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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 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) :

			Descente des charges

Charge	Valeur nominale	Coefficient	Valeur de calcul	Fraction de	Valeur de calcul
	q_n (kN/m²)	de la charge	q=q_n*n	longue durree n_ld	n_ld*q_n
Poids propre
dalle 15 cm
Isolation
phonique
Revetement
Cloissons
Charge d'ex
Neige

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

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)

rdc

bnec(cm²)

rdc

A choisie

rdc

bchoisi

rdc

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	l_min	l_max		q^c	term1	M₂	M₁



A_a1			p%	A_a2			p%



M₁^{' ,} M₁''	M₂^' , M₂''	h₀₁	h₀₂	A_a1	A_a2	A'_a1	A'_a2



A'_a1			p%	A'_a2			p%

plaque	A_a1	A_a2	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: G_t p _conv avec G_t = 1.1x (G_bat + G_s + G_f )

G_bat

	Ni (kN)	no. poteaux	force (kN)
S1
S2
S3
S4

G_s

	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 (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

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