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RËPUBLIQUE DU SËNËGAL
ÉCOLE POLVTECHNIQUE DE THIÈS
PRO JET DE FIN D' ET UDES
EN VUE DE L'OBTENTION DU DlPLÔfllE D'INGÉNIEUR DE CONCEPTION
TITRE
DATE Juin 1986
ANALYSE ET DIMENSIONNEMENT DU MARCHE DE POISSONS
DE SOUBEDIOUME-------------------------------------------------
AUTEUR MAR THIAM
DIRECTEUR Mr Moustapha NDIAYE, Ing. M.Sc.
CO-DIRECTEUR Mr Alain DEBERDT, Ing ..
,-- ---~~~ ---- -~-- --------
~ REMERCIEMENTS,.,
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LISTE DES FIGURES PAGES
Ferraillage de semelle sous le voile •••••••••••••••••••••••••••• 45
Ferraillage du voile des parois extérieures du sous-sol......... 43
Schéma des poutres 4, 5, 10, 11) ••••• ••• •••••• •••• •••••••••••••• 25
Schéma des poutres 14, 13 •• •••• •••••••••• ••••••••• •••• •••• ••• ••• 26
Schéma de la Console du plancher ht Rez de chaussée ••••••••••••• 29
Schéma de la Console du plancher ht du le étage ••••• •••••••••••• 30
Ferraillage de la semelle de'. poteau 1 ••••• •••••• ••••••••• ••••••• 37
Schéma de la Nervure Nl 21
23
24
50
52
53
55
......dans la cour de service
Vis ••••••••••••••••••••••••••••
Ferraillage et Onf f r age d'un volet de l'escalier central ••••••••
Ferraillage des marches d'escalier à Vis ••••••••••••••••••••••••
Schéma des poutres 3, 6, 9, 12 ••••••••••••••••••••••••••••••••••
Ferraillage du mur de soutenement
Coffrage de s marche s d 'escal ier à
Schéma de s poutre s 1, 2, 8, 7 ••••••••••••••••••••••••••••••••••
Figure 1
Figure 2
Figure 3
Figure q
Figure 5
Figure 6
Figure 7
Figure 8
Figure 9
Figure la
Figure 11
Figure 12
Figure 13
Figure 14
LISTE DES TABLEAUX
Tableaux des semelles isolées P 38
iii)
Composition
T A BLE f)ES MAT 1ER E' S
Rerner ci ernent s •••••••••••••••••••••••••••••••••••••••••• i
Sommaire ••••••••••••••••••••••••••••••••••••••••••••••• ~ii
Liste des figures •••••••••••••••••••••••••••••••••••••• iii
Table des matières ••••••••••••••••••••••••••••••••••••• iv
11. ELEMENTS INTRODUCTIFS
Introduction ••••••••••••••••••••••••••••••••••••••••••• 1
Options architecturales et fonctionnelles •••••••••••••• 3
II. ANALYSE STRUCIURAl.E::::l
2.1 Structure choisie •••••••••••••••••••••••••••••••••• 5
2.2 Ba se de cal cul ...........' . 6
2.3 Calcul des charges appliquees sur les ouvrages ••••• 8
2.4 Analyse structurale proprement dit ••••••••••••••••• " 14
III. ~ETHODE DE DETERMINATION DES= EFFORTS
3.1 Description du programme •••••••••••••••••••••••••••
3.2 Programme du calcul des efforts ••••••••••••••••••••
3.3 Exemple de fichier d'entrée de données •••••••••••••
3.4 Exemple de fichier de sortie de résultats ••••••••••
16
17
:IV. DIMENSIONNEMENT DE =DI:=F=F=:E=RENTS gUVRA~
4.1) Dimensionnernent des poutrelles et poutres ••••••••• 1'8
4.2) Dimensionnement de la dalle pleine ••• ••••••••••••• 27
IV
T A BLE DES MAT l E RES
4.3)
4.4)
4.5)
4.6)
4.7)
4.8)
Dimensionnement des planchers en Console •••••••••••••
Dimensionnement des poteaux ••••••••••••••••••••••••••
Dimensionnement des semelles •••••••••••••••••••••••••
Dimensionnement des parois extérieures du,sous,sol .•••
Dimensionnement de la Semelle filante sous voile •••••
Dimensionnement des murs de soutement dans
la cour de service •••••••••••••••••••••••••••••••••••
29
31
35
40
44
46
~.9) Dimensionnement des escaliers ••••••••••••••••••••••••
4.9.1 Escalier à vis reliant le sous-sol au
rez "de chauss4e •••••••••••••••••••••••••••••••••••••• 51
4.9.2 Escaliers sans limon reliant le R.C au le étage •••••• 54
4.10) Dimensionnement du dallage ••••••••••••••••••••••••••• 56
V CONCLUSION ET RECOMMANDATIONS •••••••••••••••••• 58.
Annexes
1. Calcul des charges ••••••••••••••••••••••••••••••• 60
2. Tableaux des poutres dimensionnées ••••••••••••••• 78
3. Tableaux des pteaux dimensionnées •••••••••••••••• 92
4. Vérification de sections de poutre ••••••••••••••• 97
5. Calcul de dallage ••••••••••••••• •••••••••••••••• 100
V
TABLE DES MATIERES (suite)
B l B L l ~ G R A PHI E 102
PLA N S DE COFFRAGE
1. du plancher - haut sous - sol
2. du plancher - haut Rez de chaussée
3. du plancher - haut le étage
4. de la toiture
5. de la Fondation
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2-:~) CALcUL 1)(5 CHARGES APPLIQUEECô
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t) ~~ l.l \ 5 , ~o 1 ...\ J\ (2. 0 ,<.'2. 5 )
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Q~ ·A,O~:3,lJ .Q = 3,o~\IlIl'Y\
,Ao
Q::3,o!c:NI"",
~) t0ù.hv:> 11 4 - "'0
~ ~e-vJ:,e"G
G ~ 21,5 .lk~\ "'"
Q = 5, 0 ~N 1W1
A) f~ \- eGU.JIX .A 1 :; 1 4 1 6, 1-[ '3, .A D,A 3
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s- 3.~'3,,-J,o;b ~,3.",tl_
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.cl~ ~(1N\.~
cLoJL. = )0, <+ ~N
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~ 1. -t-~ ~ ~ ~cl J ~ ((\ ',ourC'"nO fOU) '-cU ~~
,.dif~~ J t"'""'- ~ t'~~ ...e f:: O,1-.e.,.
Le~k~~~ (Y\L~e:uJtU) Amk 'UM-e tU~ A ,
AI1\~ =. ~,Aero
"'Mo ~ O,~Sfc.1..3 B T~2. A0'6
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Ob 'IlTll
o,S 5 feu, . 0.8s", '2.0 - A~,t+ t-tP,,-= -ô'l:, ..-\, S"
N. AA -=. ~,~5G ·d,5"Q. -::. .-\,:'5l\A4,~ + /{,5")\ 4,0 ::.- l.S,?> ttJ
~ ~ !(. S 1 ~ ,.. 10" ~ 10 4 -:: Âq,o CNy,t..
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~-'1
~~ ..d-t ~~ .z.o~ ~ 0 --. l = o.3'<o.Z.= t-,o • .(b m~
"<"'-
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t.. 4- ANALy5 l 51 RUc.,.U RA l é PRO PRE MENT 1);1
1)~ {cuen l}~ aiR- 1 lu ;.)()f1ùA1~ kont ,ealeM1eu .0>'1 iUlifi
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--, & jwC-tawH /d.e ~~ ~ ,~.~ /~ ,olu/~
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_._-_._-----_..--_.-._-----_._-_._---
A5 ':' . .:,-'
r, 1
._------
___ CHAR 3. _
METHODEDE
DETERMINATIO N
DES EfFOR15
3.'1
·_--------_. ----.
~ 1~ /Js- /~oy-<'--cSv- (~ CR.~~ yt /CA:Tn.5-'-"- .<ietM<l
leu (cyv~~ ~ ton-~ &aMe- .1'(~u-~. CPa.N\o 1t .cccob« ,tA.; Q
~ ,~ ,~ ~~ Jei-c-ûf:caÂ-r ,au {l\M/ec;JJJ..- (O\M. eo1cu14.t eRAA-ey
~~ ÀQ tkt~ .k~ ~~ r (0J.lt.A-'QWt- <.l ~JluAo~
/ch. ~ fu ek.~ ,~ ~'~~ .J.''1lJYU- ~dWu ~ (ClK'~.-S
~~.e~~ -cU /~cuk ~ ""~ ~ /~Jro-.~ ~~~
./~ -€ew-/~~ mm neo~ L-R'!hu) .
l.~~ .dM.- tw~mL ~~ -€Hl. /~ . ci (;U.e(" !Wr'l- f citur cL./ 1 / /
""~a& ~ 1w ~~<:tlfd ~U.<l /dM 1'\oeu.ol> l ,du>~~ e..t ,.;Lu rma1w.·4W/<1 1 •
~ ,cL:~e-o. ru~ ,aM~ , ~~4 lU' 4-ceJi,,~ ~ lI.ùl'1- ~.~ de
~cJ;, /'fU-l ()'l<ll.YJ (ot-OT"l-W /~ {au r-ut:<fcJ.lc. ~.; (Y"\1TI.lO~ 1 ,...c:Lc.vvI,o .e caCÛLl.
-c!l , ce l:t-~aiQ " I-ft.~ ~ le ,dur,.~~twYl.~ ,dl m.t'O -P"t~ et~.
Ce. F~~ MA-O- Jr-~ /OJ.X-<!- (\).XV ~ok,dL -y.~ Id'~
~ ,clt /y:c.2u;o/:Il /ck~ .
1 .
1
'1
l......c __.:._.. __ ._. __ .
-'1~
c
print 11do 100 i=l,nodread *,k,tx<k) ,ty<k)
100 print 12,k,tx<k),ty<k)c
do 90 i=l,nodiresx<i)=Oiresy<i)::O
90 iresr<i)=Oc
print 13do 110 i=l,nnrread *,k,iresK<k) ,iresy<k) ,iresr<k)
110 print 14,k,iresx<k) ,iresy<k) ,iresr<k)cc
~.
**
DE S ..(:J (,9 RIS, .<"..... . .
CA Le LI L
COORDONNEES DES NOEUDS
RESTREINTES AUX NOEUDS
calcul de l'adresse des diagonales
DONNEES ET CONNECTIVITE DES ELEMENTS
DONNEES CENERALES
print *,' ***************************************'print * **FICHIER DE LECTURE DES DONNEES ? **'print *,' ***************************************!read 99 ,stdonprint *,' ***************************************'print *,' **FICHIER DE LECTURE DES RESULTATS? **'print *,' ***************************************'read 99 ,stratopen <unit=5,file~stdon)
open <unit=6,file=strat)rewind (5)rewind (6)
print 2read *,nel,nod,ndl,nnr,icc,eprint 10,nel,nod,nnr,ic.c,enk=2*ndlnn~ndl*nod
nx=nn+l
c ***********************************************
*
c ***********************************************c
cc
c
ccc
c
cc
c
c
implicit real*8<a-h,o-z)character*6 stdon stratdimension tx(30),ty<30) ,iresx(30) ,iresy<30.),iresr<30) ,ih(90),
1 j 1 <30 ) , j 2 <30 ) , as <30 ) , a i <30 ) , a 1 <30 ) , i ad <6 ) , ma x a < 1 00 ) , Cl r k <700 ) ,2 a.ma t <6 , 6 ) , w <30 ) , f c <3 0 , 3 , 2 ) , f 1 <6 ) , f 9 <6 ) , v c <9 0 ) , n cc <3 0 ) , r x <3 0 ) ,3ry(30) ,r1;(30)
cc
print 15do 120 i=l,nelread *,k,jl<k),j2<k),as<k),ai<k)al<k)=dsqrt«tx<j2<k»-tx<jl<k»)**2+<ty<j2<k) )-ty<jl<k»)**2)
120 print 16,k,jl<1c),j20:),as<k),ai<k),al<k)cc
c
123456
789
1011121314151617181920212223242526272n293031323334353637383940414243444546474849505 15253545556575859606162636465
do 190 i=l,nel
INTRODUCTION DES RESTREINTES
RIGIDITE DES ELEMENTS ET ASSEMBLAGE
icc210 ii = 1
INTRODUCTION DES CHARGES
do 130 i::::l,nnih(i)=O
do 150 i=l,nkif(iad(i>.lt.mi) m i e La d Ci )do 160 i=l,nk"ii=iad(i>iht:::ii-miihi i=ih( i i )if(iht.gt.ihii> ih(ii):::ihtcontinuecontinuema x a ( 1 ) :: 1
maxa(2)=2do 170 i=2,nnma xa ( i + 1) =ma xa ( i ) + i h ( i ) + 1nwk=maxa(nn+l)-lprint *,'nombre d"equations =',nnp r in t 11:, 1 es p ace r e qui 5 pou r gr k =', nwk
do 140 k=l,nelii1=il(k)j j 2 = j 2 ( k )calI adres(iil,ji2,ndl,nk,iad)mi=iad(l)
dol 80 i = 1 , nwkgrk(i)::O.dO
do
calI tripld (grk,maxa,nn,nwk",nx)
do 200 i=l,nodif(iresx(i) .eq. 1) grk(maxa(3*i-2»=grk(maxa(3*i-2»+1.d20if(iresy(i) .eq.l) grk(maxa(3*i-l»=grk(maxa(3*i-l)~+1.d20if(iresr(i) .eq.l) grk"(maxa(3*i »=grk"(maxa(3*i ) )+1.d20continue
j j 1 = j 1 ( i )
ii2=i2(i)asi=as(i)ai i =a i ( i )a 1 i = ,-,.1 ( i )cs=(tx(ji2)-tx(iil» lali5 n= ( t Y ( j j 2 ) - t Y ( j j 1 ) ) 1 a 1 icalI adres(iil,jj2,ndl,nk, iad)calI rigel(amat,nk",e,asi,aii,ali,cs,sn)calI assemb(iad,ndl,nk,amat,grk,nwk,maxa,nx,nn)continue
do 220 i=l,nelw(i)=O.dOn c c c t j e ü i d ü
do 220 i=l,3do 220 k:::l,2fc(i,j,k)=O.dOdo 230 i :: 1 , nn
150
c130
160140
c
170
c
c180
190
ccc
c
c
ccc
ccc
c
200
220
666768697071727374757677787980818283848586878889909 19293949596979899
100101102103104105106107108109110Il 1112113114115116117118119120121122123124125126127128129130131
VECTEUR CHARGE
