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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