Nonlinear Analysis of Reinforced Concrete

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Nonlinear Analysis of Reinforced Concrete
Xuehui AN
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Todays Agenda

• Review of last weeks lecture
• Constitutive Models for RC (3)
• Todays Topic

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1 Method of Modeling 2 Concrete Model Prior to
Generation of Cracks (1) Elasto-Plastic and
Fracture Model (2) Cracking Criteria 3
Modeling of Cracked Concrete (1) Modeling of
Concrete under Tensile Stress (2) Modeling of
Concrete under Compressive stress (3) Modeling
of Concrete under Shear Stress (4)
Inter-relation of Each Model 4 Modeling of
Reinforcing Bar in Concrete 5 Verification
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(1) Modeling of Concrete under Tensile Stress
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(1) Modeling of Concrete under Tensile Stress
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(1) Modeling of Concrete under Tensile Stress
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Fracture energy based stress-strain model for
concrete
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Fracture energy based stress-strain model for
concrete From real crack band to finite element
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Fracture energy based stress-strain model for
concrete Applied in FEM Analysis
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Stress
Concrete
Strain
100-200 micro
Stress
Steel
Strain
2000-3000 micro
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Reinforced Concrete
Total Force
Steel Force
Tension Softening
Cracking
Tension Stiffening
Concrete
Steel
Average Strain
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Deformed Bar
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Stress
Concrete
Ac
Strain
100-200 micro

Stress
Steel
Strain
As
2000-3000 micro
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Fine Elements
One Element
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Total Force Steel Force (x) Concrete Force
(x)
Steel Force Steel Stress (x) As
Concrete Force Concrete Stress (x) Ac
AAsAc
x
Total Force
Total Force
(x)
(x)
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Total Force Steel Force (x) Concrete Force
(x)
Steel Force Steel Stress (x) As
Concrete Force Concrete Stress (x) Ac
AAsAc
x
Total Force
Total Force
(x)
Stress
Stress
Strain
Strain
?
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Concrete
100-200 micro
Stress
Steel
Strain
2000-3000 micro
Total Force - Steel Force (x) Concrete Force
(x)
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Concrete
Steel
Total Force
Steel Force
Average Concrete Force
Average Steel Force
Average Strain
Total Force Average Steel Force Average
Concrete Force
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Reinforced Concrete
Total Force
Steel Force
Total Force
Average Concrete Force
Average Steel Force
Average Strain
Total Force Average Steel Force Average
Concrete Force
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Reinforced Concrete
Total Force
Steel Force
Average
Total Force
Local
Strain distribution
Average Concrete Force
Stress distribution
Average Steel Force
Average Strain
Steel strain at cracking location
Total Force Average Steel Force Average
Concrete Force
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Stress-strain for steel in RC
Total Force
Steel Force
Average yielding strength
Average Concrete Force
Average yielding
Average Steel Force
Average Strain
Average Strain
Steel strain at cracking location
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stress
2
strain
Yield plateau jump!
Stress distribution
Strain distribution
stress
stress
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3
strain
strain
Plastic zone
Stress distribution
Strain distribution
Strain distribution
Stress distribution
Plastic zone
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Stress-Strain Relationship of Concrete in Tension
by Vecchio and Collins
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Stress-strain relationship of concrete in tension
by Okamura et al.
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Todays Topic

• English Ability