read 11 nelcuif (nelcu .ne.O) print 27if (nelcu .ne. 0) print 28 nelcuif (nelcu .ne. 0) print 29do 250 i:= 1 nelcuread 11 k, w(k)if(nelcu.ne.O) print 12 k, w(lc)continue
print 1print 33,iiread 1I,nnchif(nnch.gt.O) print 23if(n~ch.gt .0) print 25 ,nnchif(nnch.gt.O) print 24do 240 i = 1 nnchread 11 k,vc(lc 1lndl-2) ,vc(lc 1lndl-l) ,vc(k 1lndl)
p r in t 26, k, v c ( k 11 nd 1 - 2) , v c ( k 11 nd 1 - 1 ) , v c ( k 11 nd 1 )
continue
read 11 nelccif (nelcc .ne. 0) print 60 nelccdo 260 i:=l ,nelccread 11 k,ncc(k)ncclc=ncc(lc)do 270 j = 1 , ncckread 11 (fc(k,j,1),1::l,2)if(nelcc.ne.O) print 30 ,k, i, (fc(k,i, 1) ,1=1,2)continuecontinue
'Po?>
localeglobale
:vecteur charge equiv.:vecteur charge equiv
f 1
f 9
O.dO
do 300;.- 1,ndliad(j) _ nd1 1l(jjl - 1) + j
iad(j+ndl) = nd1 1l(jj2 - 1) + j
SOLUTION DES EQUATIONS - DEPLACEMENTS
v c ( i )
print 38do 320 i=l,nodprint 35 , i,vc(3 11i-2) ,vc(3 11i-l) ,vc(3 11i)
continue
calI sol(grlc,vc,maxa,nn,nwlc,nx)
do 310 j:= 1 , niev c t iad( j) )=vc( iad( j) )-fl]( j)continue
do 290 i - 1 nela 1 i = a 1 ( i )j j 1 j 1 ( i )ij2:= j2(i)cs = (t x ( j j 2) - t x ( ; ; 1 » 1 al isn := (ty(jj2)-ty(jil» 1 aliwi = wei)calI equiv(fg,fl,nk,wi,fc,cs,sn,i,ali)
c
c
c
320
c
ccc
c
300c
310
250
240
c290
270260
c
230
'c
cccccc
13213313413513613713813914014114214314414514614714814915015115215315415515615715815916016 1162163164165166167168169170171172173174175176177178179180181182183184185186187188189190191192193194195196197~-. \
lYIj
1992002012022032042052062072082092102 Il212213214215216217218219220221222223224225226227228229230231232233234235236237238239240241242243244245246247248249250251252253254255256257258259260261262263
cc
c
c
c
350340c
c
c330ccc
c
144
143
146
145
147
148
CALCUL DES EFFORTS INTERNR~------
print 1print 40
do 330 i=t,nel
j j 1 = j 1 Ci)j j 2 =j 2 Ci)asi=asCi)ai i =~ i ( i )al i =a l ( i )wi=w( i)ncci=ncc(i)cs=(txCjj2)-tx(jjl» talisn= ( t Y C j j 2) - t Y ( j j 1 ) ) ta licalI adresCjjl,jj2,ndl,nk,iad)ca Il ri gel (ama t, n k , e, as i , a i i , a li, cs, sn)calI equivC fg, fI ,nlc,wi, fc,cs,sn, i ,ali)
do 340 k=l,nlcfl(k)=fg(k)fg(k)=O.dOdo 350 j=l,nkfg(Ic)=fg(Ic')+amat(lc,j)*vc(iad(j»fgCk)=fg(k)+fl(lc)
fICl)= fg(1)*cs+fg(2)*snfl(2)=-fg(1)*sn+fg(2)*csf l ( 3 ) = f 9 ( 3 )fl(4)= fg(4)*cs+fg(5)*snfl(5)=-fg(4)*sn+fg(5)*csfl(6)= fg(6)
if(mod(i,2) .eq.O.and.i .gt.2) print 1ifCmod(i ,2) .eq.O.and.i .gt.2) print 40print 61print 17print 35,i,(fl(j),j=1,3)print 18print 35,i,(fl(j),j=4,6)xnl=fl(l)xv 1 =fI (2)xml=fl(3)calI forc(xnl,xvl,xml,wi,fc,ali,i)
continue
CALCUL DES REACTIONS
print 39do 360 i=l,nod
if(iresx(i) .eq.l) go to 144go to 143rx(i)=-vc(3*i-2)*1.d20print 50 , i,rx(i)if(iresy(i) .eq.l) go to 146go to 145ry(i)=-vc(3*i-l)*1.d20print 51 ,i,ry(i)if(iresr(i) .eq.l) go to 147go to 148rz(i)=-vc(3*i )*1.d20print 52 i,rz(i)continue
FORMATS D'ECRITURE
264265266267268269270271272273274275276277278279280281282283284285286287288289290291292293294295296297298299300301302303304305306307308309310311312313314315316317318319320321322323324325326327328329
- --II ITTr e s-i( r) . e q . 1 ) . 0 r . ( ire s y ( i ) . e q . l ) . 0 r . { 1 r e s r \ 1 1 . e q . 1 " 'PO'51 print 4
360 continue210 continueccc1 format('I'2 format(' ',tl0,'DONNEES GENERALES'I' t8,21('*'»4 format(f)10 format(' ',tl0,'nombre d"elements --------:::',t38,i51
l ',tl0,'nombre de noeuds --------':::',t38,i512 " tl0, 'nombre de noeuds restreints:::', t38, i51
3 ',tl0,'nombre de cas de chargement=:',t38,i513 ' , t 1 0 , 'mo d u 1 e d" e 1 as tic i te - - - - - -:::,' , t 3 8 , d 1 0 . 3 )
Il format(II' ',t8,22('*')/' ',tl0,'DONNEES DES NOEUDS'/' ',t81,22( '*' )11' ',t8, 'noeud' ,7K, 'coordx' ,10x, 'coordy')
12 format(' ',5K,i5,2(5x,fl0.3»13 format(III' ',t8,25('*')/tl0,'RESTREINTES AUX NOEUDS'I'
1 t8,25( '*')1 t16, 'noeud' ,12K,' iresK' ,12K,' iresy' ,12x,' iresr'14 format(' ',4(i2K,i5»15 format<lll' ',t8,24('*')/tl0,'DONNEES DES ELEMENTS'/'
1 t8,24('*' )11' ',t8, 'elmt' ,tI8, 'noeudl' ,t28, 'noeud2',2 t42, 'aire' ,t57,' inertie' ,t74,' longueur')
16 forma t (' ',3 ( 5 x, i 5) ,3 ( 7 x, dl 0 . 3) )17 format(/" ,t8, 'elmt' ,t23, 'ng' ,t40, 'vg' ,t57, 'mg'18 format(' t23, 'nd' ,t40, 'vd' ,t57, 'md')23 format(/" ,t20,22( '*'),' ',t22, 'charges aux noeuds',/' ',t20,
122('*')1)
24 format(" ,t8, 'noeud' ,t26,' fx' ,t46,' fy' ,t64, 'moment'25 format(' ',t8,'nombre de noeuds charges :::',i5/)
26 format(" ,5x,i5,3(10x,dl0.3»27 format(/" ,t20, '*lllcharge en travee*lll' l' ',t20,20( '*' )/)28 format(" ,tl0, 'nombre d' 'elements avec charge uniforme :::' ,i5/)
29 format(" ,tl0, 'elmt' ,t22, 'W')30 forma t (' " t 1 0 , i 3 , i 7 ,5 x, 2 d 1 0 . 3 )33 forma t (' " t 13 , 25 ( , 'IIr ' ) 1 t 10, 'CAS DE CHARGEMENT NO. ' , t 31 , i 5 /
It9,25(''IIr'»35 format(" ,5x,i5,6(5x,dI2.4»36 format<III", tl0, 'nombre d' 'equations' ,t31, i5/)
37 format(' ',tl0,'espace requis par grk',t31,i5/)38 format(/" ,t8,15(''IIr' )/' ',tl0, 'DEPLACEMENTS'/' ',t8,15(''IIr')1
II' • ,tB, 'noeud' ,t24, 'dx' ,t40, 'dy' ,t56, 'rot.')39 format(/,' ',tI2,13(''IIr')/' ',tI4,'REACTIONS'I' ',tI2,13('lll')/)40 format(/" ,t8,19('lll' )/' ',tl0, 'EFFORTS INTERNES' 1 ',t8,19( ''IIr'41 format(/' ',5x,i5,6(5x,d12.4»50 format(" ,tl0, 'noeud' ,tI6,i2,tI9, 'rx:::' ,fI2.4)51 format(" ,tl0, 'noeud' ,t16,i2,tI9, 'ry:::' ,fI2.4)52 format(" ,tl0, 'noeud' ,tI6,i2,tI9, 'rz:::' ,fI2.4)59 format(" ,i5)60 format</" ,tl0, 'nombre d"elements avec charges c o n c a n t r e e s e ' ,i5
111' ',tl0,'elmt',3x,'no. ch.',5x,'fy',8x,' x')61 format<II' ',t20,''IIr'llren bouts de membrure'llr'llr'/' ',t20,24(''IIr'»
,9'9 f o r ma t t a ë )
cclose(unit:::5)close(unit=6)
cstopend
csubroutine adres(jjl,jj2,ndl,n,iad)
cdimension iad(n)do 1 i:::l,ndliad(i):::ndl'llr(jjl-1)+i
330 1
331332333 c334335 c336337338 c339340341 1342 c343344345346347348 c349350351352353354 c355356357358359360361362363364365366367368369370371372373374375376 c377378379 2380381382 c383384 c385386387 c3883893903913923J13394395 2
lad( l+ndl l=ndl"( J J~-ll+lreturnend
subroutine rigel(sm,n,e,asi,aii,ali,cs,sn)
implicit real*8(a-h,0-z)dimension sm(n,n)
do 1 i=l,ndo 1 j=l,nsm(i,'j)=O.dO
cax=e*asi/alial=4.dO*e*aii/alia2=2.dO*e*aii/alia3=6.dO*e*aii/(ali**2)a4=12.dO*e*aii/(ali**3)
dl=cox*(cs**2)+a4*(sn**2)d2=(cax-a4)*cs*snd3=cax*(sn**2)+a4*(cs**2)d4=-a3*snd5:::a3*cs
sm ( 4 , 1 ) = - dlsm ( 1 , 1 ) = dlsm(4,4)= dlsm ( 2 , 1 ) = d 2sm(4,2)=-d2sm(5,l)=-d2sm(5,4)= d2sm(2,2)= d3sm(5,2)=-d3sm(5,5)= d3sm(3,l)= d4sm(4,3)=-d4sm ( 6 , 1 ) = d 4sm(6,4)=-d4sm(3,2)= d5sm(5,3)=-d5sm(6,2)= d5sm(6,5)=-d5sm(3,3)::: alsm(6,6)= alsm(6,3)= a2
do 2 i==l,ndo 2 j=i,nsm ( i , j ) == sm ( j , i )returnend
subroutine assemb(iad,ndl,nk,ptK,grK,nwK,maxa,nx,nn)
implicit real*8(a-h,o-z)dimension iad(nk) ,ptk(nk,nk) ,grk(nwk) ,maxa(nx)
do 3 i==l,nkii=iad(i)do 2 j=l,nkjj=iad(j)if(jj.lt.ii) go to 2k=maxa(jj)+jj-iigrk(k)=grk(k)+ptk(i,'j)continue
subroutine tripld (a,maxa,nn,nwK,nnm)
implicit real*8(a-h,o-z)dimension a(nwk),maxa(nnm)
continuereturnend
localglobal
syts.syts.
:charges suiv.:charges suiv.
f 1fg
CHARGES EQUIVALENTES AUX NOEUDSSYSTEME GLOBAL
f 1 ( 1 ) = O.dOf 1 ( 2 ) _. -wc * cl / 2.dOf 1 ( 3 ) = -wc * cl**2 / 12 . dOf 1 ( 4 ) - O.dOf 1 ( 5 ) = -wc * cl / 2.dOf 1 ( 6 ) = -f1(3)
do 1 j = 1 3p = fc(k,j,l)
implicit real*8(a-h,o-z)dimension fl(6) ,fg(6),fc(30,3,2)
do 140 n=l,nnkn=maxa(n)kl:::kn+lku=maxa(n+l)-lkh=ku-lclif(kh) 110,90,50k=n-kh
-, ic=Oklt=kudo 80 j=l,khic=ic+lklt=klt-lki=maxa(k)nd=maxa(k+l)-ki-lif(nd) 80,80,60kk=min(ic,nd)c=O.dOdo 70 l=l,kkc=c+a(ki+I)*a(klt+l)a(kIU=a(klt)-ck=k+lk=nb=O.dOdo 100 kk=kl,kuk=k-lki=maxa(k)c=a(kk)/a(ki)b=b+c*a(kk)a(kk)=ca t k n r e aï k n ï c-b
if(a(kn» 120,120,140print 1000,nstopf o r ma t t 'matrice singuliere rangee', is :continuereturnendsu br 0 u tin e e qui v (f g , fi, n k , wc , f c , cs, sn, Il: , cl)
396 3397398399 c400401 c402403404 c40540640740840941041 1 50412413414415416417418419420 60421422423 70424425 80426 90427428429430431432433 100434435 110436 120437438 1000439 140440441442443 . c444 c445 c446 c447 c448 c449 c450451452 c453454455456457458459 c460461
substitution a rebours
print 56
subroutine sol(a,v,maxa,nn,nwk,nnm)
subroutine forc (xnl,xvl,xml,wi,fc,al"i,le)
P08- ek)**2
:matrice decomposee:vecteur chargement
nn
a ( k )
av
eJe - t c l Je , ) , ~ } Cl
f 1 ( 2 ) - f 1 ( 2 ) - P 11 (l.dO + 2.dO * ek) * ( 1 . dOf 1 ( 3 ) - f 1 ( 3 ) - P * ek * cl * (l.dO - ek)**2f 1 ( 5 ) f 1 ( 5 ) - P * ek**2 * ( 3 . dO - 2.dO * ek)f 1 ( 6 ) - fI ( 6 ) + p * ek**2 * cl * ( 1 . dO - ek)
continue
f g ( 1 ) f 1 ( 1 ) * cs - f 1 ( 2 ) * snf 9 ( 2 ) = f 1 ( 1 ) * sn + f 1 ( 2 ) lie csfg(3) - f 1 ( 3 )f 9 ( 4 ) = f 1 ( 4 ) * cs - f 1 ( 5 ) * snf g (5 ) = f 1 ( 4 ) * sn + f 1 ( 5 ) * csf 9 ( 6 ) = f 1 ( 6 )
returnend
implicit real*8(a-h,o-z)dimension a t nwk ) ,maxa(nnm) ,v(nn)
RESOLUTION POUR LARGEUR DE BANDE VARIABLE
implicit real*8(a-h,o-z)dimension fc(30,3,2)
do 200 n = 1le = maxa(n)v(n) ::: v(n)n = nndo 230 1 = 2 , nnk 1 ::: ma x a ( n ) + 1ku ::: maxa(n + 1) - 1
do 180 n = 1 , nnk 1 = ma x a ( n ) + 1ku = maxa(n + 1) - 1kukl=ku-Ielif(leulel) 180, 160 160k = nc = O".dOdo 170 kk ::: kl leuk = le - 1c = c + a(kk) *" v(k)v t n ) ::: v t n ) - ccontinue
Ieukl=ku-klif(leulel) 230 210 210k = ndo 220 kk = kl kule = k - 1v(k) = v(k) - a(kk) * v(n)n = n - 1returnend
c
c
c
c
1
180
c
cC·
C
C
C
C
c
170
200
ccc
160
cc
210 .
