V

V. caractristiques gomtriques de la structureA. Dtermination Des Caractristiques De La Structure(auto-stable)A.1. centre de masse:

-Poids propre des lments par niveau: Niveau:1;2;3;4;5:lmentNbrg(KN/m2)q(KN/m2)S(m2)L(m)G(KN)Q(KN)

-dalle A15.341.515.47-82,6123,205

-dalle B15.341.512.58-67,1818,87

-dalle C15.341.514.33-76,52221,495

-dalle D15.341.511.65-62,2217,475

-dalle F15.341.510.92-58,3216,38

-dalle G15.341.513.88-74,1220,82

-dalleH15.341.511.29-60,2916,94

-dalleI15.341.515.47-82,6123,21

-dalleJ15.341.512.58-67,1818,87

Les escaliers:

-palier25.792.57.815-45,2519,538

-paillasse28.522.56.24-53,16515,6

pout palire12.6252.5-2.958,6622,887

Balcons:

-b1(schoir)15.643.51.715-9,676,003

-b2(schoir)15.643.51,675-9,4485,87

-b3(loggia)15.643.53.995-22,5313,98

-b4(loggia)15.643.53.995-22,5313,98

-b5(chamb)15.641.53.39-19,15,085

-b6(chamb)15.641.53.28-18,54,92

Les murs212.76/2.6--55.38484,768-

TOTAL (KN)1324,675265,128

Niveau 6:

lmentNbrg(KN/m2)q(KN/m2)S(m2)L(m)G(KN)Q(KN)

-Dalles95.341.5--631,052177,265

-Balcons065.64---101,77849,838

Les murs212.76/2.6--55.38484,768-

Les escaliers

-palier15.792.53.445-19,958,62

Paillasse18.522.53.12-26,5827,8

TOTAL(KN)1264,13243,523

Niveau 7:lmentNbrg(KN/m2q(KN/m2S(m2)L(m)G(KN)Q(KN)

-acrotere11.837-0.073561.7113,343-

-dalle A15.71115.47-88,33415,47

-dalle B15.71112.58-71,83212,58

-dalle C15.71114.33-81,82414,33

-dalle D15.71111.65-66,52211,65

-dalle E15.71113.43-76,6913,43

-dalle F15.71110.92-62,35310,92

-dalle G15.71113.88-79,25513,88

-dalle H15.71111.29-64,4711,29

-dalle I15.71115.47-88,33415,47

-dalle J15.71112.58-71,83212,58

Balcons

b1(schoir)16,0711.715-10,411,715

b2(schoir)16,0711,675-10,1671,675

-b3(loggia)16,0713.995-24,283,995

-b4(loggia)16,0713.995-24,283,995

-b5(chamb)16,0713.39-20,583,39

-b6(chamb)16,0713.28-19,913,28

Les murs212.76/2.6--55.38242,384-

TOTAL(KN)1216,8149,65

-Centre de masse par niveau:Le centre de masse de la structure par dfinition est le point dapplication de la rsultante des efforts extrieursvent; sisme;

On :

Xm= Ym=

Niveau 1;2;3;4;5:

a) Les dalles:lmentmi (KN)xi (m)yi (m)mi.xi (KN.m)mi .yi (KN.m)

-dalle A82.6115.62.4251288,716200,329

-dalle B67.1815.66.851048,008238,025

-dalle C76.52212.0252.425920,177185,566

-dalle D62.2212.0256.85748,196426,207

-dalle F58.328.6756.85505,926399,492

-dalle G74.125.3752.425398,395179,741

-dalleH60.295.3756.85324,059412,987

-dalleI82.611.852.425152,829200,330

-dalleJ67.181.856.85124,283460,183

TOTAL631.0525510,5892702,86

b) Les poutres:b-1) Poutres Transversales: G= 3 KN/ml

ElementL (m)mi (KN)xi (m)yi (m)mi.xi (KN.m)mi.yi (KN.m)

Poutre 14.4513,350.002.4250,0032,374

Poutre 24.4513,353.702.42549,39532,374

Poutre34.4513,357.052.42594,11832,374

Poutre 44.4513,3510.302.425137,50532,374

Poutre 54.4513,3513.752.425183,56332,374

Poutre 64.4513,3517.452.425232,95832,374

Poutre 73.6010,80.006.850,0073,98

Poutre 83.6010,83.706.8539,9673,98

Poutre93.6010,87.056.8576,1473,98

Poutre 103.6010,810.306.85111,2473,98

Poutre 113.6010,813.756.85148,573,98

Poutre 123.6010,817.456.85188,4673,98

poutre 131.1753,5250.009.4380,0033,269

Poutre 141.1753,5253.709.43813,04333,269

Poutre 151.0753,2257.059.38822,73630,277

Poutre 161.0753,22510.309.38833,21830,277

Poutre 171.1753,52513.759.43845,46933,269

Poutre 181.1753,52517.459.43861,51333,269

TOTAL165,451437,818831,754

b-2) Poutres Longitudinales: G= 2.625 KN/mllmentLx (m)mi (KN)xi (m)yi (m)mi .xi (KN.m)mi .yi (KN.m)

13.408,9251.850.0016,5110,00

23.408,9251.854.8516,51143,287

33.408,9251.858.8516,51178,99

43.058,0065.3750.0043,0370,00

53.058,0065.3754.8543,03738,83

63.058,0065.3758.8543,03770,86

7 (p.pal)2.957,7438.6750.0067,1790,00

82.957,7438.6754.8567,17937,554

92.957,7438.6758.8567,17968,526

103.158,26812.0250.0099,4220,00

113.158,26812.0254.8599,42240,10

123.158,26812.0258.8599,42273,172

133.308,92515.600.00139,230,00

143.308,92515.604.85139,2343,287

153.308,92515.608.85139,2378,99

TOTAL125,6011096,137573,596

C) Les Poteaux: G= 3 KN/ml

lmenth (m)mi (KN)xi (m)yi (m)mi .xi (KN.m)mi .yi (KN.m)

A-13.069.180.000.000,000.00

A-23.069.183.700.0033,970.00

A-33.069.187.050.0064,7190.00

A-43.069.1810.300.0094,5540.00

A-53.069.1813.750.00126,2250.00

A-63.069.1817.450.00160,1920.00

B-13.069.180.004.850,0044,523

B-23.069.183.704.8533,9744,523

B-33.069.187.054.8564,71944,523

B-43.069.1810.304.8594,55444,523

B-53.069.1813.754.85126,22544,523

B-63.069.1817.454.85160,19244,523

C-13.069.180.008.850,0081,244

C-23.069.183.708.8533,9781,244

C-33.069.187.058.8564,71981,244

C-43.069.1810.308.8594,55481,244

C-53.069.1813.758.85126,22581,244

C-63.069.1817.458.85160,19281,244

TOTAL165.241438,98754,602

D- Les murs: Murs extrieurs: G=2.76 KN/m

Murs doubles cloisons: G=2.60 KN/mlmentL (m)S (m2)mi (KN)xi(m)yi (m)mi.ximi.yi

M 14.4511,83732,680.002.4250.0079,225

M 23.609,57626,430.006.850.00181,05

M 33.409.38425,901.850.0047,920,00

M 43.409.38425,901.858.8547,92229,215

M 53.058.41823,245.3750.80124,8918,59

M 63.058.41823,245.3759,925124,89230,60

M 71.2253.268,9993.79,66333,2886,91

M 84.4511.8432,687.052.40230,3378,41

M 93.609.57624,907.056.85175,53170,55

M 101.0252.737,5267.059,56353,05371,963

M 112.958.14222,488.675-0.55194,95-11,24

M 122.958.14222,488.6758.85194,95198,95

M 134.4511.8432,6810.32.40336,6178,41

M 141.0252.737,52610.39.56377,5271,963

M 153.159.0124,8612.0250.80298,9519,89

M 163.159.0124,8612.0259,925298,95246,736

M 171.2253.268,99913.759.663123,73786,91

M 183.409.38425,9015.60.00404,040,00

M 193.409.38425,9015.68.85404,04229,215

M 204.4511,83732,6817.452.425570,26679,225

M 213.609,57626,4317.456.85461,21181,05

Total486,294203,0362327,622

E-les balcons:

balconmi (KN)xi (m)yi (m)mi .ximi .xi

b1(schoir)9,6712.025-0.35116,29-3,385

b2(schoir)9,4485.375-0.3550,80-3,31

-b3(loggia)22,531.859.5441,68214,937

-b4(loggia)22,5315.69.54351,468214,937

-b5(chamb)19,112.0259.49229,678181,259

-b6(chamb)18,55.3759.4999,438175,565

Total (KN)101,778889,354780,003

F-les escaliers:

escaliermi (KN)xi (m)yi (m)mi .ximi .yi

107.0778.6753.225928,893356,032

les coordonnes de centre de masse (Xm ,Ym)des niveaux:1-2-3-4

Xm= ; Ym=

Niveau 06:

Elmentsmi (KN)xi (m)yi (m)mi. ximi .yi

Escaliers46,5328.6752.70403,666125,636

Les dalles631,052--5510,5892702,86

Poteaux165,24--1438,98754,602

Poutre long125,601--1096,137573,596

Poutre tran165,45--1437,818831,754

Murs486,29--4203,0362327,622

Balcons101,778--889,354780,003

Total1721,94314979,588096,073

Niveau 7:niveau terrasse:

A-les dalles:

Dalle N0S (m2)mi (KN )xi (m)yi (m)mi .ximi .yi

A15.4788,33415.62.4251288,716200,329

B12.5871,83215.66.851048,008238,025

C14.3381,82412.0252.425920,177185,566

D11.6566,52212.0256.85748,196426,207

E13.4376,698.6752.4251325,88223,795

F10.9262,3538.6756.85505,926399,492

G13.8879,2555.3752.425398,395179,741

H11.2964,475.3756.85324,059412,987

I15.4788,3341.852.425152,829200,330

J12.5871,8321.856.85124,283460,183

TOTAL751,4466836,4692926,655

B-les poutres (T.L); les poteaux; les murs et les balcons:

elementsmi (KN)mi .xi (KN.m)mi .yi (KN.m)

Poteaux82,62719,49377,301

Poutre long125,6011096,137573,596

Poutre tran165,451437,818831,754

Murs243,1452101,5181163,811

Balcons101,778889,354780,003

Total718,5946244,3173726,465

C- Lacrotre:elementsL (m)mi (KN)xi (m)yi (m)mi .ximi .yi

A-110.22518,7840.005.1130,0096,048

A-23.706,7971.850.0012,5750,00

A-30.701,2863.7-0.354,758-0,450

A-410.0518,4628.725-0.70161,081-12,923

A-50.701,28613.75-0.3517,683-0,450

A-63.706,79715.60.00106,0330,00

A-710.22518,78417.455.113327,79996,048

A-87.1513,13513.87510.225182,248134,306

A-91.2252,25110.39.4623,18621,295

1-103.255,978.6758.8551,79052,840

C-111.2252,2517.059.4615,87021,295

C-127.0512,953.52510.22545,652132,42

Total108,753948,675540,429

-Le poids propre de la structure:

W: est gale la somme des poids Wi , calculs chaque niveau (i):

W = Wi avec: Wi= WGi + b WQi

WGi : poids d aux charges permanentes et celles des quipements fixes

ventuels, solidaires de la structure

WQi : charges dexploitation

b : Coefficient de pondration, fonction de la nature et de la dure de la charge

dexploitation et donn par le tableau 4.5.daprs lRPA.

b =0,2..Btiments dhabitation, bureaux ou assimils Niveau 1-2-3-4-5: G= 1908,089 KN ; Q=265,128 KN W= 1908,089 KN

Niveau 6: G= 1721,943 KN ; Q= 243,523 KN W= 1770,648 KN

Niveau 7: G= 1578,793 KN ; Q= 149,65 KN W= 1608,723 KNLe poids totale de la structure:

W = 1908,089x5 + 1762,749 + 1608,723 W= 12919,82 KNA.2.Centre de torsion:A.2.1- Dfinition; le centre de torsion et le centre de gravite des inerties de lensemble des voiles et des poteaux constituant le contreventement de la structure .il prsente ainsi le point par lequel passe la rsultante des ractions des voiles et des poteaux. Lorsque la rsultante des efforts extrieurs passe par le centre de gravit des inerties (centre de torsion), le btiment ne subit pas de torsion, donc le couple de torsion est nul.

Si le centre de torsion est confondu avec le centre de masse de la structure, la rsultante des forces horizontales (vent , sisme ) ne provoquequune translation des voiles et des poteaux.

Si le centre de torsion est excentr par rapports au centre de masse, la rsultante des forces horizontales provoque une translation et une rotation des voiles et des poteaux dues a cette excentricit.

A.2.2. Calcul du centre de rigidit (Mthode de MUTO):-Principe de la mthode de MUTO: La mthode de MUTO est propose par la rglementation Japonaise.

Elle sapplique essentiellement au contreventement par portique. Elle dfinit le concept de la rgidit relative de niveau dun portique dont MUTO suggre comme valeur la rigidit des poteaux supposs parfaitement encastrs multiplis par coefficient correcteur a, qui traduit la flexibilit des poutres au niveaux des nuds. La rigidit relative de niveau dun portique au sens de MUTO, est dfinit comme tant gale : R= a R -Etapes de calcul: a- calcul des raideurs K des lments (poteaux et poutres)

;

b- calcul des coefficients relatifs aux portiques transversaux et longitudinaux:a)- premier niveau(R.D.C):

b)- tage courant:

c- Calcul des coefficients correcteurs a:

tage courant:

premier niveau:

d- Calcul les rigidits des poteaux suivant les deux sens:

tage courant: r = a E:module de YOUNG longitudinal du bton premier niveau: r = a

e- Calcul des rigidits relatives de niveaudes portiques transversaux et longitudinaux:

Rjx = .. 1

Rjy =. 2

: Inertie / laxe passant par le centre de gravit de la section du poteaui

Parallle laxe y

: Inertie / laxe passant par le centre de gravit de la section du poteaui

Parallle laxe x

.APPLICATION:

A B C D E F

3 2

1

A) Portiques transversaux:

1- calcul des raideurs des poteaux et des poutres Kp, Ki:

- poteau 30x40 . ==0.0016m4

- poutre30.40 ... ==0.0016m4

Kpot ===522.875x10-6m3-Poutre de la porte 4.85 m Kpout=== 329.896x10-6 m3

Poutre de la porte 4.00 m. Kpout=== 400x10-6 2-tableau rcapatif de et a: AXES: A ,B ,C ,D ,E ,F

/123

Niveau 1

07651.3950.630/

a0.4570.5580.4291.444

tages

courant

0.7651.3950.630/

a0.2760.4100.2390.926

-calcul des rigidits relatives de niveau R

Niveau 1 : R1==1.444 x= 0.967x10-3E

Etages courant:R2-7 ==0.926x= 0.620x10-3 E

b) Portiques longitudineaux:

1-calcul des raideurs des poteaux et des poutres Kp, Ki:

- poteau 30x40 . ==0.0009m4

- poutre30.40 ... ==0.0016m4

Kpot=== 294.117-6m3-Poutre de la porte 3.7 m Kpout = = = 432.432x10-6 m3

Poutre de la porte 3.35 m Kpout = = = 477.611x10-6 m3

Poutre de la porte 3.25 m Kpout = == 492.307x10-6 m3Poutre de la porte 3.45 m Kpout = = = 463.768x10-6 m3Poutre de la porte 3.7 m Kpout = = = 432.432x10-6 m3

2-tableau rcapatif de eta:

Axes 1,2,3

/ABCDEF

Niveau 1

0.9852.0732.2092.1772.0410.985/

a0.4970.6310.6430.6400.6280.4973.536

tages

courant

0.9852.0732.2092.1772.0410.985/

a0.3300.5080.5240.5210.5050.3302.718

-calcul des rigidits relatives de niveau R

Niveau 1 : R1==3.536 x=1.334x10-3E

Etages courant: R2-7 ==2.718x=1.0224x10-3E

- Tableau rcapitulatif des rigidits relatives de niveau R:

Sens longitudinalSens transversal

/Axes 1,2,3RX (kN/m)Axes: A,B,C,D,E,FRY (kN/m)

Niveau11.334x10-3E4.002x10-3E0.967x10-3E5.08x10-3E

1287221.096186616.642

Etages

courant1.0224x10-3E3.072x10-3E0.620x10-3E3.72x10-3E

98808.397119650.794

niveau2.3.4.5.6.71

98808.397128721.096

119650.794186616.642

-dtermination du centre de torsion: niveauPOTABCDEF

2.7XJ03.77.0510.313.7517.451041958.998

RJY19941.79919941.79919941.79919941.79919941.79919941.799

1XJ03.77.0510.313.7517.451625119.889

RJY31102.73331102.73331102.73331102.73331102.73331102.733

premier niveau: Xr=1625119.889/186616.642= 8.708m tage courant: Xr=1041958.998 / 119650.794= 8.708mNiveauPOT123

2.7YJ04.858.85451225.0129

RJX32936.1323332936.1323332936.13233

1YJ04.858.85587826.3384

RJX42907.03242907.03242907.032

Premier niveau: Yr=587826.3384/128721.096= 4.566m

tage courant: Yr=451225.0129/98808.397= 4.566m A.3 Calcul de lexcentricit:

Suivant RPA2003; lexcentricit gale la plus grande des deux valeurs: -5 de plus grande dimension du btiment-excentricit thorique rsultant plans=> e= max (eth ; e0)

Excentricit thorique:

ex= Xm - XR ey= Ym - YR

Excentricit accidentelle:

e0x = e0y = 0.05Lmax ; Lmax=17,75 m

Les rsultats dans le tableau:

niveauXmYmXRYRethe0

exeyexey

18.1254.3648.7084.5660.580.2020.8890.889

28.1254.3648.7084.5660.580.2020.8890.889

38.1254.3648.7084.5660.580.2020.8890.889

48.1254.3648.7084.5660.580.2020.8890.889

58.1254.3648.7084.5660.580.2020.8890.889

68.704.708.7084.5660.0080.1340.8890.889

78.8864.5568.7084.5660.1780.0010.8890.889

Alorslexcentricit de chaque niveau sera:niveaue

exey

10.8890.889

20.8890.889

30.8890.889

40.8890.889

50.8890.889

60.8890.889

70.8890.889

B. Dtermination des caractristiques de la structure en voiles: B.1. centre de masse:

- Poids propre de la structure par niveau:Niveaux 1-2-3-4-5:

lmentq (KN/m3)S (m2)Epaisseur (m)G (KN)Q (KN)

Voile 1253,4690.1613,875-

Voile 2253,2720.1613,087-

Voile 3253,2720.1613,087-

Voile 4253,4690.1613,875-

Voile 5253,4690.1613,875-

Voile 6253,2720.1613,087-

Voile 7253,2720.1613,087-

Voile 8253,4690.1613,875-

=107,848-

Poteaux165,24-

Poutre long125,601-

Poutre tran165,45-

Dalles631,052177,265

Escaliers107,07738,025

Balcons101,77849,838

Murs486,29-

Total (KN)1890,336265,128

Niveau 6:

elementG(KN)Q(KN)

Voiles107,848-

Poteaux165,24-

Poutre long125,601-

Poutre tran165,45-

Dalles631,052177,265

Balcons101,77849,838

Escaliers46,53216,42

Murs486,29-

Total (KN)1829,791243,523

Niveau 7: niveau terrasselmentG(KN)Q(KN)

Acrotre113,343-

Poteaux82,62-

Poutre long125,601-

Poutre tran165,45-

Voiles53,924-

dalles751,446131,6

Balcons109,62718,05

Murs243,145-

Total1645,156149,65

Centre de masse par niveau:Le centre de masse de la structure est donn par:

;

Niveaux 1-2-3-4-5:

lmentmi (KN)Xi (m)Yi (m)mi.Xi (KN.m)mi.Yi (KN.m)

Voile 113,8750,790,0010,9620,00

Voile 213,0870,000,8150,0010,666

Voile 313,0870,008,0350,00105,154

Voile 413,8750,798,8510,962122,794

Voile 513,87516,668,85231,158122,794

Voile 613,08717,458,035228,369105,154

Voile 713,08717,450,815228,36910,666

Voile 813,87516,660,00231,1580,00

Dalles631,052--5510,5892702,86

Poteaux165,24--1438,98754,602

Poutre long125,601--1096,137573,596

Poutre tran165,45--1437,818831,754

Murs486,29--4203,0362327,622

Balcons101,778--889,354780,003

Escaliers107,0778.6753.225928,893356,032

Total1890,33616445,7858803,697

Les coordonnes de centre de masse:

Xm=

Ym=

Niveau 6:

lmentmi (m)mi.xi (KN.m)mi .yi (KN.m)

Voiles107,848940,978477,228

Dalles631,0525510,5892702,86

Poteaux165,241438,98754,602

Poutre long125,6011096,137573,596

Poutre tran165,451437,818831,754

Murs486,294203,0362327,622

Balcons101,778889,354780,003

Escaliers46,532403,666125,636

Total1829,79115920,5588573,301

Xm=

Ym=

Niveau 7:

lmentmi (KN)mi .xi (KN.m)mi .yi (KN.m)

Acrotre115,724999,309518,41

Voiles53,924470,489238,614

Dalles631,0525510,5892702,86

Poteaux82,62719,49377,301

Poutre long125,6011096,137573,596

Poutre tran165,451437,818831,754

Murs243,1452101,5181163,811

Balcons101,778889,354780,003

total1519,29413224,7047424,963

Xm= ; Ym=

- Le poids propre de la structure:W:est gale la somme des poids Wi , calculs chaque niveau (i):

W = Wi avec: Wi= WGi + b WQi

WGi : poids d aux charges permanentes et celles des quipements fixes

ventuels, solidaires de la structure

WQi : charges dexploitation

b : coefficient de pondration, fonction de la nature et de la dure de la charge

dexploitation et donn par le tableau 4.5.daprs lRPA.

b =0,2..Btiments dhabitation, bureaux ou assimils Niveau 1-2-3-4-5: G= 1890,336 KN ; Q=265,128 KN W= 1943,37 KN

Niveau 6: G= 1829,791 KN ; Q= 243,523 KN W= 1878,496 KN

Niveau 7: G= 1645,156 KN ; Q= 149,65 KN W= 1675,09 KNLe poids total de la structure:

W = 1943,37x5 + 1878,496 + 1675,09 W= 13270,432 KN

B.2.Centre de rigidits:

poteauxhm(m)KXI(KN/m)KYI(KN/m)XI(m)YI(m)KYIXiKXIYi

13.0621577.112137.110000

23.0621577.112137.113.7044907.3070

33.0621577.112137.117.05085566.620

43.0621577.112137.1110.30125012.2320

53.0621577.112137.1113.750166885.260

63.0621577.112137.1117.450211792.560

73.0621577.112137.1104.850104648.93

83.0621577.112137.113.74.8544907.307104648.93

93.0621577.112137.117.054.8585566.62104648.93

103.0621577.112137.1110.34.85125012.232104648.93

113.0621577.112137.1113.754.85166885.26104648.93

123.0621577.112137.1117.454.85211792.56104648.93

133.0621577.112137.1108.850190957.33

143.0621577.112137.113.78.8544907.307190957.33

153.0621577.112137.117.058.8585566.62190957.33

163.0621577.112137.1110.38.85125012.232190957.33

173.0621577.112137.1113.758.85166885.26190957.33

183.0621577.112137.1117.458.85211792.56190957.33

EMBED Equation.3

EMBED Equation.3 388387.8218467.981902491.931773637.59

voileL(m)KXI

(KN/m)KYI

(KN/m)XI(m)YI(m)KYIXiKXIYi

11.28377086.575891.9740.79-0.0124654.959-4525.038

21.28377086.575891.97416.66-0.01298160.29-4525.038

31.28377086.575891.9740.798.8624654.9593250486.2

41.28377086.575891.97416.668.86298160.2913250486.2

51.285891.974377086.57-0.070.84-26396.054949.258

61.285891.974377086.5717.520.846606556.704949.258

71.285891.974377086.57-0.078.01-26396.05947194.714

81.285891.974377086.5717.528.016606556.7047194.714

1531754.171531754.1713365951.26596210.3

TOT1920141.9717502220.115268443.18369847.9

Xr= 15268443.13/17502220.17 = 8.724m

Yr= 8369847.918/1920141.97 = 4.358 m B.3. Calcul de lexcentricit:Suivant RPA2003; lexcentricit gale la plus grande des deux valeurs: -5 de plus grande dimension du btiment-excentricit thorique rsultant plans=> e= max (eth ; e0)

Excentricit thorique:

ex= Xm - XR ey= Ym - YR

Excentricit accidentelle:

e0x = e0y = 0.05Lmax ; Lmax=17,75 m

Les rsultats dans le tableau:

niveauXmYmXRYRethe0

exeyexey

18.704.6578.7244.3580.0240.2720.8890.889

28.704.6578.7244.3580.0240.2720.8890.889

38.704.6578.7244.3580.0240.2720.8890.889

48.704.6578.7244.3580.0240.2720.8890.889

58.704.6578.7244.3580.0240.2720.8890.889

68.704.6898.7244.3580.0240.2720.8890.889

78.7044.8868.7244.3580.020.5280.8890.889

Alorslexcentricit de chaque niveau sera:niveaue

exey

10.8890.889

20.8890.889

30.8890.889

40.8890.889

50.8890.889

60.8890.889

70.8890.889

V.3. Evaluation des Charges Verticales: le principe de la rpartition des charges verticales aux niveaux des lments porteurs est bas sur la mthode de la ligne de rupture.Rpartition des charges sur les portiques:

Portiques transversaux:

1-portique daxe 01:a) Charge Permanente:

poutre terrasse: trave AB BC:

G=Gacrotere+GplancherG= 1,837+(5,71.3,40/2) = 11,544 KN/ml

GAB = GBC = 11,544 KN/ml

console terrasse:charge concentre: 1,837.1,375= 2,525 KNcharge repartie: G = Gbalcon + Gacrotere

poutre tage:

Trave AB BC:

G=Gplan+Gmur

G= 5,34.3,40/2 + 2,76.(3,06-0,4) = 16,419 KN/ml

GAB = GBC = 16,419 KN/mlConsole tage:

G =

b) charge dexploitation:

poutre terrasse:

Trave AB BC:

