contr even tement ok
DESCRIPTION
contreventementTRANSCRIPT
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CONTREVENTEMENT PAR VOILES
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CONTREVENTEMENT PAR PORTIQUES
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CONTREVENTEMENT PARCONTREVENTEMENT PAR VOILES
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bR1 = F ---------
a + b
aR2 = F ----------
a + b
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Équilibre de translation
R1 FR1 = F
Équilibre de rotationÉquilibre de rotation
R2 .h = F.d
dR2 = F ------R2 = F ------
h
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Comportement d’un voile avec ouvertures (similaire à un portique)
Formation de rotule au milieu du poteau
Il y’a 3 types de déformations Il y’a 3 types de déformations
Déformation de la flexion globale du portique (voile)
Déformation du linteau (flexion)
Déformation de flexion de chaque poteau (demi voile)
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Effort tranchant dans le linteau
hmT
Chargement uniforme
I,.h.m.Tu u0
Chargement triangulaire
I
,.h.m.Tt t0
I
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Les moments M1 et M2 dans les éléments d il 1 t 2du voile 1 et 2
Ch if
I
,.m.c.22
1H.T.II
IM22
u021
11
Charge uniforme
21
,.m.c.21H.T.IM
22
t02
2
I2
H.T.II
M t021
2
Charge triangulaire
I
,.m.c.22
1H.T.II
IM22
t021
11
,.m.c.21H.T.IM
22
t01
2
I2
H.T.II
M t021
2
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On pose :
c.m.2III;11c.2m 21
On pose :
;
A1
A1 21
21
Hx;h.
hmI
IIc2
ai
E'E
23
213
2
Hh.mIIaE2 21
Inertie équivalente du voile
e 16II
20
21
e
IIc.m.161
I
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Stabilité des fondations au droit des voiles
On pose : MN
N Effort normal ; 6Le
21
MM
Le moment Fléchissant ;
NMe l’excentricité ;
:S Surface d’appui de la semelle ;
:b La largeur
l d l ll:L La longueur de la semelle ;
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Semelle entièrement comprimée
M
N
21 21
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MN
L
On a : 6Le
216Le
SLM6
SN
1 6
M6N
SLS2
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N ( en dehors du tiers central)Le 6
NMM
max
Une partie de la semelle est soulevée
pour des charges de longue durée (vent)on a accepté que 75% de la semelle reste compriméeon a accepté que 75% de la semelle reste comprimée
Pour des charges instantanée (séisme)
t 10% d l ll t i éon accepte que 10% de la semelle reste comprimée
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L’effort normal N est équilibré par un diagramme
L
triangulaire des contraintes
be2L.3
Nmax
2
N
Et l t i t
NM
Et la contraintemax
LN2
max
be
2L3
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cas dans la quelle la stabilité de la semelle estcas dans la quelle la stabilité de la semelle est
assurée grâce à la présence des murs qui lui sont
Perpendiculaire.
E é é l l d’ bâti t t lid iEn général, les murs d’un bâtiments sont solidaires
les uns des autres. On peut envisager d’une manière es u s des aut es O peut e sage d u e a è e
globale leur stabilité.
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-V
V’/2 V’/2-V’V’/2 V /2
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N
d
M
0 sol2 01
'VV2dM'VVN 0
VI
2S
VVN1
d
sol2 I
'VV2dM
S'VVN
V
ISLa résolution du système dés deux équations donne les valeurs de V et V’
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CONTREVENTEMENT PAR PORTIQUES
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PORTIQUE A 3 NIVEAUXPOTEAUX ENCASTRES
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DIAGRMME DES MOMENTSDIAGRMME DES MOMENTS
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DEFORMEEDEFORMEE
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• Le diagramme des moments montre que le moment change de signe au milieu des g gpoteau
• La déformée montre qu’il y a formation de• La déformée montre qu il y a formation de point d’inflexion du poteau
• On peut admettre une articulation au milieu du poteaumilieu du poteau
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