conventions de base dans scia engineer - imac.epfl.ch · scia engineer petite introduction &...
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SCIA EngineerPetite introduction & conventions de base
Author: Stéphane Rossier
Date: 19 April 2018
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Version étudiant
Documentation
Version étudiant gratuite
Didacticiels complets
http://www.scia-campus.com/
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Terminologie
10
…peut différer par rapport à la théorie
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Terminologie
Portique
Cadre
Treillis
Structure composée de barres
Grille
Grille de poutres
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Terminologie
Barre
Barre ou poutre en général
Poutre
Barre ou poutre horizontale
Poteau
Barre ou poutre verticale
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Principes de calcul
13
Éléments finis vs calcul manuel
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Déformations d’un élément
u1 dxEI
MM
L
1
Flexion
dxGA
VV
L
'
1
Effort tranchant
dxEA
NN
L
1
Effort normal
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Déformations d’un élément
Flexion
Effort tranchant
Effort normal
𝐿
𝑀𝑦1𝑀𝑦
𝐸𝐼𝑦⋅ 𝑑𝑥
𝐿
𝑀𝑧1𝑀𝑧𝐸𝐼𝑧
⋅ 𝑑𝑥
𝐿
𝑉𝑦1𝑉𝑦
𝐺𝐴′𝑦⋅ 𝑑𝑥
𝐿
𝑉𝑧1𝑉𝑧𝐺𝐴′𝑧
⋅ 𝑑𝑥
𝐿
𝑁1𝑁
𝐸𝐴⋅ 𝑑𝑥
𝐿
𝑇1𝑇
𝐺𝐽⋅ 𝑑𝑥
1 ⋅ 𝑢 = + + +
+ +
Torsion
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Influence des déformations d’effort normal
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Influence des déformations d’effort normal
Déformées
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Influence des déformations d’effort normal
Moments de flexion
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Influence des déformations d’effort normal
Réactions d’appuis
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Influence des déformations d’effort tranchant
sans déformations
d’effort tranchant
h/L = 16
h/L = 8
h/L = 4
Moment de flexion avec déformations
d’effort tranchant
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sans déformations
d’effort tranchant
avec déformations
d’effort tranchant
Influence des déformations d’effort tranchant
h/L = 16
h/L = 8
h/L = 4
Flèche
+4%
+18%
+71%
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Conventions
22
Axes locaux & signes
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Efforts intérieurs – convention de signes
X
Y
Z
N
Vz
VyN
Vy
Vz
Effort normal et efforts tranchants
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Efforts intérieurs – convention de signes
Moment de flexion – axe fort
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Efforts intérieurs – convention de signes
Moment de flexion – axe faible
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Efforts intérieurs – convention de signes
Moment de torsion
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Axes locaux d’un élément
A
B
XY
Z
X’ = AB
X’
Y’ = Z X’Y’
Z’
Z’ = X’ Y’A
B
X’ = axe de l’élément
Y’ = dans un plan horizontal,
perpendiculaire à l’élément
Z’ = dans un plan vertical,
perpendiculaire à l’élément
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Axes locaux d’un élément vertical
A
B
X’
Y’
Z’
X’ = AB
Y’ = YZ’ = X’ Y’
XY
Z
A
B
X’ = axe de l’élément
Y’ = identique à l’axe global Y
Z’ = opposé à l’axe global X
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