QAB = QBC = 1.3,40/2 = 1,70 KN/ml

console terrasse:

poutre tage: Trave AB BC:

QAB = QBC = 1,5.3,40/2 = 2,55 KN/ml

Console tage:

2-portique daxe 02:a) Charge Permanente:

poutre terrasse: trave AB BC:

G= (5,71.3,40/2)+(5,71.3,05/2) = 18,414 KN/ml

GAB = GBC = 18,414 KN/ml

console terrasse:charge concentre: 1,837.(1,375+1,225) = 4,767 KNcharge repartie: G =

poutre tage:

Trave AB BC:

G=Gplan+Gmur

G= 5,34.3,40/2 + 5,34.3,05/2 = 17,221 KN/ml

GAB = GBC = 17,221 KN/ml

Console tage:charge concentre: 2,76.(3,06-0,35).0,90 = 6,731 KNcharge repartie: G =5,64.1,225/2 + 5,64.0,90/2 = 13,307 KN/mlb) charge dexploitation:

-poutre terrasse:

Trave AB BC:

QAB = QBC =1.3,40/2 + 1.3,05/2 = 3,525 KN/ml

console terrasse:Q= 1.1,02/2 + 1.1.225/2 = 1,125 KN/ml

poutre tage:

Trave AB BC:

QAB = QBC = 1,5.3,40/2 + 1,5.3,05/2 = 4,837 KN/ml

Console tage:Q= 3,5.1,225/2 + 3,5.0,90/2 = 2,818 KN/ml

3) portique daxe 03a) Charge Permanente:

poutre terrasse: trave AB BC:

G= (5,71.2,95/2)+(5,71.3,05/2) = 17,129 KN/ml

GAB = GBC = 17,129 KN/ml

console terrasse:charge concentre: 1,837.1,20 = 2,204 KNcharge repartie: G = 6,07.0,90/2 + 1,837 = 4,568 KN/mlpoutre tage:G=Gplan+GmurTrave AB :

GAB = 5,34.3,05/2 + 2,60.(3,06 - 0,40)= 15,059 KN/mlTrave BC:

GBC = 5,34.3,05/2 + 2,60.(3,06 - 0,40) + 5,34.2,95/2 = 22,935 KN/mlConsole tage:charge concentre: 2,76.(3,06-0,35).1,05 = 7,853 KNcharge repartie: G = 2,76.(3,06 0,40) + 5,64.0,90/2 = 9,879 KN/mlb) charge dexploitation:

-poutre terrasse:

Trave AB BC:

QAB = QBC =1.2,95/2 + 1.3,05/2 = 3 KN/ml

console terrasse:Q= 1.0,90/2 = 0,450 KN/ml

poutre tage:

Trave AB :

QAB = 1,5.3,05/2 = 2,287 KN/mlTrave BC:

QBC = 1,5.3,05/2 + 1,5.2,95/2 = 4,499 KN/ml

Console tage:Q= 3,5.0,90/2 = 0,675 KN/ml

4) Portique daxe 4:a) Charge Permanente:

poutre terrasse: trave AB BC:

G= (5,71.2,95/2)+(5,71.3,15/2) = 17,415 KN/ml

GAB = GBC = 17,415 KN/ml

console terrasse:charge concentre: 1,837.1,20 = 2,204 KNcharge repartie: G = 6,07.0,90/2 + 1,837 = 4,568 KN/mlpoutre tage:G=Gplan+GmurTrave AB :

GAB = 5,34.3,15/2 + 2,60.(3,06 - 0,40)= 15,326 KN/mlTrave BC:

GBC = 5,34.2,95/2 + 5,34.3,15/2 = 16,287 KN/mlConsole tage:charge concentre: 2,76.(3,06-0,35).1,05 = 7,853 KNcharge repartie: G = 2,76.(3,06 0,40) + 5,64.0,90/2 = 9,879 KN/mlb) charge dexploitation:

-poutre terrasse:

Trave AB BC:

QAB = QBC =1.2,95/2 + 1.3,15/2 = 3,05 KN/ml

console terrasse:Q= 1.0,90/2 = 0,450 KN/ml

poutre tage:

Trave AB :

QAB = 1,5.3,15/2 = 2,362 KN/mlTrave BC:

QBC = 1,5.3,15/2 + 1,5.2,95/2 = 4,575 KN/ml

Console tage:Q= 3,5.0,90/2 = 0,675 KN/ml

5) Portique daxe 5:a) Charge Permanente:

poutre terrasse: trave AB BC:

G= (5,71.3,40/2)+(5,71.3,15/2) = 18,700 KN/ml

GAB = GBC = 18,700 KN/ml

console terrasse:charge concentre: 1,837.(1,375+1,225) = 4,767 KNcharge repartie: G =

poutre tage:

Trave AB BC:

G=Gplan+Gmur

G= 5,34.3,40/2 + 5,34.3,15/2 = 17,488 KN/ml

GAB = GBC = 17,488 KN/ml

Console tage:charge concentre: 2,76.(3,06-0,35).0,90 = 6,731 KNcharge repartie: G =5,64.1,225/2 + 5,64.0,90/2 = 13,307 KN/mlb) charge dexploitation:

-poutre terrasse:

Trave AB BC:

QAB = QBC =1.3,40/2 + 1.3,15/2 = 3,270 KN/ml

console terrasse:Q= 1.1,02/2 + 1.1.225/2 = 1,125 KN/ml

poutre tage:

