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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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Fracture energy based stress-strain model for concrete

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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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Concrete Stress Strain Steel Stress Strain 2000-3000 micro 100-200 micro

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Reinforced Concrete Total Force Average Strain Steel Force Tension Stiffening Concrete Steel Stress Strain Tension Softening Cracking

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Deformed Bar

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Concrete Stress Strain Steel Stress Strain 2000-3000 micro 100-200 micro As Ac +

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Concrete Steel CrackingFEM Model One Element Fine Elements

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Total Force Total Force = Steel Force ( x ) + Concrete Force ( x ) Steel Force= Steel Stress ( x ) * As Concrete Force= Concrete Stress ( x ) * Ac A=As+Ac x (x)(x) (x)(x)

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Total Force Total Force = Steel Force ( x ) + Concrete Force ( x ) Steel Force= Steel Stress ( x ) * As Concrete Force= Concrete Stress ( x ) * Ac A=As+Ac x (x)(x) Stress Strain Stress Strain ?

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Concrete Steel Stress Strain 2000-3000 micro 100-200 micro Stress Strain Total Force - Steel Force ( x ) = Concrete Force ( x )

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ConcreteSteel Total Force Average Strain Steel Force Total Force – Average Steel Force = Average Concrete Force Average Concrete Force Average Steel Force

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Reinforced Concrete Total Force Average Strain Steel Force Total Force – Average Steel Force = Average Concrete Force Average Concrete Force Average Steel Force Total Force

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Reinforced Concrete Total Force Average Strain Steel Force Total Force – Average Steel Force = Average Concrete Force Average Concrete Force Average Steel Force Total Force Stress distribution Strain distribution Average Local Steel strain at cracking location

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Total Force Average Strain Steel Force Average Concrete Force Average Steel Force Average yielding Steel strain at cracking location Average Strain Average yielding strength Stress-strain for steel in RC

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Yield plateau jump! Stress distribution stress strain Plastic zone stress strain Strain distribution Stress distribution Strain distribution Plastic zone Stress distