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Projet à Béton IV - Notes de calcul

technique

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Projet à Béton IV

Notes de calcul :

Données du projet :




Portée L=6.30 m

Travée t=5.50 m

Nombre des étages : 2

Nombre de travées : 5

Hauteur d’étage he=2.80 m

Hauteur du sous-sol hs=2.50 m

Zone de protection paraséismique : C

Pression conventionelle du sol au niveau des fondations pconv=0.20 Mpa

Charges sur m2 de dalle plancher courant (terrasse) :

Descente des charges

Charge

Valeur nominale

Coefficient

Valeur de calcul

Fraction de

Valeur de calcul

qn (kN/m2)

de la charge

q=qn*n

longue durree nld

nld*qn

Poids propre

dalle 15 cm

Isolation

phonique

Revetement

Cloissons

Charge d'ex

Neige

qcpl cour= 11.325 kN/m2   ; qcterrasse= 9.615 kN/m2

qldpl cour= 8.05 kN/m2   ; qldterrasse= 6.89 kN/m2

S1aff = txL/2 = 5.5x6.3/2 = 17.325 m2

S2aff = tx(L/2+L1/2) = 5.5x(6.3/2+8.5/2) = 40.7 m2

S3aff = tx(L1/2+L2/2) = 5.5x(8.5/2+7/2) = 42.625m2

S4aff = txL2/2 = 5.5x7/2 = 19.25 m2

S5aff = t/2xL/2 = 5.5/2x6.3/2 = 8.66 m2

S6aff = t/2x(L/2+L1/2) = 5.5/2x(6.3/2+8.5/2) = 20.35 m2

S7aff = t/2x(L1/2+L2/2) = 5.5/2x(8.5/2+7/2) = 21.31m2

S8aff = t/2xL2/2 = 5.5/2x7/2 = 9.625 m2

L1totpoutre = t+L/2 =5.5+6.3/2 = 8.65 m

L2totpoutre = t+L/2 +L1/2=5.5+6.3/2+8.5/2 = 12.9 m

L3totpoutre = t+L1/2+L2/2 =5.5+8.5/2+7/2 = 13.25 m

L4totpoutre = t+L2/2 =5.5+7/2 = 9 m

L5totpoutre = t/2+L/2 =5.5/2+6.3/2 = 5.9 m

L6totpoutre = t/2+L/2 +L1/2=5.5/2+6.3/2+8.5/2 = 10.15 m

L7totpoutre = t/2+L1/2+L2/2 =5.5/2+8.5/2+7/2 = 10.5 m

L8totpoutre = t/2+L2/2 =5.5/2+7/2 = 6.25 m

N1CFterrasse = qterrassexSaff + 0.25x1x x1.1xt + bxhxL1totpoutrex25x1.1 = 9.615x17.325 +0.25x1x18x1.1x5.5 + 0.5x.0.5x8.65x25x1.1 = 247.87 kN

N1CSterrasse = qldterrassexSaff + 0.25x1x x1xt + bxhxL1totpoutrex25x1= 6.89x17.325 +0.25x1x18x1x5.5 + 0.5x.05x8.65x25x1 = 198.18kN

N2CFterrasse = qterrassexSaff + 0.25x1x x1.1xt + bxhxL1totpoutrex25x1.1 = 9.615x40.7 +0.25x1x18x1.1x5.5 + 0.5x.0.5x12.9x25x1.1 = 507.24 kN

N2CSterrasse = qldterrassexSaff + 0.25x1x x1xt + bxhxL1totpoutrex25x1= 6.89x40.7 +0.25x1x18x1x5.5 + 0.5x.0.5x12.9x25x1 = 385.8 kN

N3CFterrasse = qterrassexSaff + 0.25x1x x1.1xt + bxhxL1totpoutrex25x1.1 = 9.615x42.625 +0.25x1x18x1.1x5.5 + 0.5x.0.5x13.25 x25x1.1 = 528.16 kN

N3CSterrasse = qldterrassexSaff + 0.25x1x x1xt + bxhxL1totpoutrex25x1= 6.89x42.625 +0.25x1x18x1x5.5 + 0.5x.0.5x13.25x25x1 = 401.25 kN

N4CFterrasse = qterrassexSaff + 0.25x1x x1.1xt + bxhxL1totpoutrex25x1.1 = 9.615x19.25 +0.25x1x18x1.1x5.5 + 0.5x.0.5x9 x25x1.1 = 274.19 kN

N4CSterrasse = qldterrassexSaff + 0.25x1x x1xt + bxhxL1totpoutrex25x1= 6.89x19. 25 +0.25x1x18x1x5.5 + 0.5x.05x9x25x1 = 213.63kN

N5CFterrasse = qterrassexSaff + 0.25x1x x1.1xt + bxhxL1totpoutrex25x1.1 = 9.615x8.66 +0.25x1x18x1.1x5.5 + 0.5x.0.5x5.9 x25x1.1 = 148.58kN

N5CSterrasse = qldterrassexSaff + 0.25x1x x1xt + bxhxL1totpoutrex25x1= 6.89x8.66 +0.25x1x18x1x5.5 + 0.5x.05x5.9x25x1 = 121.29kN

N6CFterrasse = qterrassexSaff + 0.25x1x x1.1xt + bxhxL1totpoutrex25x1.1 = 9.615x20.35 +0.25x1x18x1.1x5.5 + 0.5x.0.5x10.15x25x1.1 = 292.67 kN

N6CSterrasse = qldterrassexSaff + 0.25x1x x1xt + bxhxL1totpoutrex25x1= 6.89x20.35 +0.25x1x18x1x5.5 + 0.5x.0.5x10.15x25x1 = 228.84 kN

N7CFterrasse = qterrassexSaff + 0.25x1x x1.1xt + bxhxL1totpoutrex25x1.1 = 9.615x21.31 +0.25x1x18x1.1x5.5 + 0.5x.0.5x10.5 x25x1.1 = 304.31kN

N7CSterrasse = qldterrassexSaff + 0.25x1x x1xt + bxhxL1totpoutrex25x1= 6.89x21.31 +0.25x1x18x1x5.5 + 0.5x.0.5x10.5x25x1 = 237.2 kN

N8CFterrasse = qterrassexSaff + 0.25x1x x1.1xt + bxhxL1totpoutrex25x1.1 = 9.615x9.625 +0.25x1x18x1.1x5.5 + 0.5x.0.5x6.25 x25x1.1 = 162.74kN

N8CSterrasse = qldterrassexSaff + 0.25x1x x1xt + bxhxL1totpoutrex25x1= 6.89x9.6 25 +0.25x1x18x1x5.5 + 0.5x.05x6.25x25x1 = 130.13kN

N1CFplcourent = qplcourentxSaff + 0.25x1x x1.1xt + bxhxL1totpoutrex25x1.1 = 11.325x17.325 +0.25x1x18x1.1x5.5 + 0.5x.0.5x8.65x25x1.1 = 282.9 kN

N1CSplcourent = qldplcourentxSaff + 0.25x1x x1xt + bxhxL1totpoutrex25x1= 8.05x17.325 +0.25x1x18x1x5.5 + 0.5x.05x8.65x25x1 = 218.28kN

N2CFplcourent = qplcourentxSaff + 0.25x1x x1.1xt + bxhxL1totpoutrex25x1.1 = 11.325x40.7 +0.25x1x18x1.1x5.5 + 0.5x.0.5x12.9x25x1.1 = 576.84 kN

N2CSplcourent = qldplcourentxSaff + 0.25x1x x1xt + bxhxL1totpoutrex25x1= 8.05x40.7 +0.25x1x18x1x5.5 + 0.5x.0.5x12.9x25x1 = 433.01 kN

N3CFplcourent = qplcourentxSaff + 0.25x1x x1.1xt + bxhxL1totpoutrex25x1.1 = 11.325x42.625 +0.25x1x18x1.1x5.5 + 0.5x.0.5x13.25 x25x1.1 = 601.05 kN

N3CSplcourent = qldplcourentxSaff + 0.25x1x x1xt + bxhxL1totpoutrex25x1= 8.05x42.625 +0.25x1x18x1x5.5 + 0.5x.0.5x13.25x25x1 = 450.7 kN

N4CFplcourent = qplcourentxSaff + 0.25x1x x1.1xt + bxhxL1totpoutrex25x1.1 = 11.325x19.25 +0.25x1x18x1.1x5.5 + 0.5x.0.5x9 x25x1.1 = 307.11 kN

N4CSplcourent = qldplcourentxSaff + 0.25x1x x1xt + bxhxL1totpoutrex25x1= 8.05x19. 25 +0.25x1x18x1x5.5 + 0.5x.05x9x25x1 = 235.96kN

N5CFplcourent = qplcourentxSaff + 0.25x1x x1.1xt + bxhxL1totpoutrex25x1.1 = 11.325x8.66 +0.25x1x18x1.1x5.5 + 0.5x.0.5x5.9 x25x1.1 = 165.86kN

N5CSplcourent = qldplcourentxSaff + 0.25x1x x1xt + bxhxL1totpoutrex25x1= 8.05x8.66 +0.25x1x18x1x5.5 + 0.5x.05x5.9x25x1 = 131.34kN

N6CFplcourent = qplcourentxSaff + 0.25x1x x1.1xt + bxhxL1totpoutrex25x1.1 = 11.325x20.35 +0.25x1x18x1.1x5.5 + 0.5x.0.5x10.15x25x1.1 = 327.47 kN

N6CSplcourent = qldplcourentxSaff + 0.25x1x x1xt + bxhxL1totpoutrex25x1= 8.05x20.35 +0.25x1x18x1x5.5 + 0.5x.0.5x10.15x25x1 = 252 kN

N7CFplcourent = qplcourentxSaff + 0.25x1x x1.1xt + bxhxL1totpoutrex25x1.1 = 11.325x21.31 +0.25x1x18x1.1x5.5 + 0.5x.0.5x10.5 x25x1.1 = 340.75 kN

N7CSplcourent = qldplcourentxSaff + 0.25x1x x1xt + bxhxL1totpoutrex25x1= 8.05x21.31 +0.25x1x18x1x5.5 + 0.5x.0.5x10.5x25x1 = 261.92kN

N8CFplcourent= qplcourentxSaff + 0.25x1x x1.1xt + bxhxL1totpoutrex25x1.1 = 11.325x9.625 +0.25x1x18x1.1x5.5 + 0.5x.0.5x6.25 x25x1.1 = 179.19kN

N8CSplcourent = qldplcourentxSaff + 0.25x1x x1xt + bxhxL1totpoutrex25x1= 8.05x9.6 25 +0.25x1x18x1x5.5 + 0.5x.05x6.25x25x1 = 141.29kN

Niveau

S1

S2

S3

S4

CF

CS

CF

CS

CF

CS

CF

CS

rdc

ss

Niveau

S5

S6

S7

S8

CF

CS

CF

CS

CF

CS

CF

CS

rdc

ss

Anec(cm2)

S1

S2

S3

S4

CF

CS

CF

CS

CF

CS

CF

CS



rdc

ss

 

S5

S6

S7

S8

 

 

CF

CS

CF

CS

CF

CS

CF

CS

 

 

 

 

 

 

 

 

 

 

 

bnec(cm2)

S1

S2

S3

S4

CF

CS

CF

CS

CF

CS

CF

CS

rdc

ss

 

S5

S6

S7

S8

 

 

CF

CS

CF

CS

CF

CS

CF

CS

 

 

 

 

 

 

 

 

 

 

 

A choisie

S1

S2

S3

S4

CF

CS

CF

CS

CF

CS

CF

CS



rdc

ss

 

S5

S6

S7

S8

 

 

CF

CS

CF

CS

CF

CS

CF

CS

 

 

 

 

 

 

 

 

 

 

 

bchoisi

S1

S2

S3

S4

CF

CS

CF

CS

CF

CS

CF

CS

rdc

ss

S5

S6

S7

S8

 

CF

CS

CF

CS

CF

CS

CF

CS

 

 

 

 

 

 

A la suite de la modelisation en ETABS j’ai choisi la section 80x80cm pour les poteaux des premiers niveaux.