Trave AB BC:

QAB = QBC = 1,5.3,40/2 + 1,5.3,15/2 = 4,912 KN/ml

Console tage:Q= 3,5.1,225/2 + 3,5.0,90/2 = 2,818 KN/ml

6) Portique daxe 6 :a) Charge Permanente:

poutre terrasse: trave AB BC:

G=Gacrotere+GplancherG= 1,837+(5,71.3,40/2) = 11,544 KN/ml

GAB = GBC = 11,544 KN/ml

console terrasse:charge concentre: 1,837.1,375= 2,525 KNcharge repartie: G = Gbalcon + Gacrotere

poutre tage:

Trave AB BC:

G=Gplan+Gmur

G= 5,34.3,40/2 + 2,76.(3,06-0,4) = 16,419 KN/ml

GAB = GBC = 16,419 KN/mlConsole tage:

G =

b) charge dexploitation:

poutre terrasse:

Trave AB BC:

QAB = QBC = 1.3,40/2 = 1,70 KN/ml

console terrasse:

poutre tage: Trave AB BC:

QAB = QBC = 1,5.3,40/2 = 2,55 KN/ml

Console tage:

Rpartition des charges sur les portiques:

Portiques longitudinaux:1) Portique daxe A:a) Poutre terrasse:

Trave1-25-6:

G = Gacrotere = 1,837 KN/ml

Q = 0,00 KN/ml

Trave2-33-4 4-5:

G = 1,837 + 6,07x0,5 = 4,872 KN/ml

Q= 1x0,5 = 0,5 KN/ml

b) Poutre tage:

Trave 1-25-6:

G = Gmur = 2,76.(3,06 0,35) = 7,479 KN/ml

Q = 0 KN/ml

Trave 2-34-5:

G = 5,64x0,50 = 2,82 KN/ml

Q = 1,5x0,50 = 0,75 KN/ml Trave 3-4(poutre paliere):G = 0,55x5,79 + 1,675x8,52 + 0,50x5,79 = 20,33 KN/ml

Q = 0,55x2,5 + 1,675x2,5 + 0,50x2,5 + 0,30x2,5 = 7,562 KN/ml

2) portique daxe B:a) Poutre terrasse:

Trave1-2 2-3 3-4 4-5 5-6 :

G = 2,91x0,30 = 0,873 KN/ml

Q = 1x0,30 = 0,3 KN/ml

b) Poutre tage:

Trave 1-22-3 4-5 5-6 :

G = 2,54x0,30 = 0,762 KN/ml

Q = 1,5x0,30 = 0,450 KN/ml

Trave 3-4(poutre paliere):G = 1,60x5,79 + 0,675x8,52 = 14,589 KN/ml

Q = 1,60x2,5 + 0,675x2,5 = 5,562 KN/ml

3) Portique daxe C:a) Poutre terrasse:

Trave 1-2 5-6: G = 4,756 + 1,837 = 6,593 KN/ml

Q = 2,664/3,4 x1= 0,78 KN/ml

Trave 2-3 4-5:

G = 1,837 + 0,888x6,07 = 7,227 KN/ml

Q = 1x0,888 = 0,888 KN/ml

Trave 3-4:

G = 1,837 KN/ml

Q = 0 KN/ml

b) Poutre tage:

Trave 1-2 5-6:

G = Gbalcon + Gmur = 4,44 + 2,76.(3,06 0,35) = 11,919 KN/ml

Q = Qbalcon = 0,70x3,5 = 2,73 KN/ml

Trave 2-3 4-5:

G = Gmu r= 2,76.(3,06 0,35) + 0,888x5,64 = 12,478 KN/ml

Q = 0,888x1,5 = 1,327 KN/ml

Trave 3-4:

G = 2,76.(3,06 0,35) = 7,479 KN/ml

Q = 0 KN/ml

Portiques longitudinaux:

SHAPE \* MERGEFORMAT

EMBED Equation.3

Kp

K2

K1

K1

Kp

EMBED Equation.3

EMBED Equation.3

Encastrement parfait

Kp

Kp

Kp

K4

K3

K3

K2

K2

K2

K1

K1

K1

EMBED Equation.3

EMBED Equation.3

EMBED Equation.3

EMBED Equation.3 EMBED Equation.3

X

Y

Rjy:rigidit d 1 portique transversale au niveau j

1 2 3

k

Rjx : rigidit d 1 portique longitudinale au niveau j

1

2

m

Y

4,85m

4,00m

0,3m

3,4m

3,05m

2.95m

0,3m

3,15m

3,4

0,4m

0,4m

X

0,3m

0,4m

0,3m

0,3m

0,3m

6,731

6,731

6,731

6,731

6,731

6,731

4,767

Q=

G=

2,53

Portique daxe 02

17,221

4,837

18,414

3,525

17,221

4,837

18,414

3,525

6,813

1,125

13,307

2,818

13,307

2,818

13,307

2,818

13,307

2,818

13,307

2,818

13,307

2,818

17,221

4,837

17,221

4,837

17,221

4,837

17,221

4,837

17,221

4,837

17,221

4,837

17,221

4,837

17,221

4,837

17,221

4,837

17,221

4,837

16,419

2,55

11,544

1,7

16,419

2,55

16,419

2,55

16,419

2,55

16,419

2,55

16,419

2,55

11,544

1,7

16,419

2,55

16,419

2,55

16,419

2,55

16,419

2,55

16,419

2,55

16,419

2,55

5,554

0,612

3,454

2,143

3,454

2,143

3,454

2,143

3,454

2,143

3,454

2,143

3,454

2,143

Portique daxe 01

4,85m

4,00m

1,375m

4,85

4,00m

1,375m

7,85

G=

Q=

2,204

7,85

7,85

7,85

7,85

7,85

7,85

7,85

7,85

7,85

2,204

15,326

2,362

17,415

3,05

16,287

4,575

17,415

3,05

4,57

0,45

9,879

0,675

9,879

0,675

9,879

0,675

9,879

0,675

9,879

0,675

9,879

0,675

15,326

2,362

15,326

2,362

15,326

2,362

15,326

2,362

15,326

2,362

16,287

4,575

16,287

4,575

16,287

4,575

16,287

4,575

16,287

4,575

7,85

7,85

22,935

4,499

17,129

3

22,935

4,499

22,935

4,499

22,935

4,499

22,935

4,499

22,935

4,499

17,129

3

15,059

2,287

15,059

2,287

15,059

2,287

15,059

2,287

15,059

2,287

15,059

2,287

4,568

0,45

9,879

0,675

9,879

0,675

9,879

0,675

9,879

0,675

9,879

0,675

9,879

0,675

Portique daxe 04

Portique daxe 03

4,85m

4,00m

1,225m

4,85

4,00m

1,225m

2,53

16,419

2,55

11,544

1,7

16,419

2,55

16,419

2,55

16,419

2,55

16,419

2,55

16,419

2,55

11,544

1,7

16,419

2,55

16,419

2,55

16,419

2,55

16,419

2,55

16,419

2,55

16,419

2,55

5,554

0,612

3,454

2,143

3,454

2,143

3,454

2,143

3,454

2,143

3,454

2,143

3,454

2,143

Portique daxe 06

4,85m

4,00m

1,375m

6,731

6,731

6,731

6,731

6,731

6,731

4,767

17,488

4,912

18,7

3,27

17,488

4,912

18,7

3,27

6,813

1,125

13,307

2,818

13,307

2,818

13,307

2,818

13,307

2,818

13,307

2,818

13,307

2,818

17,488

4,912

17,488

4,912

17,488

4,912

17,488

4,912

17,488

4,912

17,488

4,912

17,488

4,912

17,488

4,912

17,488

4,912

17,488

4,912

4,85

4,00m

1,375m

Portique daxe 05

20,33

7,56

20,33

7,56

20,33

7,56

20,33

7,56

20,33

7,56

7,48

0,00

7,48

0,00

7,48

0,00

7,48

0,00

7,48

0,00

2,82

0,75

2,82

0,75

2,82

0,75

2,82

0,75

2,82

0,75

2,82

0,75

2,82

0,75

2,82

0,75

2,82

0,75

2,82

0,75

7,48

0,00

7,48

0,00

7,48

0,00

7,48

0,00

7,48

0,00

7,48

0,00

2,82

0,75

20,33

7,56

2,82

0,75

7,48

0,00

4,872

0,50

1,837

0,00

4,872

0,50

1,837

0,00

4,872

0,50

G=

Q=

3,70m

3,70m

3,45m

3,25m

3,35m

Portique 01

14,58

5,66

14,58

5,66

14,58

5,66

14,58

5,66

14,58

5,66

0,76

0,45

0,76

0,45

0,76

0,45

0,76

0,45

0,76

0,45

0,76

0,45

0,76

0,45

0,76

0,45

0,76

0,45

0,76

0,45

0,76

0,45

0,76

0,45

0,76

0,45

0,76

0,45

0,76

0,45

0,76

0,45

0,76

0,45

0,76

0,45

0,76

0,45

0,76

0,45

0,76

0,45

0,76

0,45

14,58

5,66

0,76

0,45

0,76

0,45

0,87

0,30

0,87

0,30

0,87

0,30

0,87

0,30

0,87

0,30

G=

Q=

3,70m

3,70m

3,45m

3,25m

3,35m

Portique 02

7,48

0,00

7,48

0,00

7,48

0,00

7,48

0,00

7,48

0,00

11,92

2,73

11,92

2,73

11,92

2,73

11,92

2,73

11,92

2,73

12,49

1,33

12,49

1,33

12,49

1,33

12,49

1,33

12,49

1,33

12,49

1,33

12,49

1,33

12,49

1,33

12,49

1,33

12,49

1,33

11,92

2,73

11,92

2,73

11,92

2,73

11,92

2,73

11,92

2,73

11,92

2,73

12,49

1,33

7,48

0,00

2,82

0,75

11,92

2,73

7,23

0,89

6,59

0,78

1,84

0,00

6,59

0,78

7,23

0,89

G=

Q=

3,70m

3,70m

3,45m

3,25m

3,35m

Portique 03

_1240899255.unknown

_1241463213.unknown

_1241502282.unknown

_1241848859.unknown

_1243747800.unknown

_1243749416.unknown

_1243749454.unknown

_1243749498.unknown

_1243749417.unknown

_1243748860.unknown

_1243749005.unknown

_1243749020.unknown

_1243747920.unknown

_1243747060.unknown

_1243747103.unknown

_1241848860.unknown

_1241805207.unknown

_1241806666.unknown

_1241806743.unknown

_1241846368.unknown

_1241805271.unknown

_1241629615.unknown

_1241500885.unknown

_1241501385.unknown

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