220230
q6~
46346446546646746846947047147247347447547647747847948048148248348448548648748848949049149249349449549649749849950050150250350450550650750850951051 1512513514515516517518519520521522523524525526527
:l~~
529530531532533534535 c536537 c538539540 10541 c542543544545 11546 c547548549550551 c552 12553554555 c556 100557558559560561 20562 53563 56564565566
pl~~U.C10
p2=plp3=P2xl=fc<!<:,1,2)x2=fc<lc,2,2)x3=fc<!<:,3,2)x=O.dO
do 20 i=l,ll
if<x.gt.xl) go to 10go to 100continue
if<x.gt.x2.and.x2.gt.xl) go to 11pl=fc<k,l,l)go to 100continue
if<x.gt.x3.and.x3.gt.x2) go to 12pl=fc<k,l,l)p2"-:fc<!<:,2,l)go to 100
pl=fc<!<:,l,l)p2=fc<k,2,l)p3=fc<k,3,l)
an=-xnlav=-xvl-pl-p2-p3-wi*xam=-av*x-xml-wi*x**2/2.dO-pl*xl-p2*x2-p3*x3print 53,x,an,av,amx=x+.ldO*alicontinueformat<' ',5x,f7.2,3<5x, f12.3»format < / t20,' **aux 10-eme de portee**'
1/t20,24<'*')/tl0,' X',t26,'N',t43,'V',t60,'M')returnend
-------------------.....EXE'M PlE.J)E ~1C.UltR DE DONIfEElJI---------j .. 3)
i
'1.
®
» XH
.,'@ Li. 'l4 ç
~ li :. 3 3 -1.
..., o. ~. ,.;
-<. lt,'lljf ,J.'r
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4 '1 J S'1 -1.'5
2.
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.{. - 3 1.0
o
o
a
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A e C-<l..ll
3
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.t O. - ~'" 1f.0 O.
4 O. - '3+.0 Q.
o
-.----- .... ---_...._..-----..---..---------1It~) 1),mens \ o-n'n em. e1\l des ~ou.t'l,eUtQ
d:~~
~_ t~d ~ro-u1lteUu Âha.v-cU·~~~~rL .~~'tl_,ck ,~~ en ~~C-crYn_
-to*- ~~~e-vJ: ~ et~
.- ;) ~ ,cU. 1<1/ J.>~etiun .de -tebn.
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&PI/"'l~ A-LCOl.-.. .:i 1 ~ t:.t ~ ~ 1 ATÏL -f ea-t fa Ar7tYl1et~ mu aUrr: r ,16 1.<. /
~feCU//1l'(~ Gu.~ el LAVAUR, T~aJ;e.cU &taY>- .~e' T.H)
. 6) cLvx ,de .t ~a.lWz- /cl'~ --&nF~~ .u
~~/~ -em.~ ArÜ- lu /J-o-e&-dkalM--rw ~ (Yl1.~a.fu
<:) '])~~ - du~ ~d.t. .l~~ ,etw
JO6VW mAru..O y~~ ,cL. t Î eS~e-1 le. ,caLcul ,d..elcU.!2ii _,ete Qet-~ rv 1 ~ 'Cf<M.l 1JA f<'~ -cLu 2. (. e1acy. _
PCVL let. .ô-Uile. J ~ y~~~ ~ f~ .t~~cWt.e
~~~ ,tt~ ,olu~ .et~ -CW1 i!uut/~VYY1-&nt ~ fcÙt /uwva;rÛ 1!e~ rc1'Ll~ iOJYV(\ ea.e 'l.
~--------------------- __J
3"/1 .'., ..,.... ,E)( E M, EbE U. FleHl ER li R ~ 5 UL"~ i 5
\ l l r "
li::J(~ TRAVE.r 2, ,. z1-
7 Avr 09:35 1986 pte05 Page 2
Ro~
*****************~*******
CAS DE CHARGEMENT NO.*************************
**charges aux noeuds************************
nombre de noeuds charges = 3
noeud1
24
fx.000d+00.000d+00.000d+00
**charge en travee**********************
fy
-0.970d+02-0.234d+03-O.970d+02
moment,OOOd+OO.000d+00.000d+00
nombre d'elements avec charge uniforme - 2
elmt12
W
-37.000-37.000
DEPLACEMENTS*lt.*************
noeud12
34
dx-0.3056d-33-0.2518d-110.6164d-33
-0.3009d-33
dy-0.1657d-17-0.1908d+05-0.4625d-17-0.1657d-17
rot.-O,4718d+06
O,4080d-09-0.1965d-09
0.4718d+06
7 Avr 09:35 1986 pte05 Page 3
EFFORTS INTERNES*******************
**en bouts de membrure**************************
R.04
el m t1
ng0.3056d-13
nd-0.3056d-13
vg0.6871d+02
vd0.1143d+03
mg-0.1421d-13
md-0.1126d+03
**aUK 10-eme de portee**************************
X N V M
.00 0.000 -68.707 0.000
.49 0.000 -50.410 29.452
.99 0.000 -32.114 49.8561 . 48 0.000 -13.817 61.2121 . 98 0.000 4 . 479 ~2. q? 0.000 22.776 56.7822.97 o .000 41.072 40.9953.46 0.000 59.369 16.1613.96 0.000 77.665 -17.7214 .45 0.000 95.962
~4.95 0.000 114.258 -1 .627
**en bouts de membrure**************************
elmt2
2
ng-0.3056d-13
nd0.3056d-13
vg0.1143d+03
vd0.6871d+02
mg.0.1126d+03
md.0000d+00
x.00.49.99
1.481 . 982 . 472.973 .463.964 .454.95
**aUK 10-eme de portee**************************
N0.0000.0000.0000.000o . 0000.0000.0000.0000.0000.0000.000
**en bouts de membrure**
M-112.627-60.650-17.721
16.16140.99556.78263.52161.21249.85629.452
0.000
7 Avr 09:35 1986 pte05 Page 4
************************
R.CS
elmt3
3
ng0.4625d+03
nd-0.4625d+03
vg0.6111d-13
vd- a .61 1 1 d - 1 3
mg0.9914d-13
md0.1694d-14
**aUH 10-eme de portee**************************
X N V M.00 -462.517 a . aaa a . aaa.17 -462.517 0.000 0.000.33 -462.517 a . aaa 0.000.50 -462.517 a . aaa 0.000.66 -462.517 0.000 0.000.83 -462.517 a . aaa 0.000.99 -462.517 0.000 0.000
1 . 16 -462.517 a . aaa 0.0001.32 -462.517 0.000 0.0001.49 -462.517 0.000 0.0001.65 -462.517 0.000 0.000
*************REACTIONS
*************
(noeud 1 rH= 0.0000noeud 1 ry= 165.7065
noeud 3 rH= 0.0000noeud 3 ry= 462.5169
noeud 4 rH= 0.0000noeud 4 ry= 165.7065
7 Avr 09:35 1986· pte05 Page 5
*************************CAS DE CHARGEMENT NO. 2
*************************
**charge en travee**********************
nombre d'elements avec charge uniforme - 2
elmt12
'W
-14.800-14.800
lIr***lIr****lIr*****DEPLACEMENTS
*lIr**lIr**lIrllrllrllr*lIrllr*
noeud12
3
4
dx-0.1157d-33-0.9539d-12
0.2309d-33-0.1204d-33
dy-0.2746d-18-0.3772d+04-0.9145d-18-0.2746d-18
rot.-0.1876d+06
0.1638d-09-O. 8367d-l 0
0.1876d+06
7 Avr 09:35 1986 pte05 Page 6
R.01-
*******************EFFORTS INTERNES
*******************
*~en bouts de membrure**************************
elmt1
ng0.1157d-13
nd-0.1157d-13
vg0.2746d+02
vd0.4572d+02
mg.0000d+00
md-0.4515d+02
**aux 10~eme de portee**************************
X N V M
.00 0.000 -27.463 .000
.49 0.000 -20.145 11.771
.99 o . 000 -12.826 19.9231 . 48 0.000 -5.508 24.4561.98 0.000 1 . 8 1 1 25.3702.47 0.000 9 . 130 22.6652.97 0.000 16.448 16.3413 . 46 0.000 23.767 6.3983.96 0.000 31.085 -7.1644.45 o ; 000 ~ -24.3454.95 0.000 45.723 -45.146
**en bouts de membrure**************************
elmt2
2
ng-0.1157d-13
nd0.1157d-13
vg0.4572d+02
vd0.2746d+02
mg0.4515d+02
md.0000d+00
**aux 10-eme de portee**************************
X N V M
.00 o .000 -45.723 -45.146
.49 o .000 -38.404 -24.345
.99 o .000 -31.085 -7.1641 . 48 0.000 -23.767 6.3981.98 0.000 -16.448 1 6 . 3412.47 0.000 -9.130 22.6652.97 0.000 -1.811 25.3703 .46 0.000 5.508 24.4563.96 0.000 12.826 19.9234 . 45 o .000 20.145 11.7714 .95 o .000 27.463 o .000
**en bouts de membrure**
7 Avr 09:35 1986 pte05 Page 7
************************
R. 0 ~
**auK 10-eme de portee**************************
elmt3
3
x.00. 1 7.33.50.66.83.99
1 . 1 61.321.491.65
ng0.9145d+02
nd-0.91'l5d+02
N
-91.445-91.445-91.445-91.445-91.445-91.445-91.445-91.445-91.445-91.445-91.445
vg0.2315d-13
vd-0.2315d-13
v0.0000.0000.0000.0000.0000.000o .0000.0000.0000.000o . 000
mg0.3905d-13
md-0.8510d-15
M0.0000.0000.0000.0000.0000.000o .0000.0000.0000.0000.000
*************REACTIONS
*****lIt*******
·noeud 1 rx= 0.0000noeud 1 ry= 27.4635
noeud 3 rx= 0.0000noeud 3 ry= 91.4451
noeud 4 rK= 0.0000noeud· 4 ry= 27.4635
7 Avr 09:35 1986 pte05 Page 8
R. ,tO
CAS DE CHARGEMENT NO. 3*************************
**charge en travee**********************
nombre d'elements avec charge uniforme - 1
e lm t1
'W-14.800
DEPLACEMENTS***************
noeud12
3
4
dx-0.6830d-19-0.5629d+03
0.1366d-18-0.6830d-19
dy-0.2975d-18-0.1886d+OQ-.0 . 457 Zd - 1 8
0.2286d":19
rot.-0.2338d+06
o . 935 4 d.+ 0 5-0.4626d+05-0.4620d+05
7 Avr 09:35 1986 pte05 Page 9
*******************EFFORTS INTERNES
*******************
**en bouts de membrure**************************
elmt1
ng0.6830d+Ol
nd-0.6830d+Ol
vg0.2975d+02
- v d0.4344d+02
mg-0.3908d-13
md-0.3384d+02
**aux 10-eme de portee**************************
X N V M.00 -6.830 -29.749 0.000.49 -6.830 -22.431 12.902.99 -6.830 -15.112 22.184
1 . 48 -6.830 -7.794 27.8471.98 -6.830 - . 475 29.8922 .47 -6.830 6.844 28.3172.97 -6.830 14.162 23 1243. 46 -6.830 21.481 14.3113.96 -6.830
~1.879
4.45 -6.830 -14.1724.95 -6.830 43.437 -33.842
**en bouts de membrure****.**********************
elmt2
2
ng-0.6830d+Ol
nd0.6830d+Ol
\/g
0.2286d+Olvd
-0.2286d+Ol
mg0.1130d+02
md-0.1776d-14
**auK 10-eme de portee**************************
X N V M.00 6.830 -2.286 -11.304.49 6.830 -2.286 -10.173.99 6 . 830 -2.286 -9.043
1.48 6 .830 -2.286 -7.9131.98 6.830 -2.286 -6.7822 .47 6.830 -2.286 -5.6522.97 6.830 -2.286 -4.5223.46 6 .830 -2.286 -3.3913.96 6 . 830 -2.286 -2.2614 . 45 6.830 -2.286 -1.1304.95 6.830 -2.286 0.000
**en bouts de membrure**
7 Avr 09:35 1986 pte05 Page 10
************************
elmt3
3
ng0.4572d+02
nd-0.4572d+02
vgo .1366d+02
vd-0.1366d+02
mg0.2254d+02
md-0 ..3553d-14
**aux 10-eme de portee**************************
x.00. 17.33.50.66.83.99
1 . 1 61 . 321.491.65
N-45.723-45.723-45.723-45.723-45.723-45.723-45.723-45.723-45.723-45.723-45.723
V
-13.659-13.659-13.659-13.659-13.659-13.659-13.659-13.659-13.659-13.659-13.659
M-22.538-20.284-18.030-15.777-13.523-11.269-9.015-6.761-4.508-2.254
0.000
.,*************
REACTIONS*************
noeud 1 rH= 6.8297noeud 1 ry= 29.7494
noeud 3 rH= -13.6594noeud 3 ry= 45.7225
noeud 4 rH= 6.8297noeud 4 ry= -2.2859
· TIIMEN5IONNEMENT
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7 Avr 09:35 1986 pte05 Page
R.o2.
DONNEES GENERALES*********************
nombre d'elements --------~
nombrè de noeuds --------=nombre de noeuds restreints~
nombre de cas de chargement=module d'elasticite ------~
DONNEES DES NOEUDS**********************
343
3
O.100d+Ol
noeud1234
coordK.000
4.9454.9459.890
coordy1 . 6501.650
.0001.650
RESTREINTES AUX NOEUDS*************************
noeud13
4
DONNEES DES ELEMENTS************************
iresK iresy111
iresrooo
nombre d'equations =espace requis pour grk =
elmt1
23
noeudl122
noeud22
43
1 260
aireO.600d-Ol0.600d-010.400d-Ol
inertie0.200d-030.200d-030.133d-03
longueur0.495d+Ol0.495d+Ol0.165d+Ol
"." -.
~ -{' = .A, ~ 0 -'l,.\ -= 33 -"> 0( -::. O.:t1.
d'
La. n.<-~~~~ tY\ €. CL-t:> <:V.IU o<A..GI.
1 'J
A > '155/-+e [~0/ .
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3 ~OI'-2.o 531
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Y 30" 20 SI; 14-0 '3,51- STn 1 95 6,1- 3 671:L 40-----t-
5 40" ?<J 55 "\55 9,,~ s 'T1L-\ i 'Do 4,93 ST1Z- 40
9 1 t;)ox:w S6 2,40 ~~,U (,T201
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L
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1 go 5,05 1-T10 40-12- 40 "f.7.,0 S~o ,fbO q,~.3 i T l"-t4
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111 0 A'W ! S 41l,
1 «30 6, 'L 45-is --t'Be> -1 'l, ...( , llT14 9T101
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:
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l.t(; 30)< '/,0 5 -iq~~ ;0," GY<" '35 6,'10 1-T 1z 40
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1
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Les ehlll'l!l.:s SUlU cxpritucvs duns le premier COI enMN ("" IUO Il cl duns 1.: second CliS en daN (ew 1 kg),
I)cs précuutions doivent être .prises pour que Ilplaque uppuie SUI' toute 511 surfllce, avunt de proœderIl l'cssal (intcrposirion de sable l'in par exemple),
1>11115 les l::IS Uli l'Ill! cunnuit l'imllcc porlont c'ail·Iornicn CIIIC un l'cUI ~c paSSCI' de "culIl b ID ploqucen '1lliiisUllI le di:II!I':II11IllC de cUI...cspondance 'de laügure 17,
4 5 6 7 89 10 lS 20o 0,
100 10
K : mudulc· de réaction du sul (ou Illoduk,h: Wès\cl'gilDrtl). .
Cc mcdalc CSI d~le'l'n,in~ nu moyen I,h,: 1\:ssili sUlI"üll"\lde Wcslel'8nnrtl ~Lli .censure b mesurer l'cnfouccmcn:" d'une plnquc d'odel' .de 25 mm d'épaisseur Cl de;1 cm de dilll1lèlN ·.IOLIS lilW ehul'jlC de io kN dcl'~"
ioppunt sur le sol une.centrnintc moycùnc c pur 1;,L' 1 . •
[ormulc K r=. -,:.(1 .'
" c1~pcnd du ~y';îci;nc d'unilés choisi..' . ~ l ;, 1', '! • -1,&' .
Si on cxpnme.Ic~ p"~s.~io"s en MPII el les longueurs,'11111: ".=O,O7'(~: ." ,
, " ": f' , .'1 ~.
.f'lu, 17.- Relation entre le module K
.,~I)'lry(.I,~.e cnn,CJ,l, VERIFICATION I)U DALLAGE SOUS
L'EFFFET D'UNE CHARGE UNIFORMEMENTREPAlnlE
PAR BANDE DE LONGUEUR INFINI!
.;
" :! ;~~ '.,,< ";. ("
. .r..:~ . ,\
C,l,ll. Vérlflcollun des eonlralnle.
A t1~ruut ch: cnkul plus précls, on peUl utlll.c!" lestubleaux .ulvunlS donnum l'enveloppe de. contraintesen 'dlxlèmc de MPo, soit ton bDr, don. un dalla80 pour\1l\C' cl\l1l10 \1I\lrorml: do 10 kN/m' li I/m') n!parlledt: flll;O'1 DI~IIIOIn:, rcpollllli »ur un .ou...ol homol~ne.
Le. tableaux ci-après donnent la conlralnle maximaleen bar (enveloppe de. conlrDinle.) de traction parr1exlon pour une charge r~parllc .ur une bando partiellede largeur variable, d'un dalluge de largeur totale Lentre jolnl'. en lonction de l'épaisseur Il du COtpl dedallage el du module de rëacricn du sol K <expriméen bor/cm ou MPn/rn).
1., -,
l
~ (.~ ~ . 'J " ( : .
l' ,. u
, ,,:~, ,;,'" , ~I .
---a'
.v ' ...
K module de réaction du sul, (ULI 1110llukclc \V~sterg:l:ml),
Cc module eSI délel'lniné' au 11101'él1 dé l'éSS,\j Sl:ll1d:\\dde Wcstcrguard qui consiste il mesurer l'Cl1fUI1CClllC:,[(' dunc plaque 'u'acier de 25 111111 d'~'p:lissélll CI dL';'j l'Ill dl' dinmcu'c SOliS une l'h:II't~L' dl' jl) kN d~'\'L"
loppcllH sur lé sol 1\l1e, , coruruintc l11ul'eùllL' " Il:11' 1,1
formule K = --=:_, ..a
c dépel1d dll système dunités choisi,
S; 11n exprime lés pres,si.o,lis Cil M\':1 Cl ks longucur«en Ill: C,= 0,01,
,--,-"--,----------------
GROS ŒUVRE 34
Si 1111 cxprim,: ks 11I'l",illI1.' ,II Il:11' l'I les longueursl'Il ,III : l' ;c', O.7 ,
Les cl1aq,es SUI1I e:-:pril1\éL'S dalls le premier cas' Cili'l'lN (=ce 100 1) L'I dan s le second cas Cil daN ("",1 kg),
Dcs prccuutious duÎI'Cl11 ct re prises pour que laplaque appuie sur roure ,:1 "urfacc, avant de procéderil l'essai (irncrposition de sable [in par exemple),
!):l11S les C;lS ou 1'1111 conn.rit lindicc portant caiil'Ul'tliéll l'Ille UI1 pClIl sc p.isscr de l'essai il la plaquel'lllllilis:1111 ,le (li:lgrallll11e (le correspondance 'de lafigure 17,
()II fll,(,\/({ t'II (,(}lIlfllt' l'iudic« millimul CHR1I/1'Sl/l'l; SI/I' 1(/ [onuv,
'1 '
,Fig, 17" -' Relation cn t rc le moclute K"Cl' l'ilH\lce CBH,
5 578910 15 20 J0 1,0 sa 6~ '10 8090 100
...''"c·l,".
. ,' ...
:, .