La periode propre de vibration de la construction est de 0.52s. L’étude de design donne des résultats satisfaisants mais tout de même il faut introduire de l’armature.

Dimenssionement de l’armature :

Poutre longitudinale :

Dimenssions :

b=30cm;

h=60cm;

ha=50cm

x=20cm

A=1800cm2

Rc=12.5N/mm2

Ra=300N/mm2

Solicitations:

N=2.78kN

M=36.51kNm

Aa=(M+N*ha/2+b*x*Rc*(ha-x/2)=60.067mm2

On choisi : 2Φ8 Aeff=100.48mm2

P%=0.6≥0.45%

Poutre transversale :

Dimenssions :

b=30cm;

h=60cm;

ha=50cm

x=20cm

A=1800cm2

Rc=12.5N/mm2

Ra=300N/mm2

Solicitations:

N=7.02kN

M=106.83kNm

Anec=(M+N*ha/2+b*x*Rc*(ha-x/2)=3351mm2

On choisi : 4Φ25 +4Φ25 =8Φ25  Aeff=3925mm2

P%=0.85≥0.45%

Poteau des premiers niveaux :

Dimenssions :

b=80cm;

h=80cm;

ha=70cm

x=28cm

A=6400cm2

Rc=12.5N/mm2

Ra=300N/mm2

Solicitations:

N=1028kN

M=109.1kNm

Anec=(M+N*ha/2+b*x*Rc*(ha-x/2)=7663mm2

On choisi : 8Φ25 +8Φ25 =16Φ25  Aeff=7850mm2

P%=0.98≥0.45%

Poteau des derniers niveaux :



Dimenssions :

b=60cm;

h=60cm;

ha=50cm

x=28cm

A=3600cm2

Rc=12.5N/mm2

Ra=300N/mm2

Solicitations:

N=483.83kN

M=48.85kNm

Anec=(M+N*ha/2+b*x*Rc*(ha-x/2)= 3532mm2

On choisi : 4Φ25 +4Φ25 =8Φ25  Aeff=3925mm2

P%=0.9≥0.45%

Calcul du plancher :

plaque

lmin

lmax

qc

term1

M2

M1

Aa1

p%

Aa2

p%

M1' , M1''

M2' , M2''

h01

h02

Aa1

Aa2

A'a1

A'a2

A'a1

p%

A'a2

p%

plaque

Aa1

Aa2

A'a1

A'a2

f

f

f

f

f

f

f

f

f

f

f

f

A la fin j’ai fait une analyse statique non-linéaire qui a donné de bon résultats et une modelisation réele du comportement de la structure a un seisme majoré.

Fondations:

Remarques:

-au niveau du sous-sol on réalise une boite rigide: on aura des murs en béton sur toutes les directions de la construction;

-la fondation est continue sous les murs en béton

On va utiliser la rélation: Gt p conv avec Gt = 1.1x (Gbat + Gs + Gf )

Gbat

Ni (kN)

no. poteaux

force (kN)

S1

S2

S3

S4

Gs

plancher

no. poteaux

force (kN)

S1

S2

S3

S4

G murs = 0.25 x 2.5 x 25 x 244.64 x1.1 = 4204.75 kN

L = (2x L + L ) x (nt +1) x nt x (nL + 1) = 244.64 m

Gf = bf x hf x L x g b.a x n = 1 x 0.5 x 244.64 x 25 x 1 = 3363.8 kN

Gt = 54325 kN

bf = Gt p conv x L) = 1.1 m






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