Projet à Béton IV - Notes de calcul

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 h_e=2.80 m

Hauteur du sous-sol h_s=2.50 m

Zone de protection paraséismique : C

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

Charges sur m² de dalle plancher courant (terrasse) :

q^cpl _cour= 11.325 kN/m²   ; q^cterrasse= 9.615 kN/m²

q^ldpl _cour= 8.05 kN/m²   ; q^ldterrasse= 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

L1^tot_poutre = t+L/2 =5.5+6.3/2 = 8.65 m

L2^tot_poutre = t+L/2 +L1/2=5.5+6.3/2+8.5/2 = 12.9 m

L3^tot_poutre = t+L1/2+L2/2 =5.5+8.5/2+7/2 = 13.25 m

L4^tot_poutre = t+L2/2 =5.5+7/2 = 9 m

L5^tot_poutre = t/2+L/2 =5.5/2+6.3/2 = 5.9 m

L6^tot_poutre = t/2+L/2 +L1/2=5.5/2+6.3/2+8.5/2 = 10.15 m

L7^tot_poutre = t/2+L1/2+L2/2 =5.5/2+8.5/2+7/2 = 10.5 m

L8^tot_poutre = t/2+L2/2 =5.5/2+7/2 = 6.25 m

N^1CF_terrasse = q_terrassexSaff + 0.25x1x x1.1xt + bxhxL1^tot_poutrex25x1.1 = 9.615x17.325 +0.25x1x18x1.1x5.5 + 0.5x.0.5x8.65x25x1.1 = 247.87 kN

N^1CS_terrasse = qldterrassexSaff + 0.25x1x x1xt + bxhxL1^tot_poutrex25x1= 6.89x17.325 +0.25x1x18x1x5.5 + 0.5x.05x8.65x25x1 = 198.18kN

N^2CF_terrasse = q_terrassexSaff + 0.25x1x x1.1xt + bxhxL1^tot_poutrex25x1.1 = 9.615x40.7 +0.25x1x18x1.1x5.5 + 0.5x.0.5x12.9x25x1.1 = 507.24 kN

N^2CS_terrasse = qldterrassexSaff + 0.25x1x x1xt + bxhxL1^tot_poutrex25x1= 6.89x40.7 +0.25x1x18x1x5.5 + 0.5x.0.5x12.9x25x1 = 385.8 kN

N^3CF_terrasse = q_terrassexSaff + 0.25x1x x1.1xt + bxhxL1^tot_poutrex25x1.1 = 9.615x42.625 +0.25x1x18x1.1x5.5 + 0.5x.0.5x13.25 x25x1.1 = 528.16 kN

N^3CS_terrasse = qldterrassexSaff + 0.25x1x x1xt + bxhxL1^tot_poutrex25x1= 6.89x42.625 +0.25x1x18x1x5.5 + 0.5x.0.5x13.25x25x1 = 401.25 kN

N^4CF_terrasse = q_terrassexSaff + 0.25x1x x1.1xt + bxhxL1^tot_poutrex25x1.1 = 9.615x19.25 +0.25x1x18x1.1x5.5 + 0.5x.0.5x9 x25x1.1 = 274.19 kN

N^4CS_terrasse = qldterrassexSaff + 0.25x1x x1xt + bxhxL1^tot_poutrex25x1= 6.89x19. 25 +0.25x1x18x1x5.5 + 0.5x.05x9x25x1 = 213.63kN

N^5CF_terrasse = q_terrassexSaff + 0.25x1x x1.1xt + bxhxL1^tot_poutrex25x1.1 = 9.615x8.66 +0.25x1x18x1.1x5.5 + 0.5x.0.5x5.9 x25x1.1 = 148.58kN

N^5CS_terrasse = qldterrassexSaff + 0.25x1x x1xt + bxhxL1^tot_poutrex25x1= 6.89x8.66 +0.25x1x18x1x5.5 + 0.5x.05x5.9x25x1 = 121.29kN

N^6CF_terrasse = q_terrassexSaff + 0.25x1x x1.1xt + bxhxL1^tot_poutrex25x1.1 = 9.615x20.35 +0.25x1x18x1.1x5.5 + 0.5x.0.5x10.15x25x1.1 = 292.67 kN

N^6CS_terrasse = qldterrassexSaff + 0.25x1x x1xt + bxhxL1^tot_poutrex25x1= 6.89x20.35 +0.25x1x18x1x5.5 + 0.5x.0.5x10.15x25x1 = 228.84 kN

N^7CF_terrasse = q_terrassexSaff + 0.25x1x x1.1xt + bxhxL1^tot_poutrex25x1.1 = 9.615x21.31 +0.25x1x18x1.1x5.5 + 0.5x.0.5x10.5 x25x1.1 = 304.31kN

N^7CS_terrasse = qldterrassexSaff + 0.25x1x x1xt + bxhxL1^tot_poutrex25x1= 6.89x21.31 +0.25x1x18x1x5.5 + 0.5x.0.5x10.5x25x1 = 237.2 kN

