910

119882119890119897119910= minus1134 + 0127 = minus1007 lt 09

120572 = 021 λ119910 = 081

empty119910 = 05 [1 + 120572119910(λ119910 minus 02) + λ1199102]

empty119910 = 05[1 + 021(081 minus 02) + 0812] = 089

ꭕ119910=

1


ꭕ119910= 0794 rarr 119870119910 = 1 minus


0794 times 538 times 2350= 101

120582119911 =125

335= 3731 =gt 120582119911 = 0397 rarr empty119911 = 0611 =gt ꭕ

119911= 092

ꭕ119898119894119899

= ꭕ119910= 0794

119873119901119897119903119889 =119860119891119910

1205741198980=5380 times 235

11= 114936 119896119873

119872119910119904119889 =151198821198712

8= 9313 119896119873119898

119872119901119897119910119903119889 = 13416 119896119873119898

119873119904119889 = 135119866 = 1337 119896119873

119896119910 = 101

119872119911119904119889 = 0

63

119873119904119889120594119898119894119899 119873119901119897119903119889

+119896119910 119872119910119904119889

119872119901119897119910119903119889+119896119911 119872119911119904119889119872119901119897119911119903119889

le 10

1337

0794 times 114836+101 times 9313

13416= 071 lt 1 119862119900119899119889119894119905119894119900119899 119907eacute119903119894119891119894eacute119890




64

Chapitre 4


41 Introduction




- Le pont roulant










poteaux de la halle

65





Puissances

N (t)

Porteacutee

L(m)



B

Chariot

K

Total

B+K

Rmax Rmin

125 18 085 520 1040 6809 1151 796 814 194


66


1 035 06 2 36



I 02 11 11 A-2















Groupes II






67
















119877119898119886119909 = 814 119870119873 119877119898119894119899 = 194 119870119873

Charges verticales

119877119881119898119886119909 = Ψ1 119877119898119886119909 = 115 times 814 = 8954 119870119873

119877119881119898119894119899 = Ψ2 119877119898119894119899 = 11 times 194 = 2134 119870119873


68

119877119871119898119886119909 = 119862 119877119898119886119909 = 02 times 814 = 1628 119870119873

119877119871119898119894119899 = 119862 119877119898119894119899 = 02 times 194 = 388 119870119873



1198771198671119898119886119909 = plusmn [0024(119870 + 119873 + 119861)119871

119890+ 0021(119873 + 119870)]

= plusmn [0024(1151 + 125 + 6809)18

36+ 0021(125 + 1151)]

1198771198671119898119886119909 = plusmn274 119905

1198771198671119898119894119899 = plusmn [0024(119870 + 119873 + 119861)119871

119890minus 0021(119873 + 119870)]

= plusmn [0024(1151 + 125 + 6809)18

36minus 0021(125 + 1151)]

1198771198671119898119894119899 = plusmn2168 119905


1198771198672119898119886119909 = plusmn [00052(119870 + 119873 + 5119861)119871

119890+ 0021(119873 + 119870)]

= plusmn [00052(1151 + 125 + 5 times 6809)18

36+ 0021(125 + 1151)]

1198771198672119898119886119909 = plusmn1526 119905

1198771198672119898119894119899 = plusmn [00052(119870 + 119873 + 5119861)119871

119890minus 0021(119873 + 119870)]

= plusmn [00052(1151 + 125 + 5 times 6809)18

36minus 0021(125 + 1151)]

1198771198672119898119894119899 = plusmn0953 119905




69





Rail

Poids

(Kgm)

B

(mm)

H

(mm)

P

(mm)

Section

A (cm2)

I x

(cm4)

I y

(cm4)

A55

318

55

65

150

407

178

337



70



119891119911 le 119891119886119889119898 =119897

750= 08 119888119898



119886 = (119897

2minus119890

4) = (

6

2minus36

4) = 21 119898



119891119911 =119901 119886 1198972

24119864119868(3 minus

4 1198862

1198972)

Avec

L= 6000 mm

a= 2100 mm

P=89540 N

E=21104 Nmm2

71

119868119910 ge119901 119886 1198972(31198972 minus 41198862)



119868119910 ge 421397625 1198981198984






119902 = 119866119901119900119906119905119903119890 + 119866119903119886119894119897 = 142 + 031 = 173 119896119899119898119897

119891119911 =119901 119886 1198972

24119864119868(3 minus

4 1198862

1198972) +

5 119902 1198974

384119864119868

119891119911 =89540 times 2100 times 60002


4 times 21002

60002) +




profileacute


G

Kgm

A cm2 h

mm

b

mm

tf

mm

tw

mm

Iy

cm4

Iz

cm4

Wply

cm3

Wplz

cm 3

HEB360 142 1806 360 300 225 125 43190 10140 2683 1032

72


119902 = 119866119901119900119906119905119903119890 + 119866119903119886119894119897 = 155 + 031 = 186 119870119873119898119897

119891119911 =119901 119886 1198972

24119864119868(3 minus

4 1198862

1198972) +

5 119902 1198974

384119864119868

119891119911 =89540 times 2100 times 60002


4 times 21002

60002) +






119905119908le 72휀

Avec

휀 = radic235

119891119910

298

135le 72radic

235

235 ⟹ 2207 le 72


119888

119905119891=1198872

119905119891le 10휀 ⟹

150

24= 625 le 10




profileacute


G

Kgm

A

cm2

h

mm

b

mm

tf

mm

tw

mm

Iy

cm4

Iz

cm4

Wply

cm3

Wplz

cm 3

HEB400 155 1978 400 300 24 135 57680 10820 3232 1104

73

119881119910119904119889 le 119881119901119897119903119889 119912119955119957 120787 120786 120788 (120787 120784120782)119914119914119924120791120789

119881119901119897119903119889 =119860119907119911 119891119910

radic3 1205741198980=6998 times 235

radic3 times 11= 863154 119873 = 86315 119870119873


119881119881 = 119877119881119898119886119909 times4119886

119897=8954 times 4 times 21

6= 12535 119870119873


119881119875119875 =119866 119897

2=186 times 6

2= 558 119870119873

Drsquoougrave 119881119910119904119889 = 135119881119875119875 + 15119881119881 = 19556 119870119873

119881119910119904119889 le 119881119901119897119903119889



Suivant (z-z)


119872119881 = 119877119881119898119886119909 times(6 minus

1198902)2

4119897= 8954 times

(6 minus362 )

2

4 times 6= 6581 119870119873119898


119872119875119875 =119866 1198972

8= 837 119870119873119898


119872119910119904119889 = 135119872119875119875 + 15119872119881 = 110 119870119873119898



119872119911119904119889 = 119872119867 =21198771198671119871

(119871

2minus119890

4)2

74

119872119911119904119889 = 119872119867 =2 times 274

6times (

6

2minus36

4)2

= 4028 119870119873119898




119873119904119889119873119901119897119903119889

+119872119910119904119889

119872119890119897119910+119872119911119904119889119872119890119897119911

le 1 120787 120785120790 ndash 119810119810119820120791120789

119873119904119889 = 15119877119871119898119886119909 = 15 times 1628 = 2442 119870119873

119872119890119897119910 =119908119890119897119910 119891119910

1205741198720= 61613 119872119890119897119911 =

119908119890119897119911 119891119910

1205741198720= 1541 119873119901119897119903119889 =

119860 119891119910

1205741198720= 422573

2442

422573+

110

61613+4028

1541= 044 le 1



Si 119889


Avec

휀 = radic235

119891119910= 1

119889

119905119908=298

135= 2207 lt 69





1205741198721


75



λ119897119905 =

119871119894119911

119888105

[

1 +120(

119871119894119911ℎ119905119891

)

2

] 025 = 6522 119808119821119821119812119831119812119809 119810119810119820120791120789

Avec 119871 = 600119888119898


λ119871119879 = [λ119897119905λ1] [120573119908]

05 휀 = radic235

119891119910= 1

λ119871119879 =6522

939= 0694

On calcule

ꭕ119871119879=

1


2 )le 1




ꭕ119871119879=

1

(079 + radic0792 minus 06942)= 0856


11= 59104 119870119873119898

119872119910119904119889 = 110 119870119873119898




76



119891119904119889 le 119877119910119877119889

Avec




120590119891119864119889 =119872119910119904119889

119882119890119897119910= 381 1198701198731198881198982

119878119910 = 2(ℎ119877 + 119905119891)radic[1 minus (1205741198720120590119891119864119889

119891119910119891)

2

] = 1751 119888119898

119877119910119877119889 =119878119910 times 119905119908 times 119891119910119908

1205741198720= 505 119870119873 gt 119891119904119889 = 119877119907119898119886119909 = 8954 119870119873




119891119904119889 le 119877119886119877119889

119891119904119889119877119886119877119889

+119872119878119889119872119888119877119889

le 1 119808119825119827 120787 120789120790 minus 119810119810119820120791120789

Avec

77

119877119886119877119889 =

051199051199082 (119864 119891119910119908)

05[(119905119891119905119908)05

+ 3(119905119908119905119891) (119878119904119889 )]

1205741198720 119808119825119827 120787 120789120789 minus 119810119810119820120791120789

119877119886119877119889 = 108284 119870119873

119891119904119889 = 15119877119871119898119886119909 = 15 times 1628 = 2442 119870119873

119872119888119877119889 =3232 times 103 times 235

11= 69047 119870119873119898

119891119904119889119877119886119877119889

+119872119878119889119872119888119877119889

=2442

108284+

110

69047 = 018 le 15




119887119890119891119891 le 119887 119808119825119827 120787 120789120791 minus 119810119810119820120791120789

119887119890119891119891 = radicℎ2 + 1198781199042 = 410 119898119898 gt 119887 = 300 119898119898




efforts suivants




Charge verticale


119901prime = 119876 119871 + 119877119898119886119909 (2 minus119890

119871) ψ


36

6) times 11

119901prime = 13651 119870119873


119901 = 135119876 119871 + 15119877119898119886119909 (2 minus119890

119871) ψ


36

6) times 11

119901 = 2031 119870119873

78

Charge horizontale

119875119867 = 15119877119867119898119886119909 (1 minus119890

119897)ψ


36

6) times 11 = 1808 119870119873




119891119911 le 119891119886119889119898 =119897

500


119891119911 =119901prime 1198893

3119864119868le 119891119886119889119898

119868119910 =500 119901prime 1198892

3119864ge 782667 1198881198984


79




119905119908le 72휀

Avec

휀 = radic235

119891119910

2486

71le 72radic

235

235 ⟹ 3501 le 72


119888

119905119891=1198872

119905119891le 10휀 ⟹

75

102= 735 le 10





119881119910119904119889 le 119881119901119897119903119889

Avec 119860119907119911 = 257 cm2

119881119901119897119903119889 =119860119907119911 119891119910

radic3 1205741198980=257 times 235

radic3 times 11= 317 119870119873

119881119904119889 = 119901 = 2031 lt 05119881119901119897119877119889


profileacute


G

Kgm

A

cm2

h

mm

b

mm

tf

mm

tw

mm

Iy

cm4

Iz

cm4

Wply

cm3

Wplz

cm 3

IPE 300 422 5380 300 150 107 71 8353 604 628 125

80


119872119888119903119889 =119908119901119897119910 119891119910

1205741198720=628 times 235

11= 13416 119870119873119898

119872119910119904119889 = 119901 119889 = 2031 times 085 = 172635 119870119873119898

119872119910119904119889 lt 119872119888119903119889




119872119888119903119889 =119908119901119897119910 119891119910

1205741198720=1019 times 235

11= 2177 119870119873119898

119872119910119904119889 = 119901 119889 = 2031 times 085 = 172635 119870119873119898

119872119910119904119889 lt 119872119888119903119889


17263


profileacute


G

Kgm

A

cm2

h

mm

b

mm

tf

mm

tw

mm

Iy

cm4

Iz

cm4

Wply

cm3

Wplz

cm3

IPE 360 571 727 360 170 127 8 16270 1043 1019 191

81



chemin de roulement

119891119911 le 119891119886119889119898 =119889

500= 017

119902 = 119902119868119875119864 360 = 571 119889119886119873119898119897

119891119911 =119901prime 1198893

3119864119868+119902 1198974

8119864119868= 0082 + 0021 = 0103 119888119898 lt 017 119888119898


82

Chapitre-5








dynamiques


83




119881 =119860119863 119876

119877119882



119863 =

25120578 0 le 119879 le 1198792

25120578(1198792119879)23 1198792 le 119879 le 3119904

25120578 (11987923)

23 (3119879)

53 119879 gt 3119904


84

120578 = radic7

(2 + 120585)ge 07



119879 = 119862119879 ℎ11987334 119917119926119929119924119932119923119916 (120786 120788)119929119927119912 119933120784120782120782120785




119876 = 1 +sum119875119902

6

1


85


119876 = 1 +sum119875119902

6

1

= 1 + 02 = 12


119899119894=1

Avec 119882119894 = 119882119866119894 + 120573119882119876119894




119881 =119860119863 119876

119877119882

119860 = 005 119863 = 25 119876 = 12 119877 = 4 119882 = 189475119896119873

119881119909 = 119881119910 =005 times 25 times 12

4times 189475 = 7105119896119873


119904119886119892=

125119860 (119860 +

119879

1198791(25120578

119876

119877minus 1)) 0 le 119879 le 1198791

25120578(125119860) (119876

119877) 1198791 le 119879 le 1198792

25120578(125119860) (119876

119877)(1198792119879)23

1198792 le 119879 le 30119904

25120578(125119860) (11987923)

23(3

119879)

53(119876

119877) 119879 gt 30119904

86



η = 100 A=005 1198791=015 1198792=050


87













88










89

ℎ

150=890

150= 594119888119898 sans vent

ℎ

125=890

125= 712119888119898 avec vent






Toiture 029 076 116 304


ℎ

100=1025

100= 1025 119888119898



90

Chapitre-6


61 Introduction





119872119910119904119889 = 21902 kNm

119881119904119889 =7249 kN

119873119904119889 =2018 kN

91

Profileacute


IPE 400 A cm2

hmm

b mm

119905f

mm

119905w mm

119868y

cm4

119868z Cm4

119908ply

cm3

119908plz

cm3

MATERIAU ACIER S235

8446 400 180 14 90 231284 131782 123832 2256




119888

119905119891=60

14= 59 lt 10휀 =gt 119888119897119886119904119904119890 1


119889

119905119908=98

9= 11 lt 72휀 =gt 119888119897119886119904119904119890 1





Si 119881119904119889 le 05119881119901119897119903119889 ⟹ 119872119904119889 le 119872119888119903119889 119912119955119957120787 120786 120789 119914119914119924 120791120789


119881119898119886119909 = 119881119904119889 =7248kN

119881119901119897119911119903119889 =

119860119907119911 (119891119910

radic3)

1205741198980=

4270235

radic311

= 526674119896119873

119881119904119889 = 7247 le 05119881119901119897119911119903119889 = 52667119896119873


92



119873119904119889 le 119872119894119899(025119873119901119897119903119889 05119860119908119891119910

1205741198720)


119873119904119889 = 2018119896119873

119873119901119897119903119889 le119860 119891

119910

1205741198720=8446 235

11= 180437119896119873

025119873119901119897119903119889 =451 119896119873

119860119908 = 119860 minus 2119887 119905119891 = 34061198981198982

05119860119908119891119910

1205741198720= 36382119896119873

119873119904119889 = 2018 le 36382119896119873



119872119888119903119889 = 119872119901119897119910119903119889 =119908119901119897119910 119891119910

1205741198720=1238320 235

11= 26455119896119873119898




120594119898119894119899 119873119901119897119903119889+119896119910 119872119910119904119889

119872119901119897119910119903119889+119896119911 119872119911119904119889119872119901119897119911119903119889



120594119911 119873119901119897119903119889+119896119871119879 119872119910119904119889

120594119871119879119872119901119897119910119903119889+119896119911 119872119911119904119889119872119901119897119911119903119889



120594119898119894119899 = 119872119894119899(120594119910 120594119911)


93

120594119910 =1

(120601119910 +radic1206011199102 minus 1205821199102 )

120601119910 = 05[1 + 120572119910(120582119910 minus 02) + 1205821199102]

120582119910= (120582119910

1205821)radic120573119860 =

120582119910

1205821

Avec 120573119860 = 1 Classe 1

1205821 = 939

120582119910 =05119868119910

119894119910=455

166= 274

120582119910=274

939= 029


ℎ

119887=400

180= 222 gt 12 119894119898119901119897119894119902119906119890 120572 = 021

120601 = 05[1 + 120572119910(120582119910 minus 02) + 1205821199102 ] = 055

120594119910 =1

(055 + radic0552 minus 0292)= 098


120594119911 =1

(120601119911 +radic1206011199112 minus 120582119911

2)

120601119911 = 05[1 + 120572119911(120582119911 minus 02) + 1205821199112]

120582119911 = (1205821199111205821)radic120573119860 =

1205821199111205821

Avec 120573119860 = 1 Classe 1

120582119911 =119868119911119894119911=200

395= 5063

120582119911 =5063

939= 054


94

ℎ

119887= 222 gt 12 (119911 minus 119911)119894119898119901119897119894119902119906119890 120572 = 034

120601 = 05[1 + 034(054 minus 02) + 0542 ] = 07

120594119911 =1

(07 + radic072 minus 0542)= 087

120594119898119894119899 = 119872119894119899(120594119910 120594119911) = 087




λ119897119905 =

119871119894119911

119888105

[

1 +120(

119871119894119911ℎ119905119891

)

2

] 025 = 4367 119808119821119821119812119831119812119809 119810119810119820120791120789

Avec

IPE400 119905119891 = 14119898119898 119894119911 = 395119888119898 ℎ = 400119898119898

119870 = 1 1198881=1134 Tableau B11 CCM97


1205821 = 939휀

휀 = radic235

119891119910= 1

120582119871119879 = [1205821198971199051205821] [120573119908]

05

120582119897119905 = 4367

120582119871119879 =4367

939= 046 gt 04



119873119904119889120594119911 119873119901119897119903119889

+119896119871119879 119872119910119904119889

120594119871119879119872119901119897119910119903119889+119896119911 119872119911119904119889119872119901119897119911119903119889


Calcul de 120594119871119879


95

implique 120594119871119879 = 094

Calcul de 119896119871119879


119870119871119879 = 1 minusμLT N119904119889

120594119911 119860 119891119910= 099 lt 15


Donc

119873119904119889=7249 kN 119872119910119904119889=219 kNm 119872119901119897119910119903119889=26455 kNm 120594119911=087 119872119901119897119911119903119889=4819kNm


119873119904119889120594119911 119873119901119897119903119889

+119896119871119879 119872119910119904119889

120594119871119879119872119901119897119910119903119889+119896119911 119872119911119904119889

119872119901119897119911119903119889


7249

087 180437+

099 219

094 26455= 055










96

119872119910119904119889 = 32083 119896119873119898

119881119904119889 = 120 119896119873

119873119904119889 = 602 119896119873

Profileacute


HEA320

A cm2

hmm

b mm

119905f

mm

119905w mm

119868y

cm4

119868z cm4

119908 ply

cm3

119908 plz

cm3

MATERIAU ACIER S235

12437 310 300 16 9 229286 698524 162823 70975




119888

119905119891=60

16= 375 lt 10휀 =gt 119888119897119886119904119904119890 1


119889

119905119908=98

9= 109 lt 72휀 =gt 119888119897119886119904119904119890 1





Si 119881119904119889 le 05119881119901119897119903119889 ⟹ 119872119904119889 le 119872119888119903119889 119912119955119957120787 120786 120789 119914119914119924 120791120789


119881119898119886119909 = 119881119904119889 =120kN

119881119901119897119911119903119889 =

119860119907119911 (119891119910

radic3)

1205741198980=4113 235radic3

11= 50731119896119873

97

119881119904119889 le 05119881119901119897119911119903119889




119873119904119889 le 119872119894119899(025119873119901119897119903119889 05119860119908119891119910

1205741198720)


119873119904119889 =602kN

119873119901119897119903119889 le119860 119891

119910

1205741198720=12437 235

11= 2656995 119896119873

025119873119901119897119903119889 = 664248119896119873

119860119908 = 119860 minus 2119887 119905119891 = 2837 1198981198982

05119860119908119891119910

1205741198720= 30304119896119873

119873119904119889 = 602119896119873 le 30304119896119873



119872119888119903119889 = 119872119901119897119910119903119889 =119908119901119897119910 119891119910

1205741198720=1628000 times 235

11= 3478119896119873119898




120594119898119894119899 119873119901119897119903119889+119896119910 119872119910119904119889

119872119901119897119910119903119889+119896119911 119872119911119904119889119872119901119897119911119903119889



120594119911 119873119901119897119903119889+119896119871119879 119872119910119904119889

120594119871119879119872119901119897119910119903119889+119896119911 119872119911119904119889119872119901119897119911119903119889



120594119898119894119899 = 119872119894119899(120594119910 120594119911)


98

120594119910 =1

(120601119910 +radic1206011199102 minus 1205821199102 )

120601119910 = 05[1 + 120572119910(120582119910 minus 02) + 1205821199102]

120582119910= (120582119910

1205821)radic120573119860 =

120582119910

1205821

Avec 120573119860 = 1 Classe 1

1205821 = 939

120582119910 =05119868119910

119894119910=05 890

1358= 3276

120582119910=3276

939= 034


ℎ

119887=310

300= 1 lt 12 (119910 minus 119910)119894119898119901119897119894119902119906119890 120572 = 034

120601 = 05[1 + 120572119910(120582119910 minus 02) + 1205821199102 ] = 058

120594119910 =1

058 + radic058 minus 034= 095


120594119911 =1

(120601119911 +radic1206011199112 minus 1205821199112)

120601119911 = 05[1 + 120572119911(120582119911 minus 02) + 1205821199112]

120582119911 = (1205821199111205821)radic120573119860 =

1205821199111205821

Avec 120573119860 = 1 Classe 1

1205821 = 939

120582119911 =119868119911119894119911=07 59

749= 055


ℎ

119887= 1 lt 12 (119911 minus 119911) 119894119898119901119897119894119902119906119890 120572 = 049

120601 = 05[1 + 049(055 minus 02) + 0552] = 073

99

120594119911 =1

073 + radic073 minus 055= 082

120594119898119894119899 = 119872119894119899(120594119910 120594119911) = 082


λ119897119905 =

119871119894119911

119888105

[

1 +120(

119871119894119911ℎ119905119891

)

2

] 025 = 3536

HEA320 119905119891 = 16119898119898 119894119911 = 749119888119898 ℎ = 310119898119898

119870 = 07 1198881 = 1134 Tableau B11 CCM97


1205821 = 939휀

휀 = radic235

119891119910= 1

120582119871119879 = [1205821198971199051205821] [120573119908]

05

120582119897119905 = 3536

120582119871119879 =3536

939= 037 lt 04 119901119886119904 119889119890 119903119894119904119902119906119890 119889119890 119889119890119907119890119903119904119890119898119890119899119905


119873119904119889120594119898119894119899 119873119901119897119903119889

+119896119910 119872119910119904119889

119872119901119897119910119903119889+119896119911 119872119911119904119889119872119901119897119911119903119889


Avec

119873119904119889 =602kN 119872119910119904119889=32083kNm 119872119911119904119889=049kNm 119872119901119897119910119903119889=3478kNm

119872119901119897119911119903119889=1516kNm 120594119898119894119899= 082 119873119901119897119903119889=26570kN 119896119910= 05 119896119911= 07

602

082 26570+05 32083

3478+07 049







100





(135G+15V1)


119873119904119889 =69837kN


Profileacute


2CAE (120x12)

A Cm2

hmm

b mm

Anet

Cm2

d

mm

MATERIAU ACIER S235

5508 120 248 4658 8



119873119904119889 le 119873119905119903119889 = 119872119894119899[119873119901119897119903119889 119873119906119903119889 119873119899119890119905119903119889]

101

119873119901119897119903119889 =119860 119891119910

1205741198720= 117671119896119873

119873119906119903119889 = 09119860119899119890119905 1198911199061205741198722

= 13719119896119873

119873119899119890119905119903119889 =119860119899119890119905 119891119910

1205741198720= 995118119896119873








102


119872119910119904119889 = 02 119896119873119898

119881119904119889 = 0048 119896119873

119873119904119889 = 5628 119896119873

Profileacute


IPE300

A cm2

hmm

b mm

119905f

mm

119905w mm

119868y

cm4

119868z cm4

119908ply

cm3

119908plz

cm3

MATERIAU ACIER S235

538 300 150 107 71 8356 746 628 125







Si 119881119904119889 le 05119881119901119897119903119889 ⟹ 119872119904119889 le 119872119888119903119889 119912119955119957120787 120786 120789 119914119914119924 120791120789


119881119898119886119909 = 119881119904119889 =0048kN

119881119901119897119911119903119889 =

119860119907119911 (119891119910

radic3)

1205741198980=2570 235radic3

11= 3169119896119873

119881119904119889 le 05119881119901119897119911119903119889




119873119904119889 le 119872119894119899(025119873119901119897119903119889 05119860119908119891119910

1205741198720)

103


119873119904119889 =5628kN

119873119901119897119903119889 le119860 119891

119910

1205741198720=5380 235

11= 114936 119896119873

025119873119901119897119903119889 = 28734 119896119873

119860119908 = 119860 minus 2119887 119905119891 = 2170 1198981198982

05119860119908119891119910

1205741198720= 23179119896119873

119873119904119889 = 5628119896119873 le 23179119896119873



119872119888119903119889 = 119872119901119897119910119903119889 =119908119901119897119910 119891119910

1205741198720=628000 times 235

11= 134163 119896119873119898




120594119898119894119899 119873119901119897119903119889+119896119910 119872119910119904119889

119872119901119897119910119903119889+119896119911 119872119911119904119889119872119901119897119911119903119889



120594119911 119873119901119897119903119889+119896119871119879 119872119910119904119889

120594119871119879119872119901119897119910119903119889+119896119911 119872119911119904119889119872119901119897119911119903119889



120594119898119894119899 = 119872119894119899(120594119910 120594119911)


120594119910 =1

(120601119910 +radic1206011199102 minus 1205821199102 )

120601119910 = 05[1 + 120572119910(120582119910 minus 02) + 1205821199102]

120582119910= (120582119910

1205821)radic120573119860 =

120582119910

1205821

104

Avec 120573119860 = 1 Classe 1

1205821 = 939

120582119910 =119871119910

119894119910= 960

125= 768

120582119910=768

939= 081


ℎ

119887=300

150= 05 lt 12 (119910 minus 119910)119894119898119901119897119894119902119906119890 120572 = 021

120601 = 05[1 + 120572119910(120582119910 minus 02) + 1205821199102 ] = 089

120594119910 =1

058 + radic058 minus 034= 079


120594119911 =1

(120601119911 +radic1206011199112 minus 1205821199112)

120601119911 = 05[1 + 120572119911(120582119911 minus 02) + 1205821199112]

120582119911 = (1205821199111205821)radic120573119860 =

1205821199111205821

Avec 120573119860 = 1 Classe 1

1205821 = 939

120582119911 =119868119911119894119911=125

335= 3731 120582119911 = 039


ℎ

119887= 1 lt 12 (119911 minus 119911) 119894119898119901119897119894119902119906119890 120572 = 021

120601 = 05[1 + 021(039 minus 02) + 0392] = 061

120594119911 =1

061 + radic061 minus 039= 092

120594119898119894119899 = 119872119894119899(120594119910 120594119911) = 079


105

λ119897119905 =

119871119894119911

119888105

[

1 +120(

119871119894119911ℎ119905119891

)

2

] 025 = 3433

IPE300 119905119891 = 107119898119898 119894119911 = 335119888119898 ℎ = 300119898119898

119870 = 1 1198881 = 1134 Tableau B11 CCM97


1205821 = 939휀

휀 = radic235

119891119910= 1

120582119871119879 = [1205821198971199051205821] [120573119908]

05

120582119897119905 = 3433

120582119871119879 =3433

939= 036 lt 04 119901119886119904 119889119890 119903119894119904119902119906119890 119889119890 119889119890119907119890119903119904119890119898119890119899119905


119873119904119889120594119898119894119899 119873119901119897119903119889

+119896119910 119872119910119904119889

119872119901119897119910119903119889+119896119911 119872119911119904119889119872119901119897119911119903119889


Avec

119873119904119889 =5628kN 119872119910119904119889=02kNm 119872119911119904119889=018kNm 119872119901119897119910119903119889=134163kNm

119872119901119897119911119903119889=267kNm 120594119898119894119899= 079 119873119901119897119903119889=1149kN 119896119910= 1 119896119911= 1

5628

079 1149+

02

134163+018



106

Chapitre-7


71 Introduction










au poteau

107




119872119904119889 = 28961119896119873119898 119873119904119889 = 17878119896119873 119881119904119889 = 8941119896119873




119905 = 119872119894119899(119905119891 119905119901119897119886119905119894119899119890) = 135119898119898

Avec





12119889O = 24 119898119898 le 1198901 le 12119905 =186 119898119898 ⟹ 1198901 = 110 119898119898

15119889O = 30 119898119898 le 1198902 le 12119905 = 186 119898119898 ⟹ 1198902 = 105 119898119898

22119889O = 44 119898119898 le 1199011 le 14119905 =217 119898119898 ⟹ 1199011 = 100 119898119898


108






IPE 400 119905f = 135 119898119898 119905w = 86 119898119898

119886min= 26 le twle119886max= 8

119886min =35 le tf le119886max= 8







sum119897 = 2119887 + 4(119887 minus 119905119908) = 2180 + 4(180 minus 86) = 1045119898119898

119865119908119903119889 =7times 1045 times 360

radic2= 1862119896119873

119873119904119889 =119872119904119889

ℎ=120784120790120791 120788120783

120782 120791= 120785120784120783 120789120790





Avec 120573119908 = 125 120574119872119882 = 08


109

i

sum119897 = 4ℎ119894 = 4 times 373 = 1492119898119898

119865119907119903119889 =7 times 1492 times 360

radic3= 217074119896119873



119873119894 =119872119904119889 119889119894sum119889119894

2


119909 = 119905119891radic119887

119905119908= 135radic

180

86= 6176



- 1198891 = 712 119898119898

- 1198892 = 612 119898119898

- 1198893 = 512 119898119898 ⟹ Σ 1198892 = 129 119898sup2

- 1198894 = 312 119898119898

- 1198895 = 212 119898119898

- 1198896 = 112 119898119898


1198731 =28961 times 0712

129= 15984119896119873



1198731 = 119899119865119907119903119889 ⟹ 119860119904 ge119873119904119889

06 times 119891119906119887 times 119899=

15984

06 times 800 times 2= 16651198981198982



M18 18 20 254 192 800 291



110




119865119901 = 07 times 119891119906119887 times 119860119904 = 06 x 800 x 192 = 10752kN

119872119903119889 =119899 119865119901 sum119889119894

2

119889119894=2 times 10752 times 129

0712= 3896 gt 119872119904119889 = 28961 119896119873119898




119865119907119904119889 le 119865119904119903119889 =119870119904 119898 120583

1205741198722(119865119901119888119889 minus 08119873119904119889) 119917119926119929119924119932119923119916 120788 120789 minus 119914119914119924120791120789

Avec

119870119904 = 10 ∶ Trous normaux



119865119904119903119889 = 024 (10752 minus 08 times15984

2) = 1046119896119873

119865119907119904119889 =8941

12= 745119896119873 lt 1046119896119873




1205741198722 119813119822119825119820119828119819119812 120788 120784 minus 119810119810119820120791120789



125= 213157 119896119873

119865119905119904119889 =119865119901

2=10752

2= 5376119896119873 lt 119861119901 119903119889 = 213157 119896119873


111



1205741198722 119827119808119809119819119812119808119828 120788 120787 120785 ndash 119810119810119820120791120789

Avec 119870119904 = 25

120572119887 = min (119890131198890

(119901131198890

minus 025) 119891119906119887119891119906 1) = 1



125= 46008119896119873 gt

11986511990711990411988912

= 745119896119873



119865119907 le 119865119905119903119889 = 119905119908119888 1198871198901198911198911198911199101205741198720

Avec




⟹ 119865119905119903119889 = 9 times 90times23511

= 173045 119896119873


119865119907 =119872119904119889

ℎ minus 119905119891=28961

029= 99865 gt 119865119905119903119889 = 173045119896119873




119873119904119889 le 119865119888119903119889 =119896119888 120588 119887119890119891119891 119905119908119888 119891119910

1205741198721radic1 + 13 (119887119890119891119891ℎ)2

119887119890119891119891 = 119905119891119887 + 2119886119901radic2 + 5(119905119891119888 + 119903119888) + 2119905119901

Avec

112






119887119890119891119891 =25014mm



120590119888119904119889 =119881119904119889119860+119872119904119889

119882119890119897119910=8941 times 103

1244+28961 times 106

1479= 196533119872119875119886

120590119888119904119889 = 19653119872119875119886 lt 119891119910 = 235119872119875119886 ⟹ 119896119888 = 1


119901 = 0932radic119887119890119891119891 119889119908119888 119891119910

119864 1199051199081198882= 0932radic


21 times 104 times 092= 254

119901 gt 072⟹ 120588 =119901 minus 02

1199012=254 minus 02

2542= 036


11 radic1 + 13 (250131

)2

= 12741119896119873

119873119904119889 = 1119873119894 =119872119904119889 sum119889119894sum119889119894

2 =29861 times 247

129= 57175119896119873





119865119907 le 119881119903119889 = 058119891119910 ℎ1199051199081205741198720


11= 3457119896119873


119865119907 =119872119904119889ℎ minus 119905119891

= 46216 119896119873 gt 119881119903119889 = 3457119896119873 119888119900119899119889119894119905119894119900119899 119899119900119899 119907eacute119903119894119891119894eacute119890


113

119865119907 = 46216119896119873 le 119881119903119889 = 058119891119910 ℎ119905119908 + 04

1205741198720= 058 235 31

(09 + 04)

11= 49935119896119873







logiciel robot

119872119904119889 = 15135119896119873119898 119873119904119889 = 1324119896119873 119881119904119889 = 273119896119873






119905 = min(119905119891 119905119901119897119886119905119894119899119890) = 135119898119898


114









IPE400

tf = 135 mm tw = 86 mm






radic2 times 119861119908 120574119898119908


Donc

119865119908119903119889 =119860 times sum119871 times 119891119906


radic2 times 1= 133083119896119873

119873119904119889 =119872119904119889ℎ

=7283

08= 9103119896119873

115

119873119904119889 = 9103 le 119865119908119903119889 = 1330119896119873






Donc

119865119907119903119889 =119886 times sum119871 times 119891119906


radic3 times 1= 155053119896119873



119873119894 =119872119904119889 119889119894sum119889119894

2


119909 = 119905119891radic119887

119905119908= 135radic

180

86= 6176119898119898


- 1198891 = 700 119898119898

- 1198892 = 600 119898119898

- 1198893 = 500 119898119898 ⟹ Σ1198891198942

= 124 119898sup2

- 1198894 = 300 119898119898

- 1198895 = 200 119898119898

- 1198896 = 100 119898119898


1198731 =119872119904119889 times 119889119894Σ119889119894

2 =15135 times 070

124= 4111119896119873



116


1198731 = 119899 119865119907 ⟹ 119860119904 ge119873119904119889

05 times 119891119906119887 times 119899=

13240

05 times 800 times 2= 16551198981198982



M18 18 20 254 192 800 291




119865119901 = 07 times 119891119906119887 times 119860119904 = 10752 119896119873

119872119903119889 =119899 119865119901sum119889119894

2

119889119894=2 times 10752 times 124

07= 38092 gt 119872119904119889 = 15135119896119873119898




119865119907119904119889 le 119865119904119903119889 =119870119904 119898 120583

1205741198722(119865119901119888119889 minus 08119873119904119889) 119813119822119825119820119828119819119812 120788120789 ndash 119810119810119820120791120789

Avec




119865119904119903119889 = 024 ( 10752 minus 08 times 1324) = 2326119896119873

119865119907119904119889 =273

12= 023 lt 119865119904 119903119889 = 2326119896119873




1205741198722 119813119822119825119820119828119819119812 120788 120784 ndash 119810119810119820120791120789

Avec


117


125= 31578119896119873

119865119905119904119889 =119865119901

2= 5376 lt 31578119896119873




1205741198722 119827119808119809119819119812119808119828 120788 120787 120785 ndash 119810119810119820120791120789

Avec Ks = 25

120572119887 = min (119890131198890

(119901131198890

minus 025) 119891119906119887119891119906 1) = 1


11986511990711990411988912


125= 5184 119896119873







119865119907119904119889 =119873119904119889

119899119887119903 119889119890 119887119900119906119897119900119899=131

3= 4366 le 119865119907119903119889

118


1205741198722⟹ 119860119904 ge

1205741198722 times 119865119907119903119889

06 times 119891119906119887119909 119898=125 times 43666

06 times 800 times 2= 56851198981198982


















119873119898119886119909 le 119865119908119903119889 =119886 sum119897 119891119906

119861119908 120574119898119908 radic(3 minus 1199041198941198991205722)


120572= 30gtgtgt 11990411989411989930o = 05

119865119908119903119889 =5 times 700 times 360



119



1205741198722 119827119808119809119819119812119808119828 120788 120787 120785 minus 119810119810119820120791120789


120572119907= 06



125= 12057119896119873

119865119907119904119889 =119873119904119889

3=3124

3= 10413 le 119865119907119903119889 = 12057119896119873




1205741198722 119827119808119809119819119812119808119828 120788 120787 120785 minus 119810119810119820120791120789

Avec

Ks = 25

120572119887 = min (119890131198890

(119901131198890

minus 025) 119891119906119887119891119906 1) = 092



125= 33914119896119873 gt 119865119907119904119889 = 4366119896119873




119873119898119886119909 le 119881119890119891119891119903119889 =119860119899119905 119891119910

1205741198722+119860119899119907 119891119910

radic3 1205741198722 119812119810120785 119849119834119851119853119842119838120783 minus 120790sect120785120783120782 120784

Avec


119860119899119890119905 = (119897

2minus11988902) 119905 = (60 minus 9)12 = 6121198981198982


120

119860119899119907 = (1198901 + 21199011 minus 251198890)119905 = (50 + 140 minus 45)12 = 17401198981198982

⟹ 119881119890119891119891119903119889 =612 times 235

125+1740 times 235

radic3 times 125= 303918119896119873 gt

119873119904119889

2= 655119896119873








119865119907119904119889 =119877119907119911

119899119887119900119906119897119900119899119904=36

2= 18 119896119873

119865119907119903119889 =06 times 119860119904 times 119891119906119887

120574119872119887⟹119860119904 ge

120574119872119887 times 11986511990711990311988906 times 119891119906119887

=11 times 18000

06 times 800= 41251198981198982



119865119907119903119889 =06 times 119860119904 times 119891119906119887

120574119872119887=06 times 58 times 800

11= 253119896119873 gt 119865119907119904119889 = 18119896119873


119865119905119903119889 =09 times 119860119904 times 119891119906119887

120574119872119887=09 times 58 times 800

11= 379119896119873

121

119865119907119903119889 =06 times 119860119904 times 119891119906119887

120574119872119887= 253119896119873

119865119907119904119889119865119907119903119889

+119865119905119904119889

14 119865119905119903119889= 052 lt 1 119862119900119899119889119894119905119894119900119899 119907119890119903119894119891119894eacute119890


122

Chapitre-8




123








119865119888119896=30 MPa

119891119888119889 =085 times 119865119888119896125

= 204 MPa


119865119895119889 = 120572120573119895 119891119888119889



119865119895119889 = 120572 120573119895 119891119888119889 = 15 times2

3times 17 = 204 119872119875119886


1198601198620 ge119873119904119889119891119888119889

=148960

204

1198601198620 ge 7266341198981198982


bp ge b+2tf = 190+2times155 = 221 mm

hp ge h+2tf = 310+2times155 = 341 mm

On prend

bp =600 hp=620



124


119862 = 119905 (119891119910119901

3119891119895119889 1205741198720)

05

= 30(235


= 5605 119898119898

119862 = 5605 lt(ℎ minus 2119905119891)

2= 1395 119898119898




gorge (a) Annexe H







119890 =119872119904119889119873119904119889

= 041 119898 gt 119885119879 = 0195 119898







125


Ougrave

119871119890119891119891 = min(119887119901 119887119891119888 + 2119888) = min(600 300 + 2 times 4671) = 39342 119898119898

119887119890119891119891 = min (119888ℎ1198882minus 119905119891119888) + 119905119891119888 +min (119888

ℎ119901 minus ℎ119888

2)

119887119890119891119891 = min (4671310

2minus 155) + 155 + min (4671

620 minus 310

2) = 10892 119898119898

⟹ 119865119888119903119889 = 204 times 10892 times 39342 = 874166 119896119873


119865119907119903119889 = 119865119891119903119889 + 119899119887 119865119907119887119903119889


119865119891119903119889 = 02119873119904119889 = 1214 119896119873





119865119907119887119903119889 =120572119888119887 119891119906119887 119860119904

1205741198722

Avec 120572119888119887 = 044 minus 00003119891119910119887 = 0248


126

119865119907119887119903119889 =0248 times 800 times 561

125= 8904 119896119873

⟹ 119865119907119903119889 = 1214 + 8 times 8904 119896119873 = 72446 119896119873




Avec 120573119908 =08 120574119898119908 = 125 119886 = 6 mm


sum119897 = 470 119898119898

119865119908119903119889 =6 times 470 times 360

radic3= 58612 119896119873

119881119904119889 = 9773 119896119873 lt min(119865119907119903119889 119865119908119903119889) = 58612 119896119873





W= 150 mm e = 55 mm ex = 40 mm mx = 40 mm


119897119890119891119891119888119901 = 119898119894119899 2120587119898119909 = 25132 119898119898

120587119898119909 +119882 = 27566 119898119898120587119898119909 + 2119890 = 23566 119898119898

⟹ 119897119890119891119891119888119901 = 23566 119898119898

127


119897119890119891119891119899119888 = 119898119894119899

4119898119909 + 125119890119909 = 210 119898119898

2119898119909 + 0625119890119909 +119882

2= 180 119898119898

2119898119909 + 0625119890119909 + 119890 = 160 119898119898119887119901

2= 150 119898119898

⟹ 119897119890119891119891119899119888 = 150 119898119898


119865119905119886119899119888119903119889 = min[119865119905119887119900119899119889119903119889 119865119905119903119889]


119865119905119903119889 = 09 times119860119904 times 119891119906119887120574119898119887


125= 32314 119896119873



119865119887119889 =036radic119891119888119896

120574119888=036 times 547

15= 1313 119872119875119886


119865119905119887119900119899119889119903119889 =120587 119889 119897119887 119891119887119889

120572

Avec

1198971 = 20119889 = 600 119898119898

119903 = 3119889 = 90 119898119898

1198972 = 20119889 = 600 119898119898






07= 52929 119896119873

119865119905119886119899119888119903119889 = 119898119894119899[52929 32314] = 32314 kN

128




Lb = 8d + em +tp + twa + 05k

Avec







119871119887lowast =

881198981199093 119860119904

1198971198901198911198911 1199051199013 =


150 times 253= 13480 119898119898 lt 119871119887 = 312 119898119898




119898119901119897119903119889 =1199051199012 119891119910119901

41205741198720=252 times 235

4 times 11= 3338119896119873


Mode 1 1198721199011198971119903119889 = 119898119901119897119903119889 times 1198971198901198911198911 = 3338 times 015 = 5007119896119873119898

1198971198901198911198911 = min(119897119890119891119891119888119901 119897119890119891119891119899119888) = 150 119898119898


129




Mode 1-2

1198651199051minus2119903119889 =21198721199011198971119903119889

119898119909=2 times 5

004= 250 119896119873

Mode 3

1198651199053119903119889 = 2119865119905119903119889119886119899119888ℎ119900119903 = 2 times 32314 = 646280 119896119873

Mode 4

1198651199054119903119889 =119887119890119891119891119905 119905119908 119891119910

1205741198720=150 times 9 times 235

11= 288409119896119873

Drsquoougrave

119865119905119903119889 = min(1198651199051minus2119903119889 1198651199053119903119889 1198651199054119903119889) = 250 119896119873




119885119879119890119873minus 1

119865119879119903119889 times 119885

119885119862119890119873+ 1

) 119812119810120785 ndash 120783 120790 119827119808119809119819119812119808119828 120788 120789

119885 = 119885119879+119885119862 = 195 + 155 = 350119898119898

⟹119872119903119889 = 5646 119896119873119898 lt 6207119896119873119898



821 Introduction




- Le site (S3)



130




ELU 119872119880 = 6207119896119873119898 119873119880 = 9773119896119873

ELS 119872119878 = 4136119896119873119898 119873119878 = 7960119896119873




119886 = 119886119901 + 119888 = 062 + 02 = 082 119898


119860

119861=119886

119887= 1025 ⟹ 119860 = 1025119861



119890 =119872119904

119873119904= 052119898



120590119898119886119909 =119873

119860119861(1 +

6119890

119861) le 120590119904119900119897


368B2 - B - 312 ge 0 ⟹ B ge0765m



131

119889 = max (119861 minus 119887

4119860 minus 119886

4) = max (005 0295)

On prend d= 45 cm



On a

119890 = 052 gt119860

6= 041


3120590119898119886119909 1205901198981198941198994

lt 120590119904119900119897

Avec

120590119898119894119899 =119873

119860119861(1 minus

6119890

119860) =

14896

2(1 minus

041

2 ) = 62191198961198731198982

120590119898119894119899 =119873

119860119861(1 +

6119890

119860) =

14896

2(1 +

041

2 ) = 86771198961198731198982

3120590119898119886119909 120590119898119894119899

4= 6835 1198961198731198982 lt 120590119904119900119897 = 180 119896119873119898

2



119890 =119872

119873= 052 119898 lt

119860

4= 062 119898




119890 gt119886

6 119890 gt

119860

24


119860119886 =1198721119911 119904119905

132

1198721 = (119860

2minus 035119886)

2

(1 +119890

119860+14 times 119890 times 119886

1198602)1198731199042119860

1198721 = 2788119896119873119898

Avec 119911 = 09d =40cm

119904119905 = min (2

3119891119890 110radic12057811989111990528) =20163 MPa

11989111990528 = 00611989111988828 + 06 = 24 119872119875119886 120578 = 16 119867 119860 Donc

119860119886 =2788 times 106

400 times 20163= 345 1198881198982


119860119887 =119873prime(119861 minus 119887)

8119889 119904119905

Avec

119873prime = 119873119904 (1 +3119890

119860) = 796 (1 +

3 times 052

25) = 2993119896119873

119904119905 = min (2

3119891119890 110radic12057811989111990528) = 20163119872119875119886

11989111990528 = 00611989111988828 + 06 = 24119896119873 120578 = 16 119867 119860

Donc 119860119887 = 071198881198982


119860119886 =1198721119911 120590119904119905

1198721 = (119860

2minus 035119886)

2

(1 +119890

119860+14 times 119890 times 119886

1198602)1198731199062119860

1198721 = 349119896119873119898

Avec 119911 =09d = 40 cm

120590119904119905 =119891119890120574119904=400

115= 3478119872119875119886

Donc

133

119860119886 =349 times 106

400 times 3478= 251198881198982


119860119886 =119873119906(119861 minus 119887)

8119889 120590119904119905

Avec

119873prime = 119873119906 (1 +3119890

119860) = 23833119896119873

Donc 119860119887 = 1621198881198982


119860119898119894119899 = 023 times11989111990528119891119890

times 119860 times ℎ119905 = 17251198881198982

Sens B

119860119898119894119899 = 023 times11989111990528119891119890

times 119861 times ℎ119905 = 691198881198982



A (cm2) St (cm)

A 345 1725 10T16 201 25 B 07 69 7T16 1407 25



134



119873119905 = (119873

120572) ge 20 119896119873 [119825119823119808120791120791 119855 120784120782120782120785 119808119851119853 120783120782 120783 120783 119835]


119873119905 =14896

12= 1241119896119873

ELS

119873119905 =796

12= 663119896119873


119860119904119905 =119873119905120590119904119905

ELS

119860119904119905 =663

348= 0191198881198982

ELU

119860119904119905 =1241

348= 0351198881198982





119860119904119905 = 0905 le 119860119904 = 6791198881198982


135


120601119898119894119899 le 119898119894119899 (ℎ

35120601119897119898119894119899

119887

10) = 08 119888119898

On prend 120601119905 =8mm


On prend St=10cm


136


137

ANNEXE - 1

138

139

140

ANNEXE - 2

141

ANNEXE - 3

142

143

ANNEXE ndash 4

144

145

ANNEXE ndash 5



















































Liste des tableaux

















LISTE DES NOTATIONS

Majuscules latines








16

Chapitre-1


11 Introduction


17



18

Action

permanente (γG)




Effet favorable

γGinf

10 1 0


γGsup

135 15 15




135119866119896119895 + 15119876119896119898119886119909





1 119866119896119895 + 150119882minus


sum119866119896119895119895

+ 119876119896119898119886119909

119866119896119895 + 119876119896119898119886119909


sum119866119896119895119895

+ 09sum119876119896119894119894gt1

119866119896119895 + 09119876119896119898119886119909 + 09119878 119866119896119895 + 09119876119896119898119886119909 + 09119882


19










20




21






22




23

Chapitre-2


21 Introduction










24

- Effet du site








Ouargla (Zone 4)




Kt=017 Z0=001m Zmin=1m ξ=044






Avec




119902119901(119885) = 119902119903119890119891 times 119862119890

Avec

- 119902ref = 575 119889119886119873119898sup2


2(119885) times [1 + 7119868119907] 119825119821119829120784120782120783120785 119836119841119834119849119842119853119851119838 120784 120786 sect120784 120786 120784 119834


25


119862119903(119911)

119870119905 119871119899 (1199111198981198941198991199110

) 119901119900119906119903 119911 lt 119911119898119894119899

119870119905 119871119899 (119911

1199110) 119901119900119906119903 119911119898119894119899 le 119911 le 200119898


)=0783


Zo)=1178

On retient 119862119903= 1178


119868119907(119911)

1

119862119905(119911) 119871119899 (119911

1199110) 119901119900119906119903 119911 gt 119911119898119894119899

1

119862119905(119911) 119871119899 (1199111198981198941198991199110) 119901119900119906119903 119911 le 119911119898119894119899

Pour z gt zmin 119868119907(119911) =1

1Ln(1

001)= 0217

Pour z lt zmin 119868119907(119911) =1

1Ln(1025

001)= 0144



119862119890(119911119895) = 119862119903(119911119895)2[1 + 7 119868119881]

Pour z gt zmin

119862119890(119911) = 11782 times 12 times [1 + 7(0144)] = 2786

Pour z lt zmin

119862119890(119911) = 07832 times 12 times [1 + 7(0217)] = 154


Avec

26

- 119902119903119890119891 = 575 119889119886119873119898sup2



qp = 160195Nm2 = 16 kNm2





- b=30 m

- d=36 m

- h=89 m


e = min (d 2h)


Donc e = 2x1025 = 205m



27



119862119901119890 = 1198621199011198901 119878119894 119878 le 11198982

119862119901119890 = 1198621199011198901 + (11986211990111989010 minus 1198621199011198901) times 11989711990011989210(119878) 119878119894 11198982 lt 119878 lt 101198982

119862119901119890 = 11986211990111989010 119878119894 119878 ge 101198982



Zone


Parois sous le vent


Cpe10 -10 -08 -05 +08 -03


Versant de Toiture




28







le tableau suivant


853deg F G H

-237 -123 -083



- Parois verticales


-b=36 m

29

-d=30 m

-h=1025


e=Min (b 2h) = Min (36 205) = 205 m





30

Zone


Parois sous le vent








31




853deg -22 -192 -183 -067 -057






2(5 times 4)

30 times 89= 014 = 14


μ119901 =120

160= 075



Pour μ119901=075 on lit 119862119901119894 =-016

32




2 times (5 times 4)

36 times 9575= 0116 = 116


Pour μ119901=075 rarr 119862119901119894 =-02

33





Direction V1 V3


A 1602 -10 -0154 -0846 -135529

B 1602 -08 -0154 -0646 -103489

C 1602 -05 -0154 -0346 -55429

D 1602 +08 -0154 +0954 +152831

E 1602 -03 -0154 -0146 -23389


34

Toiture


F 1602 -237 -0154 -2276 -355003

G 1602 -123 -0154 -1076 -172375

H 1602 -084 -0154 -0676 -108295

Z1 1602 -1 -0154 -0846 -135529

Z2 1602 -06 -0154 -0446 -71449


Direction V2 et V4

Parois verticales


A 1602 -10 -0162 -0838 -134247

B 1602 -08 -0162 -0638 -102207

C 1602 -05 -0162 -0338 -54147

D 1602 +08 -0162 +0962 +154112

E 1602 -03 -0162 -0138 -22107


35

Toiture


Finf 1602 -12 -0162 -1038 -1662876

Fsup 1602 -22 -0162 -2038 -3264876

G 1602 -183 -0162 -1668 -2672136

H 1602 -067 -0162 -0508 -813816

I 1602 -057 -0162 -0408 -653616









9= 015




q1= 300 Nml

q2= 500 Nml



36











- Epaisseur 50 mm

- Largeur 1000 mm





Selon le DTR BC22




37

119902 =8119875

3119871= 044 119896119873119898

119902 = 444 119889119886119873119898













38

Chapitre-3





deacutefavorable

39

(minus354 times5125


0875

6) = minus32754 1198891198861198731198982

Qeq (vent) = 3276 daN1198982















40



41


Vzsd =119902119906119911 times 119897

2=1878 kN

Mysd=119902119906119911 times 119897

2

8=2817 kNm

Mzsd=119902119906119910 times 119897

2

8=081 kNm



IPE 180 A Cm2

h mm

b mm

119905f

mm 119905w

mm 119868y

Cm4

119868z

Cm4

119908ply cm3

119908plz cm3

MATERIAU ACIER S235

239 180 91 8 53 1317 101 146 346




4

384 times 119864 119868119910lt

119897

200=



119897

200= 3 119862119900119899119889119894119905119894119900119899 119907eacute119903119894119891119894eacute119890

Plan z-z

5 times 119902119904119910 times 1198974

384 times 119864 119868119911lt

119897

200=



119897

200= 3 119862119900119899119889119894119905119894119900119899 119907eacute119903119894119891119894eacute119890

42




1205741198721 gt 119872119910119904119889 = 2817 119896119873119898

Calcul de 119872119887119903119889




λ119871119879 =

119871119894119911

119888105

[

1 +120(

119871119894119911ℎ119905119891

)

2

] 025

Avec


(Tableau B12 CCM97)

iz =224mm tf =85mm

L=Lz=3000mm h=200mm

λ119871119879 =

119871119894119911

119888105

[

1 +120(

119871119894119911ℎ119905119891

)

2

] 025 = 9457 rarr λ119871119879 =

989

939= 1007

rarr =1092

43


rarr ꭕ119871119879=

1


2)= 066 le 1

rarr 119872119887119903119889 =ꭕ119871119879times 120573

119908times 119882119901119897119910 times 119891119910

1205741198721

=066 1 166 235

11= 234 119896119873 119898








119872119872119860119883 =119901prime 119897

3=119901 1198972

8⟹ 119901 =

8 119901prime

3119897=800

18= 4444 119889119886119873119898119897

44


(ANNEXE ndash 1)

Soit

119876119890119902 =327 + 1082

2= 2176 1198891198861198731198982









45



Vzsd =119902119906119911 times 119897

2=186 kN

Mysd=119902119906119911 times 119897

2

8=279 kNm

Mzsd=119902119906119910 times 119897

2

8=0855 kNm

46



IPE 200 A Cm2

h mm

b mm

119905f

mm 119905w

mm 119868y

Cm4

119868z

Cm4

119908ply cm3

119908plz cm3

MATERIAU ACIER S235

285 200 100 85 56 1943 142 221 446




4

384 times 119864 119868119910lt

119897

200=



119897

200= 3 119862119900119899119889119894119905119894119900119899 119907eacute119903119894119891119894eacute119890

Plan z-z

5 times 119902119904119910 times 1198974

384 times 119864 119868119911lt

119897

200=



119897

200= 3 119862119900119899119889119894119905119894119900119899 119907eacute119903119894119891119894eacute119890




1205741198721 gt 119872119910119904119889 = 279 119896119873119898

Calcul de 119872119887119903119889

47




λ119871119879 =

119871119894119911

119888105

[

1 +120(

119871119894119911ℎ119905119891

)

2

] 025

Avec


(Tableau B12 CCM97)


-L=Lz=6000mm -h=200mm

λ119871119879 =

119871119894119911

119888105

[

1 +120(

119871119894119911ℎ119905119891

)

2

] 025 = 989 ⟶ λ119871119879 =

989

939= 105

rarr =114


rarr ꭕ119897119905=

1


2)= 063 le 1

rarr 119872119887119903119889 =ꭕ119897119905times 120573

119908times 119882119901119897119910 times 119891119910

1205741198721


11= 2974119896119873119898



48


Avec

119881119901119897119911119903119889 =

119860119907119911 (119891119910

radic3)

11 119890119905 119860119907119911 = 1400 1198981198982

Donc

05119881119901119897119911119903119889 = 05

1400 (235

radic3)

11= 8634 119896119873



Si 119889


CCM97 art 561(1)

119889

119905119908 =

159





(119872119910119904119889

119872119901119897119910119903119889)

120572

+ (119872119911119904119889119872119901119897119911119903119889

)

120573

le 1 119912119955119957 120787 120786 120790 (120783120783)119914119914119924 120791120789


119872119901119897119910119903119889 =119882119901119897119910 times 119891119910

11=221 times 235

11= 4721 119896119873119898

119872119901119897119911119903119889 =119882119901119897119911 times 119891119910

11=446 times 235

11= 952 119896119873119898

119872119910119904119889 = 279 119896119873119898

119872119911119904119889 = 0855 119896119873119898

(279

4721)2

+ (0855

952) = 044 lt 1 119888119900119899119889119894119905119894119900119899 119907eacute119903119894119891119894eacute119890

49











Effort rampant


Lrsquoexcentrement


2 (119887

2) le 119905 le 3(

119887

2)


50

2 (10

2) = 10 le 119905 le 3(

10

2) = 15

On prend t=10 cm


119877119911 = 119902119906119911 times119897

2= 6 times

6

2= 18 119896119873

119877119910 = 119902119906119910 times119897

2= 054 119896119873


119877119911 = 18 times 2 = 36 119896119873

119877119910 = 054 times 2 = 108 119896119873


119872119877 = 119877119911 times 119905 + 119877119910 timesℎ

2= 36 times 10 + 108 times 10 = 3708 119896119873 119888119898 = 37119896119873119898


119872119890119897119877119889 =119908119890119897 times 119891119910

1205741198720 119912119955119957 120787 120786 120787 120783 (120784)119914119914119924120791120789

119872119890119897119877119889 =119908119890119897 times 1198911199101205741198720

=gt 119908119890119897 ge119872119890119897119877119889 times 1205741198720

119891119910=gt 119908119890119897 ge

00037 times 11

235

= 173 times 10minus51198983

119908119890119897 = 17321198881198983




119908119890119897 =119887 1198902


6 times 1732

119887= radic

6 times 1732

180

119890 ge 076


Donc on prend e=1cm

51





















52












qsy =(133 + 5) times 125=2288daNml

qsy = 0228 kN

quy=135G=03kN



W += 1541 daN m2


quz=15W

quz=288kN

53



qsz=19262daN=192kN


119891119911 =5 times 119902119904119911 times 119897

4

384 times 119864119910 times 119868le 119891119886119889119873 =

119897

200=600

200= 3 119888119898

119868119910 ge5 times 192 times 6004



Profileacute


UPN 140 A Cm2

h mm

b mm

119905f mm

119905w mm

Iy

Cm4

Iz

Cm4

119908pSy

cm3

119908pSz

cm3

MATERIAU ACIER S235

20 140 60 10 7 605 627 103 283







qsy =(133 + 5) times 125 +1568 = 3856daNml

qsy = 038 kN

quy=135G

quy =053kN


qsz=192kN

quz=15W

quz=288kN

54




119888

119905119891=60

10= 6 lt 10휀 =gt 119888119897119886119904119904119890 1


119889

119905119908=98

7= 14 lt 72휀 =gt 119888119897119886119904119904119890 1


(119872119910119904119889

119872119890119897119910119877119889)

1

+ (119872119911119904119889

119872119890119897119911119877119889)1

le 1


119872119910 =119902119906119911 times 119897

2

8=288 times 62

8= 1296 119896119873119898


119872119911 =119902119906119910 times 119897

2

8=058 times 62

8= 261119896119873119898

119872119890119897119910119877119889 =119908119890119897119910 times 119891119910

1205741198720=864 times 103 times 235

11= 1845 119896119873119898

119872119890119897119911119877119889 =119908119890119897119911 times 119891119910

1205741198720=148 times 103 times 235

11= 316 119896119873119898

Donc

(1296

1845)1+ (

261



55

Nouveau 119872119911

119872119911 =119902119906119910 times 119897

2

8=058 times 32

8= 065119896119873119898

(1296

1845)1+ (

065




119881119911119904119889 =15119882119871

2= 1296 119896119873

119881119901119897119877119889 =119860119907119911 times 119891119910

radic3times 1205741198720= 12855 119896119873





1205741198721gt 119872119910119904119889 119912119955119957 120787 120787 120784 (120787 120786120790)119914119914119924120791120789

Avec

119872119888119903 = 11986211205872 119864 1198681199111198712

radic119868119908119868119911+1198712 119866 1198681199051205872 119864 119868119911

119912119925119925119916119935119916 119913 (119913 120783 120785) minus 119914119914119924120791120789

119872119888119903=311713762 Ncm


119872119888119903


119882119901119897119910 (upn140) =103 cm3

56

λ119897119905 = 0881


2 ]


empty119897119905 = 0959

ꭕ119897119905=

1


2 )

le 1

ꭕ119897119905= 075

119872119887119903119889 = 1652 119896119873119898

119872119887119903119889 = 1652 119896119873119898 gt 119872119910119904119889 = 1296 119896119873119898 119862119900119899119889119894119905119894119900119899 119907eacute119903119894119891119894eacute119890







57

119877 = 125119902119910 times 119897

2

Avec 119902119910 = [135(119866119880119875119873140 + 119866119888119900119906119907119890119903119905119906119903119890)]

119902119910 = 0837119896119873

119897 = 6 119898

119877 = 125119902119910 times 119897

2= 125 times 0837 times 3 = 32119896119873


1198791 =119877

2= 16119896119873

1198792 = 1198791 + 119877=48 kN

1198793 =1198792

2 sin 120579= 374 119896119873 119860119907119890119888 120579 = 119886119903119888 119905119892

25 119898

3 119898= 398deg



119873119905119904119889 =119860 times 119891119910

1205741198720= 4800 119873 =gt 119860 ge

11 times 4800

235 =gt 119860 ge 22461198981198982

119860 =120587empty2

4=gt empty ge radic

4119860

120587= radic

4 times 2246

314= 534 119898119898



Introduction



58



119878ge

63

radic119904

119889times119875

Avec








Srsquo=273

4=6825 m2








59



















96=8989 daNm2





60

119891119910 =5 times119882 times 1198974

384 times 119864 times 119868119910le 119891119886119889119898 =

119897

200


384 times E= 59136 1198881198984


Profileacute


IPE300 A Cm2

h mm

b mm

tf mm

tw

mm 119868y

Cm4

119868z Cm4

Wply

cm3

Wplz

cm3

MATERIAU ACIER S235

538 300 150 107 71 8356 746 628 125





119888

119905119891=

75

107= 7 lt 10 = 10 119878119890119898119890119897119897119890 119889119890 119888119897119886119904119904119890 1


119889

119905119908=2486

71= 35 lt 38 = 38 Acirc119898119890 119889119890 119888119897119886119904119904119890 1



Si 119881119904119889 le 05 119881119901119897119903119889 ⟹119872119904119889 le 119872119888119903119889 119912119955119957120787 120786 120789 119914119914119924 120791120789

61

119881119904119889 =15 times119882 times 119897


2= 388 119896119873 lt 05 119881119901119897119903119889 = 05 (

2570 times 235

radic3 times 11) = 1585 119896119873





Si

119873119904119889 le 119872119894119899 (025119873119901119897119903119889 05119860119908 119891119910

1205741198980)


025119873119901119897119903119889 = 025119860 times 119891119910

1205741198720= 025

5380 times 235

11= 28734 119896119873

05119860119908 times 119891119910

1205741198720= 05

2170 times 235

11= 2317 119896119873

119873119904119889 = 135119866 = 1337 119896119873 lt 119898119894119899 (025119873119901119897119903119889 05119860119908 times 119891119910

1205741198720)





119872119910119904119889 =15119882 times 1198972

8= 9313119896119873119898 119872119911119904119889 = 0 119872119901119897119910119903119889 = 13416 119896119873119898

λ119897119905 =

119871119911119894119911

119888105

[

1 +120(

119871119911119894119911ℎ119905119891

)

2

] 025


62

119871119911 = 1250 119898119898 119894119911 = 335 119898119898 ℎ = 300 119898119898 119905119891 = 107 119898119898




119873119904119889ꭕ119898119894119899

119873119901119897119903119889+119870119910 119872119910119904119889

119872119901119897119910119903119889+119870119911 119872119911119904119889119872119901119897119911119903119889


Avec

λ119910 =119871119910

119894119910=960

125= 768 rarr λ119910 =

768

939= 081

=gt 120583119910 = λ119910(2119861119898119910 minus 4) +119882119901119897119910 minus119882119890119897119910

119882119890119897119910= minus1134 + 0127 = minus1007 lt 09

120572 = 021 λ119910 = 081

empty119910 = 05 [1 + 120572119910(λ119910 minus 02) + λ1199102]

empty119910 = 05[1 + 021(081 minus 02) + 0812] = 089

ꭕ119910=

1


ꭕ119910= 0794 rarr 119870119910 = 1 minus


0794 times 538 times 2350= 101

120582119911 =125

335= 3731 =gt 120582119911 = 0397 rarr empty119911 = 0611 =gt ꭕ

119911= 092

ꭕ119898119894119899

= ꭕ119910= 0794

119873119901119897119903119889 =119860119891119910

1205741198980=5380 times 235

11= 114936 119896119873

119872119910119904119889 =151198821198712

8= 9313 119896119873119898

119872119901119897119910119903119889 = 13416 119896119873119898

119873119904119889 = 135119866 = 1337 119896119873

119896119910 = 101

119872119911119904119889 = 0

63

119873119904119889120594119898119894119899 119873119901119897119903119889

+119896119910 119872119910119904119889

119872119901119897119910119903119889+119896119911 119872119911119904119889119872119901119897119911119903119889

le 10

1337

0794 times 114836+101 times 9313

13416= 071 lt 1 119862119900119899119889119894119905119894119900119899 119907eacute119903119894119891119894eacute119890




64

Chapitre 4


41 Introduction




- Le pont roulant










poteaux de la halle

65





Puissances

N (t)

Porteacutee

L(m)



B

Chariot

K

Total

B+K

Rmax Rmin

125 18 085 520 1040 6809 1151 796 814 194


66


1 035 06 2 36



I 02 11 11 A-2















Groupes II






67
















119877119898119886119909 = 814 119870119873 119877119898119894119899 = 194 119870119873

Charges verticales

119877119881119898119886119909 = Ψ1 119877119898119886119909 = 115 times 814 = 8954 119870119873

119877119881119898119894119899 = Ψ2 119877119898119894119899 = 11 times 194 = 2134 119870119873


68

119877119871119898119886119909 = 119862 119877119898119886119909 = 02 times 814 = 1628 119870119873

119877119871119898119894119899 = 119862 119877119898119894119899 = 02 times 194 = 388 119870119873



1198771198671119898119886119909 = plusmn [0024(119870 + 119873 + 119861)119871

119890+ 0021(119873 + 119870)]

= plusmn [0024(1151 + 125 + 6809)18

36+ 0021(125 + 1151)]

1198771198671119898119886119909 = plusmn274 119905

1198771198671119898119894119899 = plusmn [0024(119870 + 119873 + 119861)119871

119890minus 0021(119873 + 119870)]

= plusmn [0024(1151 + 125 + 6809)18

36minus 0021(125 + 1151)]

1198771198671119898119894119899 = plusmn2168 119905


1198771198672119898119886119909 = plusmn [00052(119870 + 119873 + 5119861)119871

119890+ 0021(119873 + 119870)]

= plusmn [00052(1151 + 125 + 5 times 6809)18

36+ 0021(125 + 1151)]

1198771198672119898119886119909 = plusmn1526 119905

1198771198672119898119894119899 = plusmn [00052(119870 + 119873 + 5119861)119871

119890minus 0021(119873 + 119870)]

= plusmn [00052(1151 + 125 + 5 times 6809)18

36minus 0021(125 + 1151)]

1198771198672119898119894119899 = plusmn0953 119905




69





Rail

Poids

(Kgm)

B

(mm)

H

(mm)

P

(mm)

Section

A (cm2)

I x

(cm4)

I y

(cm4)

A55

318

55

65

150

407

178

337



70



119891119911 le 119891119886119889119898 =119897

750= 08 119888119898



119886 = (119897

2minus119890

4) = (

6

2minus36

4) = 21 119898



119891119911 =119901 119886 1198972

24119864119868(3 minus

4 1198862

1198972)

Avec

L= 6000 mm

a= 2100 mm

P=89540 N

E=21104 Nmm2

71

119868119910 ge119901 119886 1198972(31198972 minus 41198862)



119868119910 ge 421397625 1198981198984






119902 = 119866119901119900119906119905119903119890 + 119866119903119886119894119897 = 142 + 031 = 173 119896119899119898119897

119891119911 =119901 119886 1198972

24119864119868(3 minus

4 1198862

1198972) +

5 119902 1198974

384119864119868

119891119911 =89540 times 2100 times 60002


4 times 21002

60002) +




profileacute


G

Kgm

A cm2 h

mm

b

mm

tf

mm

tw

mm

Iy

cm4

Iz

cm4

Wply

cm3

Wplz

cm 3

HEB360 142 1806 360 300 225 125 43190 10140 2683 1032

72


119902 = 119866119901119900119906119905119903119890 + 119866119903119886119894119897 = 155 + 031 = 186 119870119873119898119897

119891119911 =119901 119886 1198972

24119864119868(3 minus

4 1198862

1198972) +

5 119902 1198974

384119864119868

119891119911 =89540 times 2100 times 60002


4 times 21002

60002) +






119905119908le 72휀

Avec

휀 = radic235

119891119910

298

135le 72radic

235

235 ⟹ 2207 le 72


119888

119905119891=1198872

119905119891le 10휀 ⟹

150

24= 625 le 10




profileacute


G

Kgm

A

cm2

h

mm

b

mm

tf

mm

tw

mm

Iy

cm4

Iz

cm4

Wply

cm3

Wplz

cm 3

HEB400 155 1978 400 300 24 135 57680 10820 3232 1104

73

119881119910119904119889 le 119881119901119897119903119889 119912119955119957 120787 120786 120788 (120787 120784120782)119914119914119924120791120789

119881119901119897119903119889 =119860119907119911 119891119910

radic3 1205741198980=6998 times 235

radic3 times 11= 863154 119873 = 86315 119870119873


119881119881 = 119877119881119898119886119909 times4119886

119897=8954 times 4 times 21

6= 12535 119870119873


119881119875119875 =119866 119897

2=186 times 6

2= 558 119870119873

Drsquoougrave 119881119910119904119889 = 135119881119875119875 + 15119881119881 = 19556 119870119873

119881119910119904119889 le 119881119901119897119903119889



Suivant (z-z)


119872119881 = 119877119881119898119886119909 times(6 minus

1198902)2

4119897= 8954 times

(6 minus362 )

2

4 times 6= 6581 119870119873119898


119872119875119875 =119866 1198972

8= 837 119870119873119898


119872119910119904119889 = 135119872119875119875 + 15119872119881 = 110 119870119873119898



119872119911119904119889 = 119872119867 =21198771198671119871

(119871

2minus119890

4)2

74

119872119911119904119889 = 119872119867 =2 times 274

6times (

6

2minus36

4)2

= 4028 119870119873119898




119873119904119889119873119901119897119903119889

+119872119910119904119889

119872119890119897119910+119872119911119904119889119872119890119897119911

le 1 120787 120785120790 ndash 119810119810119820120791120789

119873119904119889 = 15119877119871119898119886119909 = 15 times 1628 = 2442 119870119873

119872119890119897119910 =119908119890119897119910 119891119910

1205741198720= 61613 119872119890119897119911 =

119908119890119897119911 119891119910

1205741198720= 1541 119873119901119897119903119889 =

119860 119891119910

1205741198720= 422573

2442

422573+

110

61613+4028

1541= 044 le 1



Si 119889


Avec

휀 = radic235

119891119910= 1

119889

119905119908=298

135= 2207 lt 69





1205741198721


75



λ119897119905 =

119871119894119911

119888105

[

1 +120(

119871119894119911ℎ119905119891

)

2

] 025 = 6522 119808119821119821119812119831119812119809 119810119810119820120791120789

Avec 119871 = 600119888119898


λ119871119879 = [λ119897119905λ1] [120573119908]

05 휀 = radic235

119891119910= 1

λ119871119879 =6522

939= 0694

On calcule

ꭕ119871119879=

1


2 )le 1




ꭕ119871119879=

1

(079 + radic0792 minus 06942)= 0856


11= 59104 119870119873119898

119872119910119904119889 = 110 119870119873119898




76



119891119904119889 le 119877119910119877119889

Avec




120590119891119864119889 =119872119910119904119889

119882119890119897119910= 381 1198701198731198881198982

119878119910 = 2(ℎ119877 + 119905119891)radic[1 minus (1205741198720120590119891119864119889

119891119910119891)

2

] = 1751 119888119898

119877119910119877119889 =119878119910 times 119905119908 times 119891119910119908

1205741198720= 505 119870119873 gt 119891119904119889 = 119877119907119898119886119909 = 8954 119870119873




119891119904119889 le 119877119886119877119889

119891119904119889119877119886119877119889

+119872119878119889119872119888119877119889

le 1 119808119825119827 120787 120789120790 minus 119810119810119820120791120789

Avec

77

119877119886119877119889 =

051199051199082 (119864 119891119910119908)

05[(119905119891119905119908)05

+ 3(119905119908119905119891) (119878119904119889 )]

1205741198720 119808119825119827 120787 120789120789 minus 119810119810119820120791120789

119877119886119877119889 = 108284 119870119873

119891119904119889 = 15119877119871119898119886119909 = 15 times 1628 = 2442 119870119873

119872119888119877119889 =3232 times 103 times 235

11= 69047 119870119873119898

119891119904119889119877119886119877119889

+119872119878119889119872119888119877119889

=2442

108284+

110

69047 = 018 le 15




119887119890119891119891 le 119887 119808119825119827 120787 120789120791 minus 119810119810119820120791120789

119887119890119891119891 = radicℎ2 + 1198781199042 = 410 119898119898 gt 119887 = 300 119898119898




efforts suivants




Charge verticale


119901prime = 119876 119871 + 119877119898119886119909 (2 minus119890

119871) ψ


36

6) times 11

119901prime = 13651 119870119873


119901 = 135119876 119871 + 15119877119898119886119909 (2 minus119890

119871) ψ


36

6) times 11

119901 = 2031 119870119873

78

Charge horizontale

119875119867 = 15119877119867119898119886119909 (1 minus119890

119897)ψ


36

6) times 11 = 1808 119870119873




119891119911 le 119891119886119889119898 =119897

500


119891119911 =119901prime 1198893

3119864119868le 119891119886119889119898

119868119910 =500 119901prime 1198892

3119864ge 782667 1198881198984


79




119905119908le 72휀

Avec

휀 = radic235

119891119910

2486

71le 72radic

235

235 ⟹ 3501 le 72


119888

119905119891=1198872

119905119891le 10휀 ⟹

75

102= 735 le 10





119881119910119904119889 le 119881119901119897119903119889

Avec 119860119907119911 = 257 cm2

119881119901119897119903119889 =119860119907119911 119891119910

radic3 1205741198980=257 times 235

radic3 times 11= 317 119870119873

119881119904119889 = 119901 = 2031 lt 05119881119901119897119877119889


profileacute


G

Kgm

A

cm2

h

mm

b

mm

tf

mm

tw

mm

Iy

cm4

Iz

cm4

Wply

cm3

Wplz

cm 3

IPE 300 422 5380 300 150 107 71 8353 604 628 125

80


119872119888119903119889 =119908119901119897119910 119891119910

1205741198720=628 times 235

11= 13416 119870119873119898

119872119910119904119889 = 119901 119889 = 2031 times 085 = 172635 119870119873119898

119872119910119904119889 lt 119872119888119903119889




119872119888119903119889 =119908119901119897119910 119891119910

1205741198720=1019 times 235

11= 2177 119870119873119898

119872119910119904119889 = 119901 119889 = 2031 times 085 = 172635 119870119873119898

119872119910119904119889 lt 119872119888119903119889


17263


profileacute


G

Kgm

A

cm2

h

mm

b

mm

tf

mm

tw

mm

Iy

cm4

Iz

cm4

Wply

cm3

Wplz

cm3

IPE 360 571 727 360 170 127 8 16270 1043 1019 191

81



chemin de roulement

119891119911 le 119891119886119889119898 =119889

500= 017

119902 = 119902119868119875119864 360 = 571 119889119886119873119898119897

119891119911 =119901prime 1198893

3119864119868+119902 1198974

8119864119868= 0082 + 0021 = 0103 119888119898 lt 017 119888119898


82

Chapitre-5








dynamiques


83




119881 =119860119863 119876

119877119882



119863 =

25120578 0 le 119879 le 1198792

25120578(1198792119879)23 1198792 le 119879 le 3119904

25120578 (11987923)

23 (3119879)

53 119879 gt 3119904


84

120578 = radic7

(2 + 120585)ge 07



119879 = 119862119879 ℎ11987334 119917119926119929119924119932119923119916 (120786 120788)119929119927119912 119933120784120782120782120785




119876 = 1 +sum119875119902

6

1


85


119876 = 1 +sum119875119902

6

1

= 1 + 02 = 12


119899119894=1

Avec 119882119894 = 119882119866119894 + 120573119882119876119894




119881 =119860119863 119876

119877119882

119860 = 005 119863 = 25 119876 = 12 119877 = 4 119882 = 189475119896119873

119881119909 = 119881119910 =005 times 25 times 12

4times 189475 = 7105119896119873


119904119886119892=

125119860 (119860 +

119879

1198791(25120578

119876

119877minus 1)) 0 le 119879 le 1198791

25120578(125119860) (119876

119877) 1198791 le 119879 le 1198792

25120578(125119860) (119876

119877)(1198792119879)23

1198792 le 119879 le 30119904

25120578(125119860) (11987923)

23(3

119879)

53(119876

119877) 119879 gt 30119904

86



η = 100 A=005 1198791=015 1198792=050


87













88










89

ℎ

150=890

150= 594119888119898 sans vent

ℎ

125=890

125= 712119888119898 avec vent






Toiture 029 076 116 304


ℎ

100=1025

100= 1025 119888119898



90

Chapitre-6


61 Introduction





119872119910119904119889 = 21902 kNm

119881119904119889 =7249 kN

119873119904119889 =2018 kN

91

Profileacute


IPE 400 A cm2

hmm

b mm

119905f

mm

119905w mm

119868y

cm4

119868z Cm4

119908ply

cm3

119908plz

cm3

MATERIAU ACIER S235

8446 400 180 14 90 231284 131782 123832 2256




119888

119905119891=60

14= 59 lt 10휀 =gt 119888119897119886119904119904119890 1


119889

119905119908=98

9= 11 lt 72휀 =gt 119888119897119886119904119904119890 1





Si 119881119904119889 le 05119881119901119897119903119889 ⟹ 119872119904119889 le 119872119888119903119889 119912119955119957120787 120786 120789 119914119914119924 120791120789


119881119898119886119909 = 119881119904119889 =7248kN

119881119901119897119911119903119889 =

119860119907119911 (119891119910

radic3)

1205741198980=

4270235

radic311

= 526674119896119873

119881119904119889 = 7247 le 05119881119901119897119911119903119889 = 52667119896119873


92



119873119904119889 le 119872119894119899(025119873119901119897119903119889 05119860119908119891119910

1205741198720)


119873119904119889 = 2018119896119873

119873119901119897119903119889 le119860 119891

119910

1205741198720=8446 235

11= 180437119896119873

025119873119901119897119903119889 =451 119896119873

119860119908 = 119860 minus 2119887 119905119891 = 34061198981198982

05119860119908119891119910

1205741198720= 36382119896119873

119873119904119889 = 2018 le 36382119896119873



119872119888119903119889 = 119872119901119897119910119903119889 =119908119901119897119910 119891119910

1205741198720=1238320 235

11= 26455119896119873119898




120594119898119894119899 119873119901119897119903119889+119896119910 119872119910119904119889

119872119901119897119910119903119889+119896119911 119872119911119904119889119872119901119897119911119903119889



120594119911 119873119901119897119903119889+119896119871119879 119872119910119904119889

120594119871119879119872119901119897119910119903119889+119896119911 119872119911119904119889119872119901119897119911119903119889



120594119898119894119899 = 119872119894119899(120594119910 120594119911)


93

120594119910 =1

(120601119910 +radic1206011199102 minus 1205821199102 )

120601119910 = 05[1 + 120572119910(120582119910 minus 02) + 1205821199102]

120582119910= (120582119910

1205821)radic120573119860 =

120582119910

1205821

Avec 120573119860 = 1 Classe 1

1205821 = 939

120582119910 =05119868119910

119894119910=455

166= 274

120582119910=274

939= 029


ℎ

119887=400

180= 222 gt 12 119894119898119901119897119894119902119906119890 120572 = 021

120601 = 05[1 + 120572119910(120582119910 minus 02) + 1205821199102 ] = 055

120594119910 =1

(055 + radic0552 minus 0292)= 098


120594119911 =1

(120601119911 +radic1206011199112 minus 120582119911

2)

120601119911 = 05[1 + 120572119911(120582119911 minus 02) + 1205821199112]

120582119911 = (1205821199111205821)radic120573119860 =

1205821199111205821

Avec 120573119860 = 1 Classe 1

120582119911 =119868119911119894119911=200

395= 5063

120582119911 =5063

939= 054


94

ℎ

119887= 222 gt 12 (119911 minus 119911)119894119898119901119897119894119902119906119890 120572 = 034

120601 = 05[1 + 034(054 minus 02) + 0542 ] = 07

120594119911 =1

(07 + radic072 minus 0542)= 087

120594119898119894119899 = 119872119894119899(120594119910 120594119911) = 087




λ119897119905 =

119871119894119911

119888105

[

1 +120(

119871119894119911ℎ119905119891

)

2

] 025 = 4367 119808119821119821119812119831119812119809 119810119810119820120791120789

Avec

IPE400 119905119891 = 14119898119898 119894119911 = 395119888119898 ℎ = 400119898119898

119870 = 1 1198881=1134 Tableau B11 CCM97


1205821 = 939휀

휀 = radic235

119891119910= 1

120582119871119879 = [1205821198971199051205821] [120573119908]

05

120582119897119905 = 4367

120582119871119879 =4367

939= 046 gt 04



119873119904119889120594119911 119873119901119897119903119889

+119896119871119879 119872119910119904119889

120594119871119879119872119901119897119910119903119889+119896119911 119872119911119904119889119872119901119897119911119903119889


Calcul de 120594119871119879


95

implique 120594119871119879 = 094

Calcul de 119896119871119879


119870119871119879 = 1 minusμLT N119904119889

120594119911 119860 119891119910= 099 lt 15


Donc

119873119904119889=7249 kN 119872119910119904119889=219 kNm 119872119901119897119910119903119889=26455 kNm 120594119911=087 119872119901119897119911119903119889=4819kNm


119873119904119889120594119911 119873119901119897119903119889

+119896119871119879 119872119910119904119889

120594119871119879119872119901119897119910119903119889+119896119911 119872119911119904119889

119872119901119897119911119903119889


7249

087 180437+

099 219

094 26455= 055










96

119872119910119904119889 = 32083 119896119873119898

119881119904119889 = 120 119896119873

119873119904119889 = 602 119896119873

Profileacute


HEA320

A cm2

hmm

b mm

119905f

mm

119905w mm

119868y

cm4

119868z cm4

119908 ply

cm3

119908 plz

cm3

MATERIAU ACIER S235

12437 310 300 16 9 229286 698524 162823 70975




119888

119905119891=60

16= 375 lt 10휀 =gt 119888119897119886119904119904119890 1


119889

119905119908=98

9= 109 lt 72휀 =gt 119888119897119886119904119904119890 1





Si 119881119904119889 le 05119881119901119897119903119889 ⟹ 119872119904119889 le 119872119888119903119889 119912119955119957120787 120786 120789 119914119914119924 120791120789


119881119898119886119909 = 119881119904119889 =120kN

119881119901119897119911119903119889 =

119860119907119911 (119891119910

radic3)

1205741198980=4113 235radic3

11= 50731119896119873

97

119881119904119889 le 05119881119901119897119911119903119889




119873119904119889 le 119872119894119899(025119873119901119897119903119889 05119860119908119891119910

1205741198720)


119873119904119889 =602kN

119873119901119897119903119889 le119860 119891

119910

1205741198720=12437 235

11= 2656995 119896119873

025119873119901119897119903119889 = 664248119896119873

119860119908 = 119860 minus 2119887 119905119891 = 2837 1198981198982

05119860119908119891119910

1205741198720= 30304119896119873

119873119904119889 = 602119896119873 le 30304119896119873



119872119888119903119889 = 119872119901119897119910119903119889 =119908119901119897119910 119891119910

1205741198720=1628000 times 235

11= 3478119896119873119898




120594119898119894119899 119873119901119897119903119889+119896119910 119872119910119904119889

119872119901119897119910119903119889+119896119911 119872119911119904119889119872119901119897119911119903119889



120594119911 119873119901119897119903119889+119896119871119879 119872119910119904119889

120594119871119879119872119901119897119910119903119889+119896119911 119872119911119904119889119872119901119897119911119903119889



120594119898119894119899 = 119872119894119899(120594119910 120594119911)


98

120594119910 =1

(120601119910 +radic1206011199102 minus 1205821199102 )

120601119910 = 05[1 + 120572119910(120582119910 minus 02) + 1205821199102]

120582119910= (120582119910

1205821)radic120573119860 =

120582119910

1205821

Avec 120573119860 = 1 Classe 1

1205821 = 939

120582119910 =05119868119910

119894119910=05 890

1358= 3276

120582119910=3276

939= 034


ℎ

119887=310

300= 1 lt 12 (119910 minus 119910)119894119898119901119897119894119902119906119890 120572 = 034

120601 = 05[1 + 120572119910(120582119910 minus 02) + 1205821199102 ] = 058

120594119910 =1

058 + radic058 minus 034= 095


120594119911 =1

(120601119911 +radic1206011199112 minus 1205821199112)

120601119911 = 05[1 + 120572119911(120582119911 minus 02) + 1205821199112]

120582119911 = (1205821199111205821)radic120573119860 =

1205821199111205821

Avec 120573119860 = 1 Classe 1

1205821 = 939

120582119911 =119868119911119894119911=07 59

749= 055


ℎ

119887= 1 lt 12 (119911 minus 119911) 119894119898119901119897119894119902119906119890 120572 = 049

120601 = 05[1 + 049(055 minus 02) + 0552] = 073

99

120594119911 =1

073 + radic073 minus 055= 082

120594119898119894119899 = 119872119894119899(120594119910 120594119911) = 082


λ119897119905 =

119871119894119911

119888105

[

1 +120(

119871119894119911ℎ119905119891

)

2

] 025 = 3536

HEA320 119905119891 = 16119898119898 119894119911 = 749119888119898 ℎ = 310119898119898

119870 = 07 1198881 = 1134 Tableau B11 CCM97


1205821 = 939휀

휀 = radic235

119891119910= 1

120582119871119879 = [1205821198971199051205821] [120573119908]

05

120582119897119905 = 3536

120582119871119879 =3536

939= 037 lt 04 119901119886119904 119889119890 119903119894119904119902119906119890 119889119890 119889119890119907119890119903119904119890119898119890119899119905


119873119904119889120594119898119894119899 119873119901119897119903119889

+119896119910 119872119910119904119889

119872119901119897119910119903119889+119896119911 119872119911119904119889119872119901119897119911119903119889


Avec

119873119904119889 =602kN 119872119910119904119889=32083kNm 119872119911119904119889=049kNm 119872119901119897119910119903119889=3478kNm

119872119901119897119911119903119889=1516kNm 120594119898119894119899= 082 119873119901119897119903119889=26570kN 119896119910= 05 119896119911= 07

602

082 26570+05 32083

3478+07 049







100





(135G+15V1)


119873119904119889 =69837kN


Profileacute


2CAE (120x12)

A Cm2

hmm

b mm

Anet

Cm2

d

mm

MATERIAU ACIER S235

5508 120 248 4658 8



119873119904119889 le 119873119905119903119889 = 119872119894119899[119873119901119897119903119889 119873119906119903119889 119873119899119890119905119903119889]

101

119873119901119897119903119889 =119860 119891119910

1205741198720= 117671119896119873

119873119906119903119889 = 09119860119899119890119905 1198911199061205741198722

= 13719119896119873

119873119899119890119905119903119889 =119860119899119890119905 119891119910

1205741198720= 995118119896119873








102


119872119910119904119889 = 02 119896119873119898

119881119904119889 = 0048 119896119873

119873119904119889 = 5628 119896119873

Profileacute


IPE300

A cm2

hmm

b mm

119905f

mm

119905w mm

119868y

cm4

119868z cm4

119908ply

cm3

119908plz

cm3

MATERIAU ACIER S235

538 300 150 107 71 8356 746 628 125







Si 119881119904119889 le 05119881119901119897119903119889 ⟹ 119872119904119889 le 119872119888119903119889 119912119955119957120787 120786 120789 119914119914119924 120791120789


119881119898119886119909 = 119881119904119889 =0048kN

119881119901119897119911119903119889 =

119860119907119911 (119891119910

radic3)

1205741198980=2570 235radic3

11= 3169119896119873

119881119904119889 le 05119881119901119897119911119903119889




119873119904119889 le 119872119894119899(025119873119901119897119903119889 05119860119908119891119910

1205741198720)

103


119873119904119889 =5628kN

119873119901119897119903119889 le119860 119891

119910

1205741198720=5380 235

11= 114936 119896119873

025119873119901119897119903119889 = 28734 119896119873

119860119908 = 119860 minus 2119887 119905119891 = 2170 1198981198982

05119860119908119891119910

1205741198720= 23179119896119873

119873119904119889 = 5628119896119873 le 23179119896119873



119872119888119903119889 = 119872119901119897119910119903119889 =119908119901119897119910 119891119910

1205741198720=628000 times 235

11= 134163 119896119873119898




120594119898119894119899 119873119901119897119903119889+119896119910 119872119910119904119889

119872119901119897119910119903119889+119896119911 119872119911119904119889119872119901119897119911119903119889



120594119911 119873119901119897119903119889+119896119871119879 119872119910119904119889

120594119871119879119872119901119897119910119903119889+119896119911 119872119911119904119889119872119901119897119911119903119889



120594119898119894119899 = 119872119894119899(120594119910 120594119911)


120594119910 =1

(120601119910 +radic1206011199102 minus 1205821199102 )

120601119910 = 05[1 + 120572119910(120582119910 minus 02) + 1205821199102]

120582119910= (120582119910

1205821)radic120573119860 =

120582119910

1205821

104

Avec 120573119860 = 1 Classe 1

1205821 = 939

120582119910 =119871119910

119894119910= 960

125= 768

120582119910=768

939= 081


ℎ

119887=300

150= 05 lt 12 (119910 minus 119910)119894119898119901119897119894119902119906119890 120572 = 021

120601 = 05[1 + 120572119910(120582119910 minus 02) + 1205821199102 ] = 089

120594119910 =1

058 + radic058 minus 034= 079


120594119911 =1

(120601119911 +radic1206011199112 minus 1205821199112)

120601119911 = 05[1 + 120572119911(120582119911 minus 02) + 1205821199112]

120582119911 = (1205821199111205821)radic120573119860 =

1205821199111205821

Avec 120573119860 = 1 Classe 1

1205821 = 939

120582119911 =119868119911119894119911=125

335= 3731 120582119911 = 039


ℎ

119887= 1 lt 12 (119911 minus 119911) 119894119898119901119897119894119902119906119890 120572 = 021

120601 = 05[1 + 021(039 minus 02) + 0392] = 061

120594119911 =1

061 + radic061 minus 039= 092

120594119898119894119899 = 119872119894119899(120594119910 120594119911) = 079


105

λ119897119905 =

119871119894119911

119888105

[

1 +120(

119871119894119911ℎ119905119891

)

2

] 025 = 3433

IPE300 119905119891 = 107119898119898 119894119911 = 335119888119898 ℎ = 300119898119898

119870 = 1 1198881 = 1134 Tableau B11 CCM97


1205821 = 939휀

휀 = radic235

119891119910= 1

120582119871119879 = [1205821198971199051205821] [120573119908]

05

120582119897119905 = 3433

120582119871119879 =3433

939= 036 lt 04 119901119886119904 119889119890 119903119894119904119902119906119890 119889119890 119889119890119907119890119903119904119890119898119890119899119905


119873119904119889120594119898119894119899 119873119901119897119903119889

+119896119910 119872119910119904119889

119872119901119897119910119903119889+119896119911 119872119911119904119889119872119901119897119911119903119889


Avec

119873119904119889 =5628kN 119872119910119904119889=02kNm 119872119911119904119889=018kNm 119872119901119897119910119903119889=134163kNm

119872119901119897119911119903119889=267kNm 120594119898119894119899= 079 119873119901119897119903119889=1149kN 119896119910= 1 119896119911= 1

5628

079 1149+

02

134163+018



106

Chapitre-7


71 Introduction










au poteau

107




119872119904119889 = 28961119896119873119898 119873119904119889 = 17878119896119873 119881119904119889 = 8941119896119873




119905 = 119872119894119899(119905119891 119905119901119897119886119905119894119899119890) = 135119898119898

Avec





12119889O = 24 119898119898 le 1198901 le 12119905 =186 119898119898 ⟹ 1198901 = 110 119898119898

15119889O = 30 119898119898 le 1198902 le 12119905 = 186 119898119898 ⟹ 1198902 = 105 119898119898

22119889O = 44 119898119898 le 1199011 le 14119905 =217 119898119898 ⟹ 1199011 = 100 119898119898


108






IPE 400 119905f = 135 119898119898 119905w = 86 119898119898

119886min= 26 le twle119886max= 8

119886min =35 le tf le119886max= 8







sum119897 = 2119887 + 4(119887 minus 119905119908) = 2180 + 4(180 minus 86) = 1045119898119898

119865119908119903119889 =7times 1045 times 360

radic2= 1862119896119873

119873119904119889 =119872119904119889

ℎ=120784120790120791 120788120783

120782 120791= 120785120784120783 120789120790





Avec 120573119908 = 125 120574119872119882 = 08


109

i

sum119897 = 4ℎ119894 = 4 times 373 = 1492119898119898

119865119907119903119889 =7 times 1492 times 360

radic3= 217074119896119873



119873119894 =119872119904119889 119889119894sum119889119894

2


119909 = 119905119891radic119887

119905119908= 135radic

180

86= 6176



- 1198891 = 712 119898119898

- 1198892 = 612 119898119898

- 1198893 = 512 119898119898 ⟹ Σ 1198892 = 129 119898sup2

- 1198894 = 312 119898119898

- 1198895 = 212 119898119898

- 1198896 = 112 119898119898


1198731 =28961 times 0712

129= 15984119896119873



1198731 = 119899119865119907119903119889 ⟹ 119860119904 ge119873119904119889

06 times 119891119906119887 times 119899=

15984

06 times 800 times 2= 16651198981198982



M18 18 20 254 192 800 291



110




119865119901 = 07 times 119891119906119887 times 119860119904 = 06 x 800 x 192 = 10752kN

119872119903119889 =119899 119865119901 sum119889119894

2

119889119894=2 times 10752 times 129

0712= 3896 gt 119872119904119889 = 28961 119896119873119898




119865119907119904119889 le 119865119904119903119889 =119870119904 119898 120583

1205741198722(119865119901119888119889 minus 08119873119904119889) 119917119926119929119924119932119923119916 120788 120789 minus 119914119914119924120791120789

Avec

119870119904 = 10 ∶ Trous normaux



119865119904119903119889 = 024 (10752 minus 08 times15984

2) = 1046119896119873

119865119907119904119889 =8941

12= 745119896119873 lt 1046119896119873




1205741198722 119813119822119825119820119828119819119812 120788 120784 minus 119810119810119820120791120789



125= 213157 119896119873

119865119905119904119889 =119865119901

2=10752

2= 5376119896119873 lt 119861119901 119903119889 = 213157 119896119873


111



1205741198722 119827119808119809119819119812119808119828 120788 120787 120785 ndash 119810119810119820120791120789

Avec 119870119904 = 25

120572119887 = min (119890131198890

(119901131198890

minus 025) 119891119906119887119891119906 1) = 1



125= 46008119896119873 gt

11986511990711990411988912

= 745119896119873



119865119907 le 119865119905119903119889 = 119905119908119888 1198871198901198911198911198911199101205741198720

Avec




⟹ 119865119905119903119889 = 9 times 90times23511

= 173045 119896119873


119865119907 =119872119904119889

ℎ minus 119905119891=28961

029= 99865 gt 119865119905119903119889 = 173045119896119873




119873119904119889 le 119865119888119903119889 =119896119888 120588 119887119890119891119891 119905119908119888 119891119910

1205741198721radic1 + 13 (119887119890119891119891ℎ)2

119887119890119891119891 = 119905119891119887 + 2119886119901radic2 + 5(119905119891119888 + 119903119888) + 2119905119901

Avec

112






119887119890119891119891 =25014mm



120590119888119904119889 =119881119904119889119860+119872119904119889

119882119890119897119910=8941 times 103

1244+28961 times 106

1479= 196533119872119875119886

120590119888119904119889 = 19653119872119875119886 lt 119891119910 = 235119872119875119886 ⟹ 119896119888 = 1


119901 = 0932radic119887119890119891119891 119889119908119888 119891119910

119864 1199051199081198882= 0932radic


21 times 104 times 092= 254

119901 gt 072⟹ 120588 =119901 minus 02

1199012=254 minus 02

2542= 036


11 radic1 + 13 (250131

)2

= 12741119896119873

119873119904119889 = 1119873119894 =119872119904119889 sum119889119894sum119889119894

2 =29861 times 247

129= 57175119896119873





119865119907 le 119881119903119889 = 058119891119910 ℎ1199051199081205741198720


11= 3457119896119873


119865119907 =119872119904119889ℎ minus 119905119891

= 46216 119896119873 gt 119881119903119889 = 3457119896119873 119888119900119899119889119894119905119894119900119899 119899119900119899 119907eacute119903119894119891119894eacute119890


113

119865119907 = 46216119896119873 le 119881119903119889 = 058119891119910 ℎ119905119908 + 04

1205741198720= 058 235 31

(09 + 04)

11= 49935119896119873







logiciel robot

119872119904119889 = 15135119896119873119898 119873119904119889 = 1324119896119873 119881119904119889 = 273119896119873






119905 = min(119905119891 119905119901119897119886119905119894119899119890) = 135119898119898


114









IPE400

tf = 135 mm tw = 86 mm






radic2 times 119861119908 120574119898119908


Donc

119865119908119903119889 =119860 times sum119871 times 119891119906


radic2 times 1= 133083119896119873

119873119904119889 =119872119904119889ℎ

=7283

08= 9103119896119873

115

119873119904119889 = 9103 le 119865119908119903119889 = 1330119896119873






Donc

119865119907119903119889 =119886 times sum119871 times 119891119906


radic3 times 1= 155053119896119873



119873119894 =119872119904119889 119889119894sum119889119894

2


119909 = 119905119891radic119887

119905119908= 135radic

180

86= 6176119898119898


- 1198891 = 700 119898119898

- 1198892 = 600 119898119898

- 1198893 = 500 119898119898 ⟹ Σ1198891198942

= 124 119898sup2

- 1198894 = 300 119898119898

- 1198895 = 200 119898119898

- 1198896 = 100 119898119898


1198731 =119872119904119889 times 119889119894Σ119889119894

2 =15135 times 070

124= 4111119896119873



116


1198731 = 119899 119865119907 ⟹ 119860119904 ge119873119904119889

05 times 119891119906119887 times 119899=

13240

05 times 800 times 2= 16551198981198982



M18 18 20 254 192 800 291




119865119901 = 07 times 119891119906119887 times 119860119904 = 10752 119896119873

119872119903119889 =119899 119865119901sum119889119894

2

119889119894=2 times 10752 times 124

07= 38092 gt 119872119904119889 = 15135119896119873119898




119865119907119904119889 le 119865119904119903119889 =119870119904 119898 120583

1205741198722(119865119901119888119889 minus 08119873119904119889) 119813119822119825119820119828119819119812 120788120789 ndash 119810119810119820120791120789

Avec




119865119904119903119889 = 024 ( 10752 minus 08 times 1324) = 2326119896119873

119865119907119904119889 =273

12= 023 lt 119865119904 119903119889 = 2326119896119873




1205741198722 119813119822119825119820119828119819119812 120788 120784 ndash 119810119810119820120791120789

Avec


117


125= 31578119896119873

119865119905119904119889 =119865119901

2= 5376 lt 31578119896119873




1205741198722 119827119808119809119819119812119808119828 120788 120787 120785 ndash 119810119810119820120791120789

Avec Ks = 25

120572119887 = min (119890131198890

(119901131198890

minus 025) 119891119906119887119891119906 1) = 1


11986511990711990411988912


125= 5184 119896119873







119865119907119904119889 =119873119904119889

119899119887119903 119889119890 119887119900119906119897119900119899=131

3= 4366 le 119865119907119903119889

118


1205741198722⟹ 119860119904 ge

1205741198722 times 119865119907119903119889

06 times 119891119906119887119909 119898=125 times 43666

06 times 800 times 2= 56851198981198982


















119873119898119886119909 le 119865119908119903119889 =119886 sum119897 119891119906

119861119908 120574119898119908 radic(3 minus 1199041198941198991205722)


120572= 30gtgtgt 11990411989411989930o = 05

119865119908119903119889 =5 times 700 times 360



119



1205741198722 119827119808119809119819119812119808119828 120788 120787 120785 minus 119810119810119820120791120789


120572119907= 06



125= 12057119896119873

119865119907119904119889 =119873119904119889

3=3124

3= 10413 le 119865119907119903119889 = 12057119896119873




1205741198722 119827119808119809119819119812119808119828 120788 120787 120785 minus 119810119810119820120791120789

Avec

Ks = 25

120572119887 = min (119890131198890

(119901131198890

minus 025) 119891119906119887119891119906 1) = 092



125= 33914119896119873 gt 119865119907119904119889 = 4366119896119873




119873119898119886119909 le 119881119890119891119891119903119889 =119860119899119905 119891119910

1205741198722+119860119899119907 119891119910

radic3 1205741198722 119812119810120785 119849119834119851119853119842119838120783 minus 120790sect120785120783120782 120784

Avec


119860119899119890119905 = (119897

2minus11988902) 119905 = (60 minus 9)12 = 6121198981198982


120

119860119899119907 = (1198901 + 21199011 minus 251198890)119905 = (50 + 140 minus 45)12 = 17401198981198982

⟹ 119881119890119891119891119903119889 =612 times 235

125+1740 times 235

radic3 times 125= 303918119896119873 gt

119873119904119889

2= 655119896119873








119865119907119904119889 =119877119907119911

119899119887119900119906119897119900119899119904=36

2= 18 119896119873

119865119907119903119889 =06 times 119860119904 times 119891119906119887

120574119872119887⟹119860119904 ge

120574119872119887 times 11986511990711990311988906 times 119891119906119887

=11 times 18000

06 times 800= 41251198981198982



119865119907119903119889 =06 times 119860119904 times 119891119906119887

120574119872119887=06 times 58 times 800

11= 253119896119873 gt 119865119907119904119889 = 18119896119873


119865119905119903119889 =09 times 119860119904 times 119891119906119887

120574119872119887=09 times 58 times 800

11= 379119896119873

121

119865119907119903119889 =06 times 119860119904 times 119891119906119887

120574119872119887= 253119896119873

119865119907119904119889119865119907119903119889

+119865119905119904119889

14 119865119905119903119889= 052 lt 1 119862119900119899119889119894119905119894119900119899 119907119890119903119894119891119894eacute119890


122

Chapitre-8




123








119865119888119896=30 MPa

119891119888119889 =085 times 119865119888119896125

= 204 MPa


119865119895119889 = 120572120573119895 119891119888119889



119865119895119889 = 120572 120573119895 119891119888119889 = 15 times2

3times 17 = 204 119872119875119886


1198601198620 ge119873119904119889119891119888119889

=148960

204

1198601198620 ge 7266341198981198982


bp ge b+2tf = 190+2times155 = 221 mm

hp ge h+2tf = 310+2times155 = 341 mm

On prend

bp =600 hp=620



124


119862 = 119905 (119891119910119901

3119891119895119889 1205741198720)

05

= 30(235


= 5605 119898119898

119862 = 5605 lt(ℎ minus 2119905119891)

2= 1395 119898119898




gorge (a) Annexe H







119890 =119872119904119889119873119904119889

= 041 119898 gt 119885119879 = 0195 119898







125


Ougrave

119871119890119891119891 = min(119887119901 119887119891119888 + 2119888) = min(600 300 + 2 times 4671) = 39342 119898119898

119887119890119891119891 = min (119888ℎ1198882minus 119905119891119888) + 119905119891119888 +min (119888

ℎ119901 minus ℎ119888

2)

119887119890119891119891 = min (4671310

2minus 155) + 155 + min (4671

620 minus 310

2) = 10892 119898119898

⟹ 119865119888119903119889 = 204 times 10892 times 39342 = 874166 119896119873


119865119907119903119889 = 119865119891119903119889 + 119899119887 119865119907119887119903119889


119865119891119903119889 = 02119873119904119889 = 1214 119896119873





119865119907119887119903119889 =120572119888119887 119891119906119887 119860119904

1205741198722

Avec 120572119888119887 = 044 minus 00003119891119910119887 = 0248


126

119865119907119887119903119889 =0248 times 800 times 561

125= 8904 119896119873

⟹ 119865119907119903119889 = 1214 + 8 times 8904 119896119873 = 72446 119896119873




Avec 120573119908 =08 120574119898119908 = 125 119886 = 6 mm


sum119897 = 470 119898119898

119865119908119903119889 =6 times 470 times 360

radic3= 58612 119896119873

119881119904119889 = 9773 119896119873 lt min(119865119907119903119889 119865119908119903119889) = 58612 119896119873





W= 150 mm e = 55 mm ex = 40 mm mx = 40 mm


119897119890119891119891119888119901 = 119898119894119899 2120587119898119909 = 25132 119898119898

120587119898119909 +119882 = 27566 119898119898120587119898119909 + 2119890 = 23566 119898119898

⟹ 119897119890119891119891119888119901 = 23566 119898119898

127


119897119890119891119891119899119888 = 119898119894119899

4119898119909 + 125119890119909 = 210 119898119898

2119898119909 + 0625119890119909 +119882

2= 180 119898119898

2119898119909 + 0625119890119909 + 119890 = 160 119898119898119887119901

2= 150 119898119898

⟹ 119897119890119891119891119899119888 = 150 119898119898


119865119905119886119899119888119903119889 = min[119865119905119887119900119899119889119903119889 119865119905119903119889]


119865119905119903119889 = 09 times119860119904 times 119891119906119887120574119898119887


125= 32314 119896119873



119865119887119889 =036radic119891119888119896

120574119888=036 times 547

15= 1313 119872119875119886


119865119905119887119900119899119889119903119889 =120587 119889 119897119887 119891119887119889

120572

Avec

1198971 = 20119889 = 600 119898119898

119903 = 3119889 = 90 119898119898

1198972 = 20119889 = 600 119898119898






07= 52929 119896119873

119865119905119886119899119888119903119889 = 119898119894119899[52929 32314] = 32314 kN

128




Lb = 8d + em +tp + twa + 05k

Avec







119871119887lowast =

881198981199093 119860119904

1198971198901198911198911 1199051199013 =


150 times 253= 13480 119898119898 lt 119871119887 = 312 119898119898




119898119901119897119903119889 =1199051199012 119891119910119901

41205741198720=252 times 235

4 times 11= 3338119896119873


Mode 1 1198721199011198971119903119889 = 119898119901119897119903119889 times 1198971198901198911198911 = 3338 times 015 = 5007119896119873119898

1198971198901198911198911 = min(119897119890119891119891119888119901 119897119890119891119891119899119888) = 150 119898119898


129




Mode 1-2

1198651199051minus2119903119889 =21198721199011198971119903119889

119898119909=2 times 5

004= 250 119896119873

Mode 3

1198651199053119903119889 = 2119865119905119903119889119886119899119888ℎ119900119903 = 2 times 32314 = 646280 119896119873

Mode 4

1198651199054119903119889 =119887119890119891119891119905 119905119908 119891119910

1205741198720=150 times 9 times 235

11= 288409119896119873

Drsquoougrave

119865119905119903119889 = min(1198651199051minus2119903119889 1198651199053119903119889 1198651199054119903119889) = 250 119896119873




119885119879119890119873minus 1

119865119879119903119889 times 119885

119885119862119890119873+ 1

) 119812119810120785 ndash 120783 120790 119827119808119809119819119812119808119828 120788 120789

119885 = 119885119879+119885119862 = 195 + 155 = 350119898119898

⟹119872119903119889 = 5646 119896119873119898 lt 6207119896119873119898



821 Introduction




- Le site (S3)



130




ELU 119872119880 = 6207119896119873119898 119873119880 = 9773119896119873

ELS 119872119878 = 4136119896119873119898 119873119878 = 7960119896119873




119886 = 119886119901 + 119888 = 062 + 02 = 082 119898


119860

119861=119886

119887= 1025 ⟹ 119860 = 1025119861



119890 =119872119904

119873119904= 052119898



120590119898119886119909 =119873

119860119861(1 +

6119890

119861) le 120590119904119900119897


368B2 - B - 312 ge 0 ⟹ B ge0765m



131

119889 = max (119861 minus 119887

4119860 minus 119886

4) = max (005 0295)

On prend d= 45 cm



On a

119890 = 052 gt119860

6= 041


3120590119898119886119909 1205901198981198941198994

lt 120590119904119900119897

Avec

120590119898119894119899 =119873

119860119861(1 minus

6119890

119860) =

14896

2(1 minus

041

2 ) = 62191198961198731198982

120590119898119894119899 =119873

119860119861(1 +

6119890

119860) =

14896

2(1 +

041

2 ) = 86771198961198731198982

3120590119898119886119909 120590119898119894119899

4= 6835 1198961198731198982 lt 120590119904119900119897 = 180 119896119873119898

2



119890 =119872

119873= 052 119898 lt

119860

4= 062 119898




119890 gt119886

6 119890 gt

119860

24


119860119886 =1198721119911 119904119905

132

1198721 = (119860

2minus 035119886)

2

(1 +119890

119860+14 times 119890 times 119886

1198602)1198731199042119860

1198721 = 2788119896119873119898

Avec 119911 = 09d =40cm

119904119905 = min (2

3119891119890 110radic12057811989111990528) =20163 MPa

11989111990528 = 00611989111988828 + 06 = 24 119872119875119886 120578 = 16 119867 119860 Donc

119860119886 =2788 times 106

400 times 20163= 345 1198881198982


119860119887 =119873prime(119861 minus 119887)

8119889 119904119905

Avec

119873prime = 119873119904 (1 +3119890

119860) = 796 (1 +

3 times 052

25) = 2993119896119873

119904119905 = min (2

3119891119890 110radic12057811989111990528) = 20163119872119875119886

11989111990528 = 00611989111988828 + 06 = 24119896119873 120578 = 16 119867 119860

Donc 119860119887 = 071198881198982


119860119886 =1198721119911 120590119904119905

1198721 = (119860

2minus 035119886)

2

(1 +119890

119860+14 times 119890 times 119886

1198602)1198731199062119860

1198721 = 349119896119873119898

Avec 119911 =09d = 40 cm

120590119904119905 =119891119890120574119904=400

115= 3478119872119875119886

Donc

133

119860119886 =349 times 106

400 times 3478= 251198881198982


119860119886 =119873119906(119861 minus 119887)

8119889 120590119904119905

Avec

119873prime = 119873119906 (1 +3119890

119860) = 23833119896119873

Donc 119860119887 = 1621198881198982


119860119898119894119899 = 023 times11989111990528119891119890

times 119860 times ℎ119905 = 17251198881198982

Sens B

119860119898119894119899 = 023 times11989111990528119891119890

times 119861 times ℎ119905 = 691198881198982



A (cm2) St (cm)

A 345 1725 10T16 201 25 B 07 69 7T16 1407 25



134



119873119905 = (119873

120572) ge 20 119896119873 [119825119823119808120791120791 119855 120784120782120782120785 119808119851119853 120783120782 120783 120783 119835]


119873119905 =14896

12= 1241119896119873

ELS

119873119905 =796

12= 663119896119873


119860119904119905 =119873119905120590119904119905

ELS

119860119904119905 =663

348= 0191198881198982

ELU

119860119904119905 =1241

348= 0351198881198982





119860119904119905 = 0905 le 119860119904 = 6791198881198982


135


120601119898119894119899 le 119898119894119899 (ℎ

35120601119897119898119894119899

119887

10) = 08 119888119898

On prend 120601119905 =8mm


On prend St=10cm


136


137

ANNEXE - 1

138

139

140

ANNEXE - 2

141

ANNEXE - 3

142

143

ANNEXE ndash 4

144

145

ANNEXE ndash 5









Liste des tableaux

















LISTE DES NOTATIONS

Majuscules latines








16

Chapitre-1


11 Introduction


17



18

Action

permanente (γG)




Effet favorable

γGinf

10 1 0


γGsup

135 15 15




135119866119896119895 + 15119876119896119898119886119909





1 119866119896119895 + 150119882minus


sum119866119896119895119895

+ 119876119896119898119886119909

119866119896119895 + 119876119896119898119886119909


sum119866119896119895119895

+ 09sum119876119896119894119894gt1

119866119896119895 + 09119876119896119898119886119909 + 09119878 119866119896119895 + 09119876119896119898119886119909 + 09119882


19










20




21






22




23

Chapitre-2


21 Introduction










24

- Effet du site








Ouargla (Zone 4)




Kt=017 Z0=001m Zmin=1m ξ=044






Avec




119902119901(119885) = 119902119903119890119891 times 119862119890

Avec

- 119902ref = 575 119889119886119873119898sup2


2(119885) times [1 + 7119868119907] 119825119821119829120784120782120783120785 119836119841119834119849119842119853119851119838 120784 120786 sect120784 120786 120784 119834


25


119862119903(119911)

119870119905 119871119899 (1199111198981198941198991199110

) 119901119900119906119903 119911 lt 119911119898119894119899

119870119905 119871119899 (119911

1199110) 119901119900119906119903 119911119898119894119899 le 119911 le 200119898


)=0783


Zo)=1178

On retient 119862119903= 1178


119868119907(119911)

1

119862119905(119911) 119871119899 (119911

1199110) 119901119900119906119903 119911 gt 119911119898119894119899

1

119862119905(119911) 119871119899 (1199111198981198941198991199110) 119901119900119906119903 119911 le 119911119898119894119899

Pour z gt zmin 119868119907(119911) =1

1Ln(1

001)= 0217

Pour z lt zmin 119868119907(119911) =1

1Ln(1025

001)= 0144



119862119890(119911119895) = 119862119903(119911119895)2[1 + 7 119868119881]

Pour z gt zmin

119862119890(119911) = 11782 times 12 times [1 + 7(0144)] = 2786

Pour z lt zmin

119862119890(119911) = 07832 times 12 times [1 + 7(0217)] = 154


Avec

26

- 119902119903119890119891 = 575 119889119886119873119898sup2



qp = 160195Nm2 = 16 kNm2





- b=30 m

- d=36 m

- h=89 m


e = min (d 2h)


Donc e = 2x1025 = 205m



27



119862119901119890 = 1198621199011198901 119878119894 119878 le 11198982

119862119901119890 = 1198621199011198901 + (11986211990111989010 minus 1198621199011198901) times 11989711990011989210(119878) 119878119894 11198982 lt 119878 lt 101198982

119862119901119890 = 11986211990111989010 119878119894 119878 ge 101198982



Zone


Parois sous le vent


Cpe10 -10 -08 -05 +08 -03


Versant de Toiture




28







le tableau suivant


853deg F G H

-237 -123 -083



- Parois verticales


-b=36 m

29

-d=30 m

-h=1025


e=Min (b 2h) = Min (36 205) = 205 m





30

Zone


Parois sous le vent








31




853deg -22 -192 -183 -067 -057






2(5 times 4)

30 times 89= 014 = 14


μ119901 =120

160= 075



Pour μ119901=075 on lit 119862119901119894 =-016

32




2 times (5 times 4)

36 times 9575= 0116 = 116


Pour μ119901=075 rarr 119862119901119894 =-02

33





Direction V1 V3


A 1602 -10 -0154 -0846 -135529

B 1602 -08 -0154 -0646 -103489

C 1602 -05 -0154 -0346 -55429

D 1602 +08 -0154 +0954 +152831

E 1602 -03 -0154 -0146 -23389


34

Toiture


F 1602 -237 -0154 -2276 -355003

G 1602 -123 -0154 -1076 -172375

H 1602 -084 -0154 -0676 -108295

Z1 1602 -1 -0154 -0846 -135529

Z2 1602 -06 -0154 -0446 -71449


Direction V2 et V4

Parois verticales


A 1602 -10 -0162 -0838 -134247

B 1602 -08 -0162 -0638 -102207

C 1602 -05 -0162 -0338 -54147

D 1602 +08 -0162 +0962 +154112

E 1602 -03 -0162 -0138 -22107


35

Toiture


Finf 1602 -12 -0162 -1038 -1662876

Fsup 1602 -22 -0162 -2038 -3264876

G 1602 -183 -0162 -1668 -2672136

H 1602 -067 -0162 -0508 -813816

I 1602 -057 -0162 -0408 -653616









9= 015




q1= 300 Nml

q2= 500 Nml



36











- Epaisseur 50 mm

- Largeur 1000 mm





Selon le DTR BC22




37

119902 =8119875

3119871= 044 119896119873119898

119902 = 444 119889119886119873119898













38

Chapitre-3





deacutefavorable

39

(minus354 times5125


0875

6) = minus32754 1198891198861198731198982

Qeq (vent) = 3276 daN1198982















40



41


Vzsd =119902119906119911 times 119897

2=1878 kN

Mysd=119902119906119911 times 119897

2

8=2817 kNm

Mzsd=119902119906119910 times 119897

2

8=081 kNm



IPE 180 A Cm2

h mm

b mm

119905f

mm 119905w

mm 119868y

Cm4

119868z

Cm4

119908ply cm3

119908plz cm3

MATERIAU ACIER S235

239 180 91 8 53 1317 101 146 346




4

384 times 119864 119868119910lt

119897

200=



119897

200= 3 119862119900119899119889119894119905119894119900119899 119907eacute119903119894119891119894eacute119890

Plan z-z

5 times 119902119904119910 times 1198974

384 times 119864 119868119911lt

119897

200=



119897

200= 3 119862119900119899119889119894119905119894119900119899 119907eacute119903119894119891119894eacute119890

42




1205741198721 gt 119872119910119904119889 = 2817 119896119873119898

Calcul de 119872119887119903119889




λ119871119879 =

119871119894119911

119888105

[

1 +120(

119871119894119911ℎ119905119891

)

2

] 025

Avec


(Tableau B12 CCM97)

iz =224mm tf =85mm

L=Lz=3000mm h=200mm

λ119871119879 =

119871119894119911

119888105

[

1 +120(

119871119894119911ℎ119905119891

)

2

] 025 = 9457 rarr λ119871119879 =

989

939= 1007

rarr =1092

43


rarr ꭕ119871119879=

1


2)= 066 le 1

rarr 119872119887119903119889 =ꭕ119871119879times 120573

119908times 119882119901119897119910 times 119891119910

1205741198721

=066 1 166 235

11= 234 119896119873 119898








119872119872119860119883 =119901prime 119897

3=119901 1198972

8⟹ 119901 =

8 119901prime

3119897=800

18= 4444 119889119886119873119898119897

44


(ANNEXE ndash 1)

Soit

119876119890119902 =327 + 1082

2= 2176 1198891198861198731198982









45



Vzsd =119902119906119911 times 119897

2=186 kN

Mysd=119902119906119911 times 119897

2

8=279 kNm

Mzsd=119902119906119910 times 119897

2

8=0855 kNm

46



IPE 200 A Cm2

h mm

b mm

119905f

mm 119905w

mm 119868y

Cm4

119868z

Cm4

119908ply cm3

119908plz cm3

MATERIAU ACIER S235

285 200 100 85 56 1943 142 221 446




4

384 times 119864 119868119910lt

119897

200=



119897

200= 3 119862119900119899119889119894119905119894119900119899 119907eacute119903119894119891119894eacute119890

Plan z-z

5 times 119902119904119910 times 1198974

384 times 119864 119868119911lt

119897

200=



119897

200= 3 119862119900119899119889119894119905119894119900119899 119907eacute119903119894119891119894eacute119890




1205741198721 gt 119872119910119904119889 = 279 119896119873119898

Calcul de 119872119887119903119889

47




λ119871119879 =

119871119894119911

119888105

[

1 +120(

119871119894119911ℎ119905119891

)

2

] 025

Avec


(Tableau B12 CCM97)


-L=Lz=6000mm -h=200mm

λ119871119879 =

119871119894119911

119888105

[

1 +120(

119871119894119911ℎ119905119891

)

2

] 025 = 989 ⟶ λ119871119879 =

989

939= 105

rarr =114


rarr ꭕ119897119905=

1


2)= 063 le 1

rarr 119872119887119903119889 =ꭕ119897119905times 120573

119908times 119882119901119897119910 times 119891119910

1205741198721


11= 2974119896119873119898



48


Avec

119881119901119897119911119903119889 =

119860119907119911 (119891119910

radic3)

11 119890119905 119860119907119911 = 1400 1198981198982

Donc

05119881119901119897119911119903119889 = 05

1400 (235

radic3)

11= 8634 119896119873



Si 119889


CCM97 art 561(1)

119889

119905119908 =

159





(119872119910119904119889

119872119901119897119910119903119889)

120572

+ (119872119911119904119889119872119901119897119911119903119889

)

120573

le 1 119912119955119957 120787 120786 120790 (120783120783)119914119914119924 120791120789


119872119901119897119910119903119889 =119882119901119897119910 times 119891119910

11=221 times 235

11= 4721 119896119873119898

119872119901119897119911119903119889 =119882119901119897119911 times 119891119910

11=446 times 235

11= 952 119896119873119898

119872119910119904119889 = 279 119896119873119898

119872119911119904119889 = 0855 119896119873119898

(279

4721)2

+ (0855

952) = 044 lt 1 119888119900119899119889119894119905119894119900119899 119907eacute119903119894119891119894eacute119890

49











Effort rampant


Lrsquoexcentrement


2 (119887

2) le 119905 le 3(

119887

2)


50

2 (10

2) = 10 le 119905 le 3(

10

2) = 15

On prend t=10 cm


119877119911 = 119902119906119911 times119897

2= 6 times

6

2= 18 119896119873

119877119910 = 119902119906119910 times119897

2= 054 119896119873


119877119911 = 18 times 2 = 36 119896119873

119877119910 = 054 times 2 = 108 119896119873


119872119877 = 119877119911 times 119905 + 119877119910 timesℎ

2= 36 times 10 + 108 times 10 = 3708 119896119873 119888119898 = 37119896119873119898


119872119890119897119877119889 =119908119890119897 times 119891119910

1205741198720 119912119955119957 120787 120786 120787 120783 (120784)119914119914119924120791120789

119872119890119897119877119889 =119908119890119897 times 1198911199101205741198720

=gt 119908119890119897 ge119872119890119897119877119889 times 1205741198720

119891119910=gt 119908119890119897 ge

00037 times 11

235

= 173 times 10minus51198983

119908119890119897 = 17321198881198983




119908119890119897 =119887 1198902


6 times 1732

119887= radic

6 times 1732

180

119890 ge 076


Donc on prend e=1cm

51





















52












qsy =(133 + 5) times 125=2288daNml

qsy = 0228 kN

quy=135G=03kN



W += 1541 daN m2


quz=15W

quz=288kN

53



qsz=19262daN=192kN


119891119911 =5 times 119902119904119911 times 119897

4

384 times 119864119910 times 119868le 119891119886119889119873 =

119897

200=600

200= 3 119888119898

119868119910 ge5 times 192 times 6004



Profileacute


UPN 140 A Cm2

h mm

b mm

119905f mm

119905w mm

Iy

Cm4

Iz

Cm4

119908pSy

cm3

119908pSz

cm3

MATERIAU ACIER S235

20 140 60 10 7 605 627 103 283







qsy =(133 + 5) times 125 +1568 = 3856daNml

qsy = 038 kN

quy=135G

quy =053kN


qsz=192kN

quz=15W

quz=288kN

54




119888

119905119891=60

10= 6 lt 10휀 =gt 119888119897119886119904119904119890 1


119889

119905119908=98

7= 14 lt 72휀 =gt 119888119897119886119904119904119890 1


(119872119910119904119889

119872119890119897119910119877119889)

1

+ (119872119911119904119889

119872119890119897119911119877119889)1

le 1


119872119910 =119902119906119911 times 119897

2

8=288 times 62

8= 1296 119896119873119898


119872119911 =119902119906119910 times 119897

2

8=058 times 62

8= 261119896119873119898

119872119890119897119910119877119889 =119908119890119897119910 times 119891119910

1205741198720=864 times 103 times 235

11= 1845 119896119873119898

119872119890119897119911119877119889 =119908119890119897119911 times 119891119910

1205741198720=148 times 103 times 235

11= 316 119896119873119898

Donc

(1296

1845)1+ (

261



55

Nouveau 119872119911

119872119911 =119902119906119910 times 119897

2

8=058 times 32

8= 065119896119873119898

(1296

1845)1+ (

065




119881119911119904119889 =15119882119871

2= 1296 119896119873

119881119901119897119877119889 =119860119907119911 times 119891119910

radic3times 1205741198720= 12855 119896119873





1205741198721gt 119872119910119904119889 119912119955119957 120787 120787 120784 (120787 120786120790)119914119914119924120791120789

Avec

119872119888119903 = 11986211205872 119864 1198681199111198712

radic119868119908119868119911+1198712 119866 1198681199051205872 119864 119868119911

119912119925119925119916119935119916 119913 (119913 120783 120785) minus 119914119914119924120791120789

119872119888119903=311713762 Ncm


119872119888119903


119882119901119897119910 (upn140) =103 cm3

56

λ119897119905 = 0881


2 ]


empty119897119905 = 0959

ꭕ119897119905=

1


2 )

le 1

ꭕ119897119905= 075

119872119887119903119889 = 1652 119896119873119898

119872119887119903119889 = 1652 119896119873119898 gt 119872119910119904119889 = 1296 119896119873119898 119862119900119899119889119894119905119894119900119899 119907eacute119903119894119891119894eacute119890







57

119877 = 125119902119910 times 119897

2

Avec 119902119910 = [135(119866119880119875119873140 + 119866119888119900119906119907119890119903119905119906119903119890)]

119902119910 = 0837119896119873

119897 = 6 119898

119877 = 125119902119910 times 119897

2= 125 times 0837 times 3 = 32119896119873


1198791 =119877

2= 16119896119873

1198792 = 1198791 + 119877=48 kN

1198793 =1198792

2 sin 120579= 374 119896119873 119860119907119890119888 120579 = 119886119903119888 119905119892

25 119898

3 119898= 398deg



119873119905119904119889 =119860 times 119891119910

1205741198720= 4800 119873 =gt 119860 ge

11 times 4800

235 =gt 119860 ge 22461198981198982

119860 =120587empty2

4=gt empty ge radic

4119860

120587= radic

4 times 2246

314= 534 119898119898



Introduction



58



119878ge

63

radic119904

119889times119875

Avec








Srsquo=273

4=6825 m2








59



















96=8989 daNm2





60

119891119910 =5 times119882 times 1198974

384 times 119864 times 119868119910le 119891119886119889119898 =

119897

200


384 times E= 59136 1198881198984


Profileacute


IPE300 A Cm2

h mm

b mm

tf mm

tw

mm 119868y

Cm4

119868z Cm4

Wply

cm3

Wplz

cm3

MATERIAU ACIER S235

538 300 150 107 71 8356 746 628 125





119888

119905119891=

75

107= 7 lt 10 = 10 119878119890119898119890119897119897119890 119889119890 119888119897119886119904119904119890 1


119889

119905119908=2486

71= 35 lt 38 = 38 Acirc119898119890 119889119890 119888119897119886119904119904119890 1



Si 119881119904119889 le 05 119881119901119897119903119889 ⟹119872119904119889 le 119872119888119903119889 119912119955119957120787 120786 120789 119914119914119924 120791120789

61

119881119904119889 =15 times119882 times 119897


2= 388 119896119873 lt 05 119881119901119897119903119889 = 05 (

2570 times 235

radic3 times 11) = 1585 119896119873





Si

119873119904119889 le 119872119894119899 (025119873119901119897119903119889 05119860119908 119891119910

1205741198980)


025119873119901119897119903119889 = 025119860 times 119891119910

1205741198720= 025

5380 times 235

11= 28734 119896119873

05119860119908 times 119891119910

1205741198720= 05

2170 times 235

11= 2317 119896119873

119873119904119889 = 135119866 = 1337 119896119873 lt 119898119894119899 (025119873119901119897119903119889 05119860119908 times 119891119910

1205741198720)





119872119910119904119889 =15119882 times 1198972

8= 9313119896119873119898 119872119911119904119889 = 0 119872119901119897119910119903119889 = 13416 119896119873119898

λ119897119905 =

119871119911119894119911

119888105

[

1 +120(

119871119911119894119911ℎ119905119891

)

2

] 025


62

119871119911 = 1250 119898119898 119894119911 = 335 119898119898 ℎ = 300 119898119898 119905119891 = 107 119898119898




119873119904119889ꭕ119898119894119899

119873119901119897119903119889+119870119910 119872119910119904119889

119872119901119897119910119903119889+119870119911 119872119911119904119889119872119901119897119911119903119889


Avec

λ119910 =119871119910

119894119910=960

125= 768 rarr λ119910 =

768

939= 081

=gt 120583119910 = λ119910(2119861119898119910 minus 4) +119882119901119897119910 minus119882119890119897119910

119882119890119897119910= minus1134 + 0127 = minus1007 lt 09

120572 = 021 λ119910 = 081

empty119910 = 05 [1 + 120572119910(λ119910 minus 02) + λ1199102]

empty119910 = 05[1 + 021(081 minus 02) + 0812] = 089

ꭕ119910=

1


ꭕ119910= 0794 rarr 119870119910 = 1 minus


0794 times 538 times 2350= 101

120582119911 =125

335= 3731 =gt 120582119911 = 0397 rarr empty119911 = 0611 =gt ꭕ

119911= 092

ꭕ119898119894119899

= ꭕ119910= 0794

119873119901119897119903119889 =119860119891119910

1205741198980=5380 times 235

11= 114936 119896119873

119872119910119904119889 =151198821198712

8= 9313 119896119873119898

119872119901119897119910119903119889 = 13416 119896119873119898

119873119904119889 = 135119866 = 1337 119896119873

119896119910 = 101

119872119911119904119889 = 0

63

119873119904119889120594119898119894119899 119873119901119897119903119889

+119896119910 119872119910119904119889

119872119901119897119910119903119889+119896119911 119872119911119904119889119872119901119897119911119903119889

le 10

1337

0794 times 114836+101 times 9313

13416= 071 lt 1 119862119900119899119889119894119905119894119900119899 119907eacute119903119894119891119894eacute119890




64

Chapitre 4


41 Introduction




- Le pont roulant










poteaux de la halle

65





Puissances

N (t)

Porteacutee

L(m)



B

Chariot

K

Total

B+K

Rmax Rmin

125 18 085 520 1040 6809 1151 796 814 194


66


1 035 06 2 36



I 02 11 11 A-2















Groupes II






67
















119877119898119886119909 = 814 119870119873 119877119898119894119899 = 194 119870119873

Charges verticales

119877119881119898119886119909 = Ψ1 119877119898119886119909 = 115 times 814 = 8954 119870119873

119877119881119898119894119899 = Ψ2 119877119898119894119899 = 11 times 194 = 2134 119870119873


68

119877119871119898119886119909 = 119862 119877119898119886119909 = 02 times 814 = 1628 119870119873

119877119871119898119894119899 = 119862 119877119898119894119899 = 02 times 194 = 388 119870119873



1198771198671119898119886119909 = plusmn [0024(119870 + 119873 + 119861)119871

119890+ 0021(119873 + 119870)]

= plusmn [0024(1151 + 125 + 6809)18

36+ 0021(125 + 1151)]

1198771198671119898119886119909 = plusmn274 119905

1198771198671119898119894119899 = plusmn [0024(119870 + 119873 + 119861)119871

119890minus 0021(119873 + 119870)]

= plusmn [0024(1151 + 125 + 6809)18

36minus 0021(125 + 1151)]

1198771198671119898119894119899 = plusmn2168 119905


1198771198672119898119886119909 = plusmn [00052(119870 + 119873 + 5119861)119871

119890+ 0021(119873 + 119870)]

= plusmn [00052(1151 + 125 + 5 times 6809)18

36+ 0021(125 + 1151)]

1198771198672119898119886119909 = plusmn1526 119905

1198771198672119898119894119899 = plusmn [00052(119870 + 119873 + 5119861)119871

119890minus 0021(119873 + 119870)]

= plusmn [00052(1151 + 125 + 5 times 6809)18

36minus 0021(125 + 1151)]

1198771198672119898119894119899 = plusmn0953 119905




69





Rail

Poids

(Kgm)

B

(mm)

H

(mm)

P

(mm)

Section

A (cm2)

I x

(cm4)

I y

(cm4)