C.3.3, VERIFICATION DU DALLAGE SOUSL'EFFFET D'UNE CHARGE UNIFORMEMENT
REPARTIEPAR BANDE DE LONGUEUR INFINIE
C.3,3I, Vérificuriun des conrruinrcs
A déluu: de culcul plus nrécls. 011 peu: utiliser- les'tublcaux suivants d0I1IH11l1 l'enveloppe des contraintesen 'dixième de MPu, soit en bar. dons un dallage pourune: charge uniforme de 10 kN/m l (1 t/m l ) "répartied\:,:ru~'ol1 uléurolrc, rcposnnt sur lIll sous-sol homogène:
Les tableaux ci-après donnent la contrainte maximaleen bar (enveloppe des contraintes) de traction parflexion' pour une charge répartie sur une bande partiellede largeur variable,d'uil dallage de largeur totale Lentre joints, Cil fonction de l'épaisseur Il du corps dedallage ct du module de réuct ion du sol K (expriméen bar/cm ou MPa/Ill),
, .....
~: ~.
1".
N' 424 MAI 1984 ~
!:'\.
r:. = 12000 MPa (120000 hMS) E " .'~ oon MPa (380000 bars)
.'f;,
. î',~
1
~l~
• sou du SlHIS'Slll SUI)IJUI'! de 1<1 forme. sur une profondeur de 1./2 sous réserve que K augmente avec1;1 pl'O(ondL'ur,
K=9
K ... IH
: K .. Iilit)
90
120
, ·c-------...-.':(L'Ill) 1 8 10 I~ 1 IH
r- - - - , - - - - ...:'-' -:.:.l:..:,(~C.:.:'l.:..:l)_·__· ..._:----:::::.1 ------,--
, , 1
lit' 1
K [1J:,'rjcI11! : 1 1 l 'i, i Iii \
,1 1 1 [1 i~-::----I----l::-::.Ir-I--! -~-\-.1,-1I~ \-1.-,1 -1-.1 -1-
-----·~~;\î·'~'-- !"'~ ~~; i--(,'-'I--S~! -'~,Î.· .\,--"''-' ".... i '...... -- ',.
1,__ .'IH~_._ .. i~~I.~~I_('l.~~I! 71 7; 'Il' l''''s (l' (-'1 -) t:
1---:""'--"'-.'':",i oLi. i~l~i-"-i-'-" ,_1_", _1_,'
i·-·,- ~I~::-" !. ~:'~,l-~,~!··~~~ 1 :,~! 1:: ~~,i' --- ~lll) ", '-\11'; ,1 1
1
1'1 1\ ~ ,1 l' ~,i -- ,~ilt i --- -! -.1 li .1-~ -'17' - ~ . ~-,~ .~ "l ,,'
1---'--- --.-..--1-1-1- - -i-
i ..._.. I~U .... _ i ...l,:' 1 .:1 : __ '~I ..~I .~7 0/,
i .'1111 1 l.~, l ..' i' l.7 2.') n ' \1"'-' ._-1 ;(l(l 1 l.~ 2." il 2.X 2.t) 2" .11
i -, ...:~~) i2~'; _']" ~'2~)-·.~2·1:,1--'---1' 1__-- __ :_
1_
, I.~O i 19 IR U 1 (l,o 11'I ..__.~....... i ._-- ...-- -- ..--.- -.. ...._......
,! .100 i Lt) 2 2,1 2J 2 ~ 2 1K~, 12 . , i ... -
...,.-----'-i= :: 1:; [=:\1 ::1 ~-;~::,:l
i:;~~-I+H:; ,c;:~ ::::::i ........ ·......·........·_.. 1·.··-..-: ..--- ..._-- -.--. ---" --i ~Oli 1 ul r.s ] 1,6 1.7 1.9 2
Les valeurs; dc",',K il prendre en COl11ptC dans CL'Stableaux correspondent [lUX plus [aib lcs vulcurs dl"modules de 'ré~i'l:lions normnlisés. obtenues pur cssai :
• soit delu [cimc 'ei,'surf,n;c :
C,)j:!, Evaluilli~li. 'dcstùsSCI1lCIlIS d ifféreut icls. " '...':'
Les iasscmcuts dir'f0i::dnlicls eurre les .IlICS de stOCk:tgL'clics zones dc-circulutiou doivent èrrc l'v;r1ul's ;1 p'lrtir,iL's pnrnmètrcs sulvnnts; .
• résùÙlllsde' I~" n:COlln;!iSSIII1CL' géOIL'chl1iquc :• 'hélér~géliéiit'dl'l~is51'.:• rép:lr1 iiio'n ~id~;~i;D~ges : . . ,• dislalH;c:cnlrC~)lxc,s;des bandes chllrgc~~ :
é1"11 isscur clc:'fil:,' ~ôticll\;eo1i1 press ible,Le I;ISscl'~cnlcsL ,.~siil11é ;1 pun ir des essais de
corn press ibi1i lé,
;1) Cns d'un sol homogèuc soumis il des charges légères
J\ dél'aut de justifiL';lliullS plliS précises el lorsqueonl'CUI ;Idlllcllrc «lIL' 1:1 ré'alïioll du sol est uniforme. uneestimation approchée du i asscmcn: différcntiel imoycn~ (, en t l'L' les bords cl il' milicll de /<1 zone chargée delurgcur 1\ est clonné; 1';11'
l'K
avec l' churuc lIl1iforllll'mcl1l répartie sur 10 largeurIl :
K module de réaction du sol.
i;.'
-;
.r:1.1;"
j'
BIBL10GRAPHI E
Pierre CHARON
1, CcJ~ ,cl~ 01W2-a~ -&n. Umv &2.me
SAWU~ M ne~ B. A.E.L ~O ~~. ~~_
~ . Gue tri '1Î et LAVA UR
z. T'L~ ,ili ..Ge!..tM.-~é T"{: gen~(~ - ~~ b UM-<rd -
2. - -II - -II •••, - _, _ T:t: CcJ.cu1.d.u\'.v:.m J:wm~ - 'ln~rt\L cdAh..u.r
k -" -l' - ." - 'J 3: lu rJ.~ . "'em.< <! dJ.:lEur
5 -,'- -.'- -1' - Tl-j:
G';:)~~ ,d'.wwmW~ d' .cL'~C-d . P.e~ehw. ts~.
~W\.~ •~ ~e10 ~ .G-~wJ; . r(\;~~edJ.tCWL
A", d re. CO\''i\
". oss~ ,C*.tI.l~~
G~ 'b (' i Cd.UiX-
n. fa .JYW.~~ _~ ~.
CGJrvuk E~ k ~
'6 R~~~~~rn-~~~
..Q'-e?Ucu..t~ ~~~ ~ .
J)cr~_~e~~
~, ~~~ 1~ ~ GM.~ â.ett .coJ.w2 "Glu ~o.-~
e-t .&wak~ e.M. \j~ ~ ~ev.-t.t Q0- tVY\.et4lt-o- c4 "dM
é.b:Jb ~iwt~,
I.....-- ~-----------------------'
} ea 'Y\ Le. Co \l e.c.
AO M!"ffl(.'f\to ,d'~ l'o..u.. ~.A.f".\..-.'Z>~ <t re~~"'VH..'l'ltrCI.'('Y'\l:'j(<.o
E~ \e~ ~~~~ _ \..aJ\T""'~
A n n o..Q.v. ..cl es 1.1. 'è-:T.p.
~~~ COb.
1
-{ (; lL. Ç{ <: 1'\ aM cl "Te~~ .d-u.- .t~ ~ -QeWV'U," 1
L..2-~ FoU c.u EP-.
... _--_ _ -.- _---_ _ _. __._--------
.1103