N^8CF_terrasse = q_terrassexSaff + 0.25x1x x1.1xt + bxhxL1^tot_poutrex25x1.1 = 9.615x9.625 +0.25x1x18x1.1x5.5 + 0.5x.0.5x6.25 x25x1.1 = 162.74kN

N^8CS_terrasse = qldterrassexSaff + 0.25x1x x1xt + bxhxL1^tot_poutrex25x1= 6.89x9.6 25 +0.25x1x18x1x5.5 + 0.5x.05x6.25x25x1 = 130.13kN

N^1CF_plcourent = q_plcourentxSaff + 0.25x1x x1.1xt + bxhxL1^tot_poutrex25x1.1 = 11.325x17.325 +0.25x1x18x1.1x5.5 + 0.5x.0.5x8.65x25x1.1 = 282.9 kN

N^1CS_plcourent = qld_plcourentxSaff + 0.25x1x x1xt + bxhxL1^tot_poutrex25x1= 8.05x17.325 +0.25x1x18x1x5.5 + 0.5x.05x8.65x25x1 = 218.28kN

N^2CF_plcourent = q_plcourentxSaff + 0.25x1x x1.1xt + bxhxL1^tot_poutrex25x1.1 = 11.325x40.7 +0.25x1x18x1.1x5.5 + 0.5x.0.5x12.9x25x1.1 = 576.84 kN

N^2CS_plcourent = qld_plcourentxSaff + 0.25x1x x1xt + bxhxL1^tot_poutrex25x1= 8.05x40.7 +0.25x1x18x1x5.5 + 0.5x.0.5x12.9x25x1 = 433.01 kN

N^3CF_plcourent = q_plcourentxSaff + 0.25x1x x1.1xt + bxhxL1^tot_poutrex25x1.1 = 11.325x42.625 +0.25x1x18x1.1x5.5 + 0.5x.0.5x13.25 x25x1.1 = 601.05 kN

N^3CS_plcourent = qld_plcourentxSaff + 0.25x1x x1xt + bxhxL1^tot_poutrex25x1= 8.05x42.625 +0.25x1x18x1x5.5 + 0.5x.0.5x13.25x25x1 = 450.7 kN

N^4CF_plcourent = q_plcourentxSaff + 0.25x1x x1.1xt + bxhxL1^tot_poutrex25x1.1 = 11.325x19.25 +0.25x1x18x1.1x5.5 + 0.5x.0.5x9 x25x1.1 = 307.11 kN

N^4CS_plcourent = qld_plcourentxSaff + 0.25x1x x1xt + bxhxL1^tot_poutrex25x1= 8.05x19. 25 +0.25x1x18x1x5.5 + 0.5x.05x9x25x1 = 235.96kN

N^5CF_plcourent = q_plcourentxSaff + 0.25x1x x1.1xt + bxhxL1^tot_poutrex25x1.1 = 11.325x8.66 +0.25x1x18x1.1x5.5 + 0.5x.0.5x5.9 x25x1.1 = 165.86kN

N^5CS_plcourent = qld_plcourentxSaff + 0.25x1x x1xt + bxhxL1^tot_poutrex25x1= 8.05x8.66 +0.25x1x18x1x5.5 + 0.5x.05x5.9x25x1 = 131.34kN

N^6CF_plcourent = q_plcourentxSaff + 0.25x1x x1.1xt + bxhxL1^tot_poutrex25x1.1 = 11.325x20.35 +0.25x1x18x1.1x5.5 + 0.5x.0.5x10.15x25x1.1 = 327.47 kN

N^6CS_plcourent = qld_plcourentxSaff + 0.25x1x x1xt + bxhxL1^tot_poutrex25x1= 8.05x20.35 +0.25x1x18x1x5.5 + 0.5x.0.5x10.15x25x1 = 252 kN

N^7CF_plcourent = q_plcourentxSaff + 0.25x1x x1.1xt + bxhxL1^tot_poutrex25x1.1 = 11.325x21.31 +0.25x1x18x1.1x5.5 + 0.5x.0.5x10.5 x25x1.1 = 340.75 kN

N^7CS_plcourent = qld_plcourentxSaff + 0.25x1x x1xt + bxhxL1^tot_poutrex25x1= 8.05x21.31 +0.25x1x18x1x5.5 + 0.5x.0.5x10.5x25x1 = 261.92kN

N^8CF_plcourent= q_plcourentxSaff + 0.25x1x x1.1xt + bxhxL1^tot_poutrex25x1.1 = 11.325x9.625 +0.25x1x18x1.1x5.5 + 0.5x.0.5x6.25 x25x1.1 = 179.19kN

N^8CS_plcourent = qld_plcourentxSaff + 0.25x1x x1xt + bxhxL1^tot_poutrex25x1= 8.05x9.6 25 +0.25x1x18x1x5.5 + 0.5x.05x6.25x25x1 = 141.29kN

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 :

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: G_t p _conv avec G_t = 1.1x (G_bat + G_s + G_f )

G_bat

G_s

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

L = (2x L + L ) x (n_t +1) x n_t x (n_L + 1) = 244.64 m

G_f = 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

G_t = 54325 kN

bf = G_t p _conv x L) = 1.1 m