A55

318

55

65

150

407

178

337



70



119891119911 le 119891119886119889119898 =119897

750= 08 119888119898



119886 = (119897

2minus119890

4) = (

6

2minus36

4) = 21 119898



119891119911 =119901 119886 1198972

24119864119868(3 minus

4 1198862

1198972)

Avec

L= 6000 mm

a= 2100 mm

P=89540 N

E=21104 Nmm2

71

119868119910 ge119901 119886 1198972(31198972 minus 41198862)



119868119910 ge 421397625 1198981198984






119902 = 119866119901119900119906119905119903119890 + 119866119903119886119894119897 = 142 + 031 = 173 119896119899119898119897

119891119911 =119901 119886 1198972

24119864119868(3 minus

4 1198862

1198972) +

5 119902 1198974

384119864119868

119891119911 =89540 times 2100 times 60002


4 times 21002

60002) +




profileacute


G

Kgm

A cm2 h

mm

b

mm

tf

mm

tw

mm

Iy

cm4

Iz

cm4

Wply

cm3

Wplz

cm 3

HEB360 142 1806 360 300 225 125 43190 10140 2683 1032

72


119902 = 119866119901119900119906119905119903119890 + 119866119903119886119894119897 = 155 + 031 = 186 119870119873119898119897

119891119911 =119901 119886 1198972

24119864119868(3 minus

4 1198862

1198972) +

5 119902 1198974

384119864119868

119891119911 =89540 times 2100 times 60002


4 times 21002

60002) +






119905119908le 72휀

Avec

휀 = radic235

119891119910

298

135le 72radic

235

235 ⟹ 2207 le 72


119888

119905119891=1198872

119905119891le 10휀 ⟹

150

24= 625 le 10




profileacute


G

Kgm

A

cm2

h

mm

b

mm

tf

mm

tw

mm

Iy

cm4

Iz

cm4

Wply

cm3

Wplz

cm 3

HEB400 155 1978 400 300 24 135 57680 10820 3232 1104

73

119881119910119904119889 le 119881119901119897119903119889 119912119955119957 120787 120786 120788 (120787 120784120782)119914119914119924120791120789

119881119901119897119903119889 =119860119907119911 119891119910

radic3 1205741198980=6998 times 235

radic3 times 11= 863154 119873 = 86315 119870119873


119881119881 = 119877119881119898119886119909 times4119886

119897=8954 times 4 times 21

6= 12535 119870119873


119881119875119875 =119866 119897

2=186 times 6

2= 558 119870119873

Drsquoougrave 119881119910119904119889 = 135119881119875119875 + 15119881119881 = 19556 119870119873

119881119910119904119889 le 119881119901119897119903119889



Suivant (z-z)


119872119881 = 119877119881119898119886119909 times(6 minus

1198902)2

4119897= 8954 times

(6 minus362 )

2

4 times 6= 6581 119870119873119898


119872119875119875 =119866 1198972

8= 837 119870119873119898


119872119910119904119889 = 135119872119875119875 + 15119872119881 = 110 119870119873119898



119872119911119904119889 = 119872119867 =21198771198671119871

(119871

2minus119890

4)2

74

119872119911119904119889 = 119872119867 =2 times 274

6times (

6

2minus36

4)2

= 4028 119870119873119898




119873119904119889119873119901119897119903119889

+119872119910119904119889

119872119890119897119910+119872119911119904119889119872119890119897119911

le 1 120787 120785120790 ndash 119810119810119820120791120789

119873119904119889 = 15119877119871119898119886119909 = 15 times 1628 = 2442 119870119873

119872119890119897119910 =119908119890119897119910 119891119910

1205741198720= 61613 119872119890119897119911 =

119908119890119897119911 119891119910

1205741198720= 1541 119873119901119897119903119889 =

119860 119891119910

1205741198720= 422573

2442

422573+

110

61613+4028

1541= 044 le 1



Si 119889


Avec

휀 = radic235

119891119910= 1

119889

119905119908=298

135= 2207 lt 69





1205741198721


75



λ119897119905 =

119871119894119911

119888105

[

1 +120(

119871119894119911ℎ119905119891

)

2

] 025 = 6522 119808119821119821119812119831119812119809 119810119810119820120791120789

Avec 119871 = 600119888119898


λ119871119879 = [λ119897119905λ1] [120573119908]

05 휀 = radic235

119891119910= 1

λ119871119879 =6522

939= 0694

On calcule

ꭕ119871119879=

1


2 )le 1




ꭕ119871119879=

1

(079 + radic0792 minus 06942)= 0856


11= 59104 119870119873119898

119872119910119904119889 = 110 119870119873119898




76



119891119904119889 le 119877119910119877119889

Avec




120590119891119864119889 =119872119910119904119889

119882119890119897119910= 381 1198701198731198881198982

119878119910 = 2(ℎ119877 + 119905119891)radic[1 minus (1205741198720120590119891119864119889

119891119910119891)

2

] = 1751 119888119898

119877119910119877119889 =119878119910 times 119905119908 times 119891119910119908

1205741198720= 505 119870119873 gt 119891119904119889 = 119877119907119898119886119909 = 8954 119870119873




119891119904119889 le 119877119886119877119889

119891119904119889119877119886119877119889

+119872119878119889119872119888119877119889

le 1 119808119825119827 120787 120789120790 minus 119810119810119820120791120789

Avec

77

119877119886119877119889 =

051199051199082 (119864 119891119910119908)

05[(119905119891119905119908)05

+ 3(119905119908119905119891) (119878119904119889 )]

1205741198720 119808119825119827 120787 120789120789 minus 119810119810119820120791120789

119877119886119877119889 = 108284 119870119873

119891119904119889 = 15119877119871119898119886119909 = 15 times 1628 = 2442 119870119873

119872119888119877119889 =3232 times 103 times 235

11= 69047 119870119873119898

119891119904119889119877119886119877119889

+119872119878119889119872119888119877119889

=2442

108284+

110

69047 = 018 le 15




119887119890119891119891 le 119887 119808119825119827 120787 120789120791 minus 119810119810119820120791120789

119887119890119891119891 = radicℎ2 + 1198781199042 = 410 119898119898 gt 119887 = 300 119898119898




efforts suivants




Charge verticale


119901prime = 119876 119871 + 119877119898119886119909 (2 minus119890

119871) ψ


36

6) times 11

119901prime = 13651 119870119873


119901 = 135119876 119871 + 15119877119898119886119909 (2 minus119890

119871) ψ


36

6) times 11

119901 = 2031 119870119873

78

Charge horizontale

119875119867 = 15119877119867119898119886119909 (1 minus119890

119897)ψ


36

6) times 11 = 1808 119870119873




119891119911 le 119891119886119889119898 =119897

500


119891119911 =119901prime 1198893

3119864119868le 119891119886119889119898

119868119910 =500 119901prime 1198892

3119864ge 782667 1198881198984


79




119905119908le 72휀

Avec

휀 = radic235

119891119910

2486

71le 72radic

235

235 ⟹ 3501 le 72


119888

119905119891=1198872

119905119891le 10휀 ⟹

75

102= 735 le 10





119881119910119904119889 le 119881119901119897119903119889

Avec 119860119907119911 = 257 cm2

119881119901119897119903119889 =119860119907119911 119891119910

radic3 1205741198980=257 times 235

radic3 times 11= 317 119870119873

119881119904119889 = 119901 = 2031 lt 05119881119901119897119877119889


profileacute


G

Kgm

A

cm2

h

mm

b

mm

tf

mm

tw

mm

Iy

cm4

Iz

cm4

Wply

cm3

Wplz

cm 3

IPE 300 422 5380 300 150 107 71 8353 604 628 125

80


119872119888119903119889 =119908119901119897119910 119891119910

1205741198720=628 times 235

11= 13416 119870119873119898

119872119910119904119889 = 119901 119889 = 2031 times 085 = 172635 119870119873119898

119872119910119904119889 lt 119872119888119903119889




119872119888119903119889 =119908119901119897119910 119891119910

1205741198720=1019 times 235

11= 2177 119870119873119898

119872119910119904119889 = 119901 119889 = 2031 times 085 = 172635 119870119873119898

119872119910119904119889 lt 119872119888119903119889


17263


profileacute


G

Kgm

A

cm2

h

mm

b

mm

tf

mm

tw

mm

Iy

cm4

Iz

cm4

Wply

cm3

Wplz

cm3

IPE 360 571 727 360 170 127 8 16270 1043 1019 191

81



chemin de roulement

119891119911 le 119891119886119889119898 =119889

500= 017

119902 = 119902119868119875119864 360 = 571 119889119886119873119898119897

119891119911 =119901prime 1198893

3119864119868+119902 1198974

8119864119868= 0082 + 0021 = 0103 119888119898 lt 017 119888119898


82

Chapitre-5








dynamiques


83




119881 =119860119863 119876

119877119882



119863 =

25120578 0 le 119879 le 1198792

25120578(1198792119879)23 1198792 le 119879 le 3119904

25120578 (11987923)

23 (3119879)

53 119879 gt 3119904


84

120578 = radic7

(2 + 120585)ge 07



119879 = 119862119879 ℎ11987334 119917119926119929119924119932119923119916 (120786 120788)119929119927119912 119933120784120782120782120785




119876 = 1 +sum119875119902

6

1


85


119876 = 1 +sum119875119902

6

1

= 1 + 02 = 12


119899119894=1

Avec 119882119894 = 119882119866119894 + 120573119882119876119894




119881 =119860119863 119876

119877119882

119860 = 005 119863 = 25 119876 = 12 119877 = 4 119882 = 189475119896119873

119881119909 = 119881119910 =005 times 25 times 12

4times 189475 = 7105119896119873


119904119886119892=

125119860 (119860 +

119879

1198791(25120578

119876

119877minus 1)) 0 le 119879 le 1198791

25120578(125119860) (119876

119877) 1198791 le 119879 le 1198792

25120578(125119860) (119876

119877)(1198792119879)23

1198792 le 119879 le 30119904

25120578(125119860) (11987923)

23(3

119879)

53(119876

119877) 119879 gt 30119904

86



η = 100 A=005 1198791=015 1198792=050


87













88










89

ℎ

150=890

150= 594119888119898 sans vent

ℎ

125=890

125= 712119888119898 avec vent






Toiture 029 076 116 304


ℎ

100=1025

100= 1025 119888119898



90

Chapitre-6


61 Introduction





119872119910119904119889 = 21902 kNm

119881119904119889 =7249 kN

119873119904119889 =2018 kN

91

Profileacute


IPE 400 A cm2

hmm

b mm

119905f

mm

119905w mm

119868y

cm4

119868z Cm4

119908ply

cm3

119908plz

cm3

MATERIAU ACIER S235

8446 400 180 14 90 231284 131782 123832 2256




119888

119905119891=60

14= 59 lt 10휀 =gt 119888119897119886119904119904119890 1


119889

119905119908=98

9= 11 lt 72휀 =gt 119888119897119886119904119904119890 1





Si 119881119904119889 le 05119881119901119897119903119889 ⟹ 119872119904119889 le 119872119888119903119889 119912119955119957120787 120786 120789 119914119914119924 120791120789


119881119898119886119909 = 119881119904119889 =7248kN

119881119901119897119911119903119889 =

119860119907119911 (119891119910

radic3)

1205741198980=

4270235

radic311

= 526674119896119873

119881119904119889 = 7247 le 05119881119901119897119911119903119889 = 52667119896119873


92



119873119904119889 le 119872119894119899(025119873119901119897119903119889 05119860119908119891119910

1205741198720)


119873119904119889 = 2018119896119873

119873119901119897119903119889 le119860 119891

119910

1205741198720=8446 235

11= 180437119896119873

025119873119901119897119903119889 =451 119896119873

119860119908 = 119860 minus 2119887 119905119891 = 34061198981198982

05119860119908119891119910

1205741198720= 36382119896119873

119873119904119889 = 2018 le 36382119896119873



119872119888119903119889 = 119872119901119897119910119903119889 =119908119901119897119910 119891119910

1205741198720=1238320 235

11= 26455119896119873119898




120594119898119894119899 119873119901119897119903119889+119896119910 119872119910119904119889

119872119901119897119910119903119889+119896119911 119872119911119904119889119872119901119897119911119903119889



120594119911 119873119901119897119903119889+119896119871119879 119872119910119904119889

120594119871119879119872119901119897119910119903119889+119896119911 119872119911119904119889119872119901119897119911119903119889



120594119898119894119899 = 119872119894119899(120594119910 120594119911)


93

120594119910 =1

(120601119910 +radic1206011199102 minus 1205821199102 )

120601119910 = 05[1 + 120572119910(120582119910 minus 02) + 1205821199102]

120582119910= (120582119910

1205821)radic120573119860 =

120582119910

1205821

Avec 120573119860 = 1 Classe 1

1205821 = 939

120582119910 =05119868119910

119894119910=455

166= 274

120582119910=274

939= 029


ℎ

119887=400

180= 222 gt 12 119894119898119901119897119894119902119906119890 120572 = 021

120601 = 05[1 + 120572119910(120582119910 minus 02) + 1205821199102 ] = 055

120594119910 =1

(055 + radic0552 minus 0292)= 098


120594119911 =1

(120601119911 +radic1206011199112 minus 120582119911

2)

120601119911 = 05[1 + 120572119911(120582119911 minus 02) + 1205821199112]

120582119911 = (1205821199111205821)radic120573119860 =

1205821199111205821

Avec 120573119860 = 1 Classe 1

120582119911 =119868119911119894119911=200

395= 5063

120582119911 =5063

939= 054


94

ℎ

119887= 222 gt 12 (119911 minus 119911)119894119898119901119897119894119902119906119890 120572 = 034

120601 = 05[1 + 034(054 minus 02) + 0542 ] = 07

120594119911 =1

(07 + radic072 minus 0542)= 087

120594119898119894119899 = 119872119894119899(120594119910 120594119911) = 087




λ119897119905 =

119871119894119911

119888105

[

1 +120(

119871119894119911ℎ119905119891

)

2

] 025 = 4367 119808119821119821119812119831119812119809 119810119810119820120791120789

Avec

IPE400 119905119891 = 14119898119898 119894119911 = 395119888119898 ℎ = 400119898119898

119870 = 1 1198881=1134 Tableau B11 CCM97


1205821 = 939휀

휀 = radic235

119891119910= 1

120582119871119879 = [1205821198971199051205821] [120573119908]

05

120582119897119905 = 4367

120582119871119879 =4367

939= 046 gt 04



119873119904119889120594119911 119873119901119897119903119889

+119896119871119879 119872119910119904119889

120594119871119879119872119901119897119910119903119889+119896119911 119872119911119904119889119872119901119897119911119903119889


Calcul de 120594119871119879


95

implique 120594119871119879 = 094

Calcul de 119896119871119879


119870119871119879 = 1 minusμLT N119904119889

120594119911 119860 119891119910= 099 lt 15


Donc

119873119904119889=7249 kN 119872119910119904119889=219 kNm 119872119901119897119910119903119889=26455 kNm 120594119911=087 119872119901119897119911119903119889=4819kNm


119873119904119889120594119911 119873119901119897119903119889

+119896119871119879 119872119910119904119889

120594119871119879119872119901119897119910119903119889+119896119911 119872119911119904119889

119872119901119897119911119903119889


7249

087 180437+

099 219

094 26455= 055










96

119872119910119904119889 = 32083 119896119873119898

119881119904119889 = 120 119896119873

119873119904119889 = 602 119896119873

Profileacute


HEA320

A cm2

hmm

b mm

119905f

mm

119905w mm

119868y

cm4

119868z cm4

119908 ply

cm3

119908 plz

cm3

MATERIAU ACIER S235

12437 310 300 16 9 229286 698524 162823 70975




119888

119905119891=60

16= 375 lt 10휀 =gt 119888119897119886119904119904119890 1


119889

119905119908=98

9= 109 lt 72휀 =gt 119888119897119886119904119904119890 1





Si 119881119904119889 le 05119881119901119897119903119889 ⟹ 119872119904119889 le 119872119888119903119889 119912119955119957120787 120786 120789 119914119914119924 120791120789


119881119898119886119909 = 119881119904119889 =120kN

119881119901119897119911119903119889 =

119860119907119911 (119891119910

radic3)

1205741198980=4113 235radic3

11= 50731119896119873

97

119881119904119889 le 05119881119901119897119911119903119889




119873119904119889 le 119872119894119899(025119873119901119897119903119889 05119860119908119891119910

1205741198720)


119873119904119889 =602kN

119873119901119897119903119889 le119860 119891

119910

1205741198720=12437 235

11= 2656995 119896119873

025119873119901119897119903119889 = 664248119896119873

119860119908 = 119860 minus 2119887 119905119891 = 2837 1198981198982

05119860119908119891119910

1205741198720= 30304119896119873

119873119904119889 = 602119896119873 le 30304119896119873



119872119888119903119889 = 119872119901119897119910119903119889 =119908119901119897119910 119891119910

1205741198720=1628000 times 235

11= 3478119896119873119898




120594119898119894119899 119873119901119897119903119889+119896119910 119872119910119904119889

119872119901119897119910119903119889+119896119911 119872119911119904119889119872119901119897119911119903119889



120594119911 119873119901119897119903119889+119896119871119879 119872119910119904119889

120594119871119879119872119901119897119910119903119889+119896119911 119872119911119904119889119872119901119897119911119903119889



120594119898119894119899 = 119872119894119899(120594119910 120594119911)


98

120594119910 =1

(120601119910 +radic1206011199102 minus 1205821199102 )

120601119910 = 05[1 + 120572119910(120582119910 minus 02) + 1205821199102]

120582119910= (120582119910

1205821)radic120573119860 =

120582119910

1205821

Avec 120573119860 = 1 Classe 1

1205821 = 939

120582119910 =05119868119910

119894119910=05 890

1358= 3276

120582119910=3276

939= 034


ℎ

119887=310

300= 1 lt 12 (119910 minus 119910)119894119898119901119897119894119902119906119890 120572 = 034

120601 = 05[1 + 120572119910(120582119910 minus 02) + 1205821199102 ] = 058

120594119910 =1

058 + radic058 minus 034= 095


120594119911 =1

(120601119911 +radic1206011199112 minus 1205821199112)

120601119911 = 05[1 + 120572119911(120582119911 minus 02) + 1205821199112]

120582119911 = (1205821199111205821)radic120573119860 =

1205821199111205821

Avec 120573119860 = 1 Classe 1

1205821 = 939

120582119911 =119868119911119894119911=07 59

749= 055


ℎ

119887= 1 lt 12 (119911 minus 119911) 119894119898119901119897119894119902119906119890 120572 = 049

120601 = 05[1 + 049(055 minus 02) + 0552] = 073

99

120594119911 =1

073 + radic073 minus 055= 082

120594119898119894119899 = 119872119894119899(120594119910 120594119911) = 082


λ119897119905 =

119871119894119911

119888105

[

1 +120(

119871119894119911ℎ119905119891

)

2

] 025 = 3536

HEA320 119905119891 = 16119898119898 119894119911 = 749119888119898 ℎ = 310119898119898

119870 = 07 1198881 = 1134 Tableau B11 CCM97


1205821 = 939휀

휀 = radic235

119891119910= 1

120582119871119879 = [1205821198971199051205821] [120573119908]

05

120582119897119905 = 3536

120582119871119879 =3536

939= 037 lt 04 119901119886119904 119889119890 119903119894119904119902119906119890 119889119890 119889119890119907119890119903119904119890119898119890119899119905


119873119904119889120594119898119894119899 119873119901119897119903119889

+119896119910 119872119910119904119889

119872119901119897119910119903119889+119896119911 119872119911119904119889119872119901119897119911119903119889


Avec

119873119904119889 =602kN 119872119910119904119889=32083kNm 119872119911119904119889=049kNm 119872119901119897119910119903119889=3478kNm

119872119901119897119911119903119889=1516kNm 120594119898119894119899= 082 119873119901119897119903119889=26570kN 119896119910= 05 119896119911= 07

602

082 26570+05 32083

3478+07 049







100





(135G+15V1)


119873119904119889 =69837kN


Profileacute


2CAE (120x12)

A Cm2

hmm

b mm

Anet

Cm2

d

mm

MATERIAU ACIER S235

5508 120 248 4658 8



119873119904119889 le 119873119905119903119889 = 119872119894119899[119873119901119897119903119889 119873119906119903119889 119873119899119890119905119903119889]

101

119873119901119897119903119889 =119860 119891119910

1205741198720= 117671119896119873

119873119906119903119889 = 09119860119899119890119905 1198911199061205741198722

= 13719119896119873

119873119899119890119905119903119889 =119860119899119890119905 119891119910

1205741198720= 995118119896119873








102


119872119910119904119889 = 02 119896119873119898

119881119904119889 = 0048 119896119873

119873119904119889 = 5628 119896119873

Profileacute


IPE300

A cm2

hmm

b mm

119905f

mm

119905w mm

119868y

cm4

119868z cm4

119908ply

cm3

119908plz

cm3

MATERIAU ACIER S235

538 300 150 107 71 8356 746 628 125







Si 119881119904119889 le 05119881119901119897119903119889 ⟹ 119872119904119889 le 119872119888119903119889 119912119955119957120787 120786 120789 119914119914119924 120791120789


119881119898119886119909 = 119881119904119889 =0048kN

119881119901119897119911119903119889 =

119860119907119911 (119891119910

radic3)

1205741198980=2570 235radic3

11= 3169119896119873

119881119904119889 le 05119881119901119897119911119903119889




119873119904119889 le 119872119894119899(025119873119901119897119903119889 05119860119908119891119910

1205741198720)

103


119873119904119889 =5628kN

119873119901119897119903119889 le119860 119891

119910

1205741198720=5380 235

11= 114936 119896119873

025119873119901119897119903119889 = 28734 119896119873

119860119908 = 119860 minus 2119887 119905119891 = 2170 1198981198982

05119860119908119891119910

1205741198720= 23179119896119873

119873119904119889 = 5628119896119873 le 23179119896119873



119872119888119903119889 = 119872119901119897119910119903119889 =119908119901119897119910 119891119910

1205741198720=628000 times 235

11= 134163 119896119873119898




120594119898119894119899 119873119901119897119903119889+119896119910 119872119910119904119889

119872119901119897119910119903119889+119896119911 119872119911119904119889119872119901119897119911119903119889



120594119911 119873119901119897119903119889+119896119871119879 119872119910119904119889

120594119871119879119872119901119897119910119903119889+119896119911 119872119911119904119889119872119901119897119911119903119889



120594119898119894119899 = 119872119894119899(120594119910 120594119911)


120594119910 =1

(120601119910 +radic1206011199102 minus 1205821199102 )

120601119910 = 05[1 + 120572119910(120582119910 minus 02) + 1205821199102]

120582119910= (120582119910

1205821)radic120573119860 =

120582119910

1205821

104

Avec 120573119860 = 1 Classe 1

1205821 = 939

120582119910 =119871119910

119894119910= 960

125= 768

120582119910=768

939= 081


ℎ

119887=300

150= 05 lt 12 (119910 minus 119910)119894119898119901119897119894119902119906119890 120572 = 021

120601 = 05[1 + 120572119910(120582119910 minus 02) + 1205821199102 ] = 089

120594119910 =1

058 + radic058 minus 034= 079


120594119911 =1

(120601119911 +radic1206011199112 minus 1205821199112)

120601119911 = 05[1 + 120572119911(120582119911 minus 02) + 1205821199112]

120582119911 = (1205821199111205821)radic120573119860 =

1205821199111205821

Avec 120573119860 = 1 Classe 1

1205821 = 939

120582119911 =119868119911119894119911=125

335= 3731 120582119911 = 039


ℎ

119887= 1 lt 12 (119911 minus 119911) 119894119898119901119897119894119902119906119890 120572 = 021

120601 = 05[1 + 021(039 minus 02) + 0392] = 061

120594119911 =1

061 + radic061 minus 039= 092

120594119898119894119899 = 119872119894119899(120594119910 120594119911) = 079


105

λ119897119905 =

119871119894119911

119888105

[

1 +120(

119871119894119911ℎ119905119891

)

2

] 025 = 3433

IPE300 119905119891 = 107119898119898 119894119911 = 335119888119898 ℎ = 300119898119898

119870 = 1 1198881 = 1134 Tableau B11 CCM97


1205821 = 939휀

휀 = radic235

119891119910= 1

120582119871119879 = [1205821198971199051205821] [120573119908]

05

120582119897119905 = 3433

120582119871119879 =3433

939= 036 lt 04 119901119886119904 119889119890 119903119894119904119902119906119890 119889119890 119889119890119907119890119903119904119890119898119890119899119905


119873119904119889120594119898119894119899 119873119901119897119903119889

+119896119910 119872119910119904119889

119872119901119897119910119903119889+119896119911 119872119911119904119889119872119901119897119911119903119889


Avec

119873119904119889 =5628kN 119872119910119904119889=02kNm 119872119911119904119889=018kNm 119872119901119897119910119903119889=134163kNm

119872119901119897119911119903119889=267kNm 120594119898119894119899= 079 119873119901119897119903119889=1149kN 119896119910= 1 119896119911= 1

5628

079 1149+

02

134163+018



106

Chapitre-7


71 Introduction










au poteau

107




119872119904119889 = 28961119896119873119898 119873119904119889 = 17878119896119873 119881119904119889 = 8941119896119873




119905 = 119872119894119899(119905119891 119905119901119897119886119905119894119899119890) = 135119898119898

Avec





12119889O = 24 119898119898 le 1198901 le 12119905 =186 119898119898 ⟹ 1198901 = 110 119898119898

15119889O = 30 119898119898 le 1198902 le 12119905 = 186 119898119898 ⟹ 1198902 = 105 119898119898

22119889O = 44 119898119898 le 1199011 le 14119905 =217 119898119898 ⟹ 1199011 = 100 119898119898


108






IPE 400 119905f = 135 119898119898 119905w = 86 119898119898

119886min= 26 le twle119886max= 8

119886min =35 le tf le119886max= 8







sum119897 = 2119887 + 4(119887 minus 119905119908) = 2180 + 4(180 minus 86) = 1045119898119898

119865119908119903119889 =7times 1045 times 360

radic2= 1862119896119873

119873119904119889 =119872119904119889

ℎ=120784120790120791 120788120783

120782 120791= 120785120784120783 120789120790





Avec 120573119908 = 125 120574119872119882 = 08


109

i

sum119897 = 4ℎ119894 = 4 times 373 = 1492119898119898

119865119907119903119889 =7 times 1492 times 360

radic3= 217074119896119873



119873119894 =119872119904119889 119889119894sum119889119894

2


119909 = 119905119891radic119887

119905119908= 135radic

180

86= 6176



- 1198891 = 712 119898119898

- 1198892 = 612 119898119898

- 1198893 = 512 119898119898 ⟹ Σ 1198892 = 129 119898sup2

- 1198894 = 312 119898119898

- 1198895 = 212 119898119898

- 1198896 = 112 119898119898


1198731 =28961 times 0712

129= 15984119896119873



1198731 = 119899119865119907119903119889 ⟹ 119860119904 ge119873119904119889

06 times 119891119906119887 times 119899=

15984

06 times 800 times 2= 16651198981198982



M18 18 20 254 192 800 291



110




119865119901 = 07 times 119891119906119887 times 119860119904 = 06 x 800 x 192 = 10752kN

119872119903119889 =119899 119865119901 sum119889119894

2

119889119894=2 times 10752 times 129

0712= 3896 gt 119872119904119889 = 28961 119896119873119898




119865119907119904119889 le 119865119904119903119889 =119870119904 119898 120583

1205741198722(119865119901119888119889 minus 08119873119904119889) 119917119926119929119924119932119923119916 120788 120789 minus 119914119914119924120791120789

Avec

119870119904 = 10 ∶ Trous normaux



119865119904119903119889 = 024 (10752 minus 08 times15984

2) = 1046119896119873

119865119907119904119889 =8941

12= 745119896119873 lt 1046119896119873




1205741198722 119813119822119825119820119828119819119812 120788 120784 minus 119810119810119820120791120789



125= 213157 119896119873

119865119905119904119889 =119865119901

2=10752

2= 5376119896119873 lt 119861119901 119903119889 = 213157 119896119873


111



1205741198722 119827119808119809119819119812119808119828 120788 120787 120785 ndash 119810119810119820120791120789

Avec 119870119904 = 25

120572119887 = min (119890131198890

(119901131198890

minus 025) 119891119906119887119891119906 1) = 1



125= 46008119896119873 gt

11986511990711990411988912

= 745119896119873



119865119907 le 119865119905119903119889 = 119905119908119888 1198871198901198911198911198911199101205741198720

Avec




⟹ 119865119905119903119889 = 9 times 90times23511

= 173045 119896119873


119865119907 =119872119904119889

ℎ minus 119905119891=28961

029= 99865 gt 119865119905119903119889 = 173045119896119873




119873119904119889 le 119865119888119903119889 =119896119888 120588 119887119890119891119891 119905119908119888 119891119910

1205741198721radic1 + 13 (119887119890119891119891ℎ)2

119887119890119891119891 = 119905119891119887 + 2119886119901radic2 + 5(119905119891119888 + 119903119888) + 2119905119901

Avec

112






119887119890119891119891 =25014mm



120590119888119904119889 =119881119904119889119860+119872119904119889

119882119890119897119910=8941 times 103

1244+28961 times 106

1479= 196533119872119875119886

120590119888119904119889 = 19653119872119875119886 lt 119891119910 = 235119872119875119886 ⟹ 119896119888 = 1


119901 = 0932radic119887119890119891119891 119889119908119888 119891119910

119864 1199051199081198882= 0932radic


21 times 104 times 092= 254

119901 gt 072⟹ 120588 =119901 minus 02

1199012=254 minus 02

2542= 036


11 radic1 + 13 (250131

)2

= 12741119896119873

119873119904119889 = 1119873119894 =119872119904119889 sum119889119894sum119889119894

2 =29861 times 247

129= 57175119896119873





119865119907 le 119881119903119889 = 058119891119910 ℎ1199051199081205741198720


11= 3457119896119873


119865119907 =119872119904119889ℎ minus 119905119891

= 46216 119896119873 gt 119881119903119889 = 3457119896119873 119888119900119899119889119894119905119894119900119899 119899119900119899 119907eacute119903119894119891119894eacute119890


113

119865119907 = 46216119896119873 le 119881119903119889 = 058119891119910 ℎ119905119908 + 04

1205741198720= 058 235 31

(09 + 04)

11= 49935119896119873







logiciel robot

119872119904119889 = 15135119896119873119898 119873119904119889 = 1324119896119873 119881119904119889 = 273119896119873






119905 = min(119905119891 119905119901119897119886119905119894119899119890) = 135119898119898


114









IPE400

tf = 135 mm tw = 86 mm






radic2 times 119861119908 120574119898119908


Donc

119865119908119903119889 =119860 times sum119871 times 119891119906


radic2 times 1= 133083119896119873

119873119904119889 =119872119904119889ℎ

=7283

08= 9103119896119873

115

119873119904119889 = 9103 le 119865119908119903119889 = 1330119896119873






Donc

119865119907119903119889 =119886 times sum119871 times 119891119906


radic3 times 1= 155053119896119873



119873119894 =119872119904119889 119889119894sum119889119894

2


119909 = 119905119891radic119887

119905119908= 135radic

180

86= 6176119898119898


- 1198891 = 700 119898119898

- 1198892 = 600 119898119898

- 1198893 = 500 119898119898 ⟹ Σ1198891198942

= 124 119898sup2

- 1198894 = 300 119898119898

- 1198895 = 200 119898119898

- 1198896 = 100 119898119898


1198731 =119872119904119889 times 119889119894Σ119889119894

2 =15135 times 070

124= 4111119896119873



116


1198731 = 119899 119865119907 ⟹ 119860119904 ge119873119904119889

05 times 119891119906119887 times 119899=

13240

05 times 800 times 2= 16551198981198982



M18 18 20 254 192 800 291




119865119901 = 07 times 119891119906119887 times 119860119904 = 10752 119896119873

119872119903119889 =119899 119865119901sum119889119894

2

119889119894=2 times 10752 times 124

07= 38092 gt 119872119904119889 = 15135119896119873119898




119865119907119904119889 le 119865119904119903119889 =119870119904 119898 120583

1205741198722(119865119901119888119889 minus 08119873119904119889) 119813119822119825119820119828119819119812 120788120789 ndash 119810119810119820120791120789

Avec




119865119904119903119889 = 024 ( 10752 minus 08 times 1324) = 2326119896119873

119865119907119904119889 =273

12= 023 lt 119865119904 119903119889 = 2326119896119873




1205741198722 119813119822119825119820119828119819119812 120788 120784 ndash 119810119810119820120791120789

Avec


117


125= 31578119896119873

119865119905119904119889 =119865119901

2= 5376 lt 31578119896119873




1205741198722 119827119808119809119819119812119808119828 120788 120787 120785 ndash 119810119810119820120791120789

Avec Ks = 25

120572119887 = min (119890131198890

(119901131198890

minus 025) 119891119906119887119891119906 1) = 1


11986511990711990411988912


125= 5184 119896119873







119865119907119904119889 =119873119904119889

119899119887119903 119889119890 119887119900119906119897119900119899=131

3= 4366 le 119865119907119903119889

118


1205741198722⟹ 119860119904 ge

1205741198722 times 119865119907119903119889

06 times 119891119906119887119909 119898=125 times 43666

06 times 800 times 2= 56851198981198982


















119873119898119886119909 le 119865119908119903119889 =119886 sum119897 119891119906

119861119908 120574119898119908 radic(3 minus 1199041198941198991205722)


120572= 30gtgtgt 11990411989411989930o = 05

119865119908119903119889 =5 times 700 times 360



119



1205741198722 119827119808119809119819119812119808119828 120788 120787 120785 minus 119810119810119820120791120789


120572119907= 06



125= 12057119896119873

119865119907119904119889 =119873119904119889

3=3124

3= 10413 le 119865119907119903119889 = 12057119896119873




1205741198722 119827119808119809119819119812119808119828 120788 120787 120785 minus 119810119810119820120791120789

Avec

Ks = 25

120572119887 = min (119890131198890

(119901131198890

minus 025) 119891119906119887119891119906 1) = 092



125= 33914119896119873 gt 119865119907119904119889 = 4366119896119873




119873119898119886119909 le 119881119890119891119891119903119889 =119860119899119905 119891119910

1205741198722+119860119899119907 119891119910

radic3 1205741198722 119812119810120785 119849119834119851119853119842119838120783 minus 120790sect120785120783120782 120784

Avec


119860119899119890119905 = (119897

2minus11988902) 119905 = (60 minus 9)12 = 6121198981198982


120

119860119899119907 = (1198901 + 21199011 minus 251198890)119905 = (50 + 140 minus 45)12 = 17401198981198982

⟹ 119881119890119891119891119903119889 =612 times 235

125+1740 times 235

radic3 times 125= 303918119896119873 gt

119873119904119889

2= 655119896119873








119865119907119904119889 =119877119907119911

119899119887119900119906119897119900119899119904=36

2= 18 119896119873

119865119907119903119889 =06 times 119860119904 times 119891119906119887

120574119872119887⟹119860119904 ge

120574119872119887 times 11986511990711990311988906 times 119891119906119887

=11 times 18000

06 times 800= 41251198981198982



119865119907119903119889 =06 times 119860119904 times 119891119906119887

120574119872119887=06 times 58 times 800

11= 253119896119873 gt 119865119907119904119889 = 18119896119873


119865119905119903119889 =09 times 119860119904 times 119891119906119887

120574119872119887=09 times 58 times 800

11= 379119896119873

121

119865119907119903119889 =06 times 119860119904 times 119891119906119887

120574119872119887= 253119896119873

119865119907119904119889119865119907119903119889

+119865119905119904119889

14 119865119905119903119889= 052 lt 1 119862119900119899119889119894119905119894119900119899 119907119890119903119894119891119894eacute119890


122

Chapitre-8




123








119865119888119896=30 MPa

119891119888119889 =085 times 119865119888119896125

= 204 MPa


119865119895119889 = 120572120573119895 119891119888119889



119865119895119889 = 120572 120573119895 119891119888119889 = 15 times2

3times 17 = 204 119872119875119886


1198601198620 ge119873119904119889119891119888119889

=148960

204

1198601198620 ge 7266341198981198982


bp ge b+2tf = 190+2times155 = 221 mm

hp ge h+2tf = 310+2times155 = 341 mm

On prend

bp =600 hp=620



124


119862 = 119905 (119891119910119901

3119891119895119889 1205741198720)

05

= 30(235


= 5605 119898119898

119862 = 5605 lt(ℎ minus 2119905119891)

2= 1395 119898119898




gorge (a) Annexe H







119890 =119872119904119889119873119904119889

= 041 119898 gt 119885119879 = 0195 119898







125


Ougrave

119871119890119891119891 = min(119887119901 119887119891119888 + 2119888) = min(600 300 + 2 times 4671) = 39342 119898119898

119887119890119891119891 = min (119888ℎ1198882minus 119905119891119888) + 119905119891119888 +min (119888

ℎ119901 minus ℎ119888

2)

119887119890119891119891 = min (4671310

2minus 155) + 155 + min (4671

620 minus 310

2) = 10892 119898119898

⟹ 119865119888119903119889 = 204 times 10892 times 39342 = 874166 119896119873


119865119907119903119889 = 119865119891119903119889 + 119899119887 119865119907119887119903119889


119865119891119903119889 = 02119873119904119889 = 1214 119896119873





119865119907119887119903119889 =120572119888119887 119891119906119887 119860119904

1205741198722

Avec 120572119888119887 = 044 minus 00003119891119910119887 = 0248


126

119865119907119887119903119889 =0248 times 800 times 561

125= 8904 119896119873

⟹ 119865119907119903119889 = 1214 + 8 times 8904 119896119873 = 72446 119896119873




Avec 120573119908 =08 120574119898119908 = 125 119886 = 6 mm


sum119897 = 470 119898119898

119865119908119903119889 =6 times 470 times 360

radic3= 58612 119896119873

119881119904119889 = 9773 119896119873 lt min(119865119907119903119889 119865119908119903119889) = 58612 119896119873





W= 150 mm e = 55 mm ex = 40 mm mx = 40 mm


119897119890119891119891119888119901 = 119898119894119899 2120587119898119909 = 25132 119898119898

120587119898119909 +119882 = 27566 119898119898120587119898119909 + 2119890 = 23566 119898119898

⟹ 119897119890119891119891119888119901 = 23566 119898119898

127


119897119890119891119891119899119888 = 119898119894119899

4119898119909 + 125119890119909 = 210 119898119898

2119898119909 + 0625119890119909 +119882

2= 180 119898119898

2119898119909 + 0625119890119909 + 119890 = 160 119898119898119887119901

2= 150 119898119898

⟹ 119897119890119891119891119899119888 = 150 119898119898


119865119905119886119899119888119903119889 = min[119865119905119887119900119899119889119903119889 119865119905119903119889]


119865119905119903119889 = 09 times119860119904 times 119891119906119887120574119898119887


125= 32314 119896119873



119865119887119889 =036radic119891119888119896

120574119888=036 times 547

15= 1313 119872119875119886


119865119905119887119900119899119889119903119889 =120587 119889 119897119887 119891119887119889

120572

Avec

1198971 = 20119889 = 600 119898119898

119903 = 3119889 = 90 119898119898

1198972 = 20119889 = 600 119898119898






07= 52929 119896119873

119865119905119886119899119888119903119889 = 119898119894119899[52929 32314] = 32314 kN

128




Lb = 8d + em +tp + twa + 05k

Avec







119871119887lowast =

881198981199093 119860119904

1198971198901198911198911 1199051199013 =


150 times 253= 13480 119898119898 lt 119871119887 = 312 119898119898




119898119901119897119903119889 =1199051199012 119891119910119901

41205741198720=252 times 235

4 times 11= 3338119896119873


Mode 1 1198721199011198971119903119889 = 119898119901119897119903119889 times 1198971198901198911198911 = 3338 times 015 = 5007119896119873119898

1198971198901198911198911 = min(119897119890119891119891119888119901 119897119890119891119891119899119888) = 150 119898119898


129




Mode 1-2

1198651199051minus2119903119889 =21198721199011198971119903119889

119898119909=2 times 5

004= 250 119896119873

Mode 3

1198651199053119903119889 = 2119865119905119903119889119886119899119888ℎ119900119903 = 2 times 32314 = 646280 119896119873

Mode 4

1198651199054119903119889 =119887119890119891119891119905 119905119908 119891119910

1205741198720=150 times 9 times 235

11= 288409119896119873

Drsquoougrave

119865119905119903119889 = min(1198651199051minus2119903119889 1198651199053119903119889 1198651199054119903119889) = 250 119896119873




119885119879119890119873minus 1

119865119879119903119889 times 119885

119885119862119890119873+ 1

) 119812119810120785 ndash 120783 120790 119827119808119809119819119812119808119828 120788 120789

119885 = 119885119879+119885119862 = 195 + 155 = 350119898119898

⟹119872119903119889 = 5646 119896119873119898 lt 6207119896119873119898



821 Introduction




- Le site (S3)



130




ELU 119872119880 = 6207119896119873119898 119873119880 = 9773119896119873

ELS 119872119878 = 4136119896119873119898 119873119878 = 7960119896119873




119886 = 119886119901 + 119888 = 062 + 02 = 082 119898


119860

119861=119886

119887= 1025 ⟹ 119860 = 1025119861



119890 =119872119904

119873119904= 052119898



120590119898119886119909 =119873

119860119861(1 +

6119890

119861) le 120590119904119900119897


368B2 - B - 312 ge 0 ⟹ B ge0765m



131

119889 = max (119861 minus 119887

4119860 minus 119886

4) = max (005 0295)

On prend d= 45 cm



On a

119890 = 052 gt119860

6= 041


3120590119898119886119909 1205901198981198941198994

lt 120590119904119900119897

Avec

120590119898119894119899 =119873

119860119861(1 minus

6119890

119860) =

14896

2(1 minus

041

2 ) = 62191198961198731198982

120590119898119894119899 =119873

119860119861(1 +

6119890

119860) =

14896

2(1 +

041

2 ) = 86771198961198731198982

3120590119898119886119909 120590119898119894119899

4= 6835 1198961198731198982 lt 120590119904119900119897 = 180 119896119873119898

2



119890 =119872

119873= 052 119898 lt

119860

4= 062 119898




119890 gt119886

6 119890 gt

119860

24


119860119886 =1198721119911 119904119905

132

1198721 = (119860

2minus 035119886)

2

(1 +119890

119860+14 times 119890 times 119886

1198602)1198731199042119860

1198721 = 2788119896119873119898

Avec 119911 = 09d =40cm

119904119905 = min (2

3119891119890 110radic12057811989111990528) =20163 MPa

11989111990528 = 00611989111988828 + 06 = 24 119872119875119886 120578 = 16 119867 119860 Donc

119860119886 =2788 times 106

400 times 20163= 345 1198881198982


119860119887 =119873prime(119861 minus 119887)

8119889 119904119905

Avec

119873prime = 119873119904 (1 +3119890

119860) = 796 (1 +

3 times 052

25) = 2993119896119873

119904119905 = min (2

3119891119890 110radic12057811989111990528) = 20163119872119875119886

11989111990528 = 00611989111988828 + 06 = 24119896119873 120578 = 16 119867 119860

Donc 119860119887 = 071198881198982


119860119886 =1198721119911 120590119904119905

1198721 = (119860

2minus 035119886)

2

(1 +119890

119860+14 times 119890 times 119886

1198602)1198731199062119860

1198721 = 349119896119873119898

Avec 119911 =09d = 40 cm

120590119904119905 =119891119890120574119904=400

115= 3478119872119875119886

Donc

133

119860119886 =349 times 106

400 times 3478= 251198881198982


119860119886 =119873119906(119861 minus 119887)

8119889 120590119904119905

Avec

119873prime = 119873119906 (1 +3119890

119860) = 23833119896119873

Donc 119860119887 = 1621198881198982


119860119898119894119899 = 023 times11989111990528119891119890

times 119860 times ℎ119905 = 17251198881198982

Sens B

119860119898119894119899 = 023 times11989111990528119891119890

times 119861 times ℎ119905 = 691198881198982



A (cm2) St (cm)

A 345 1725 10T16 201 25 B 07 69 7T16 1407 25



134



119873119905 = (119873

120572) ge 20 119896119873 [119825119823119808120791120791 119855 120784120782120782120785 119808119851119853 120783120782 120783 120783 119835]


119873119905 =14896

12= 1241119896119873

ELS

119873119905 =796

12= 663119896119873


119860119904119905 =119873119905120590119904119905

ELS

119860119904119905 =663

348= 0191198881198982

ELU

119860119904119905 =1241

348= 0351198881198982





119860119904119905 = 0905 le 119860119904 = 6791198881198982


135


120601119898119894119899 le 119898119894119899 (ℎ

35120601119897119898119894119899

119887

10) = 08 119888119898

On prend 120601119905 =8mm


On prend St=10cm


136


137

ANNEXE - 1

138

139

140

ANNEXE - 2

141

ANNEXE - 3

142

143

ANNEXE ndash 4

144

145

ANNEXE ndash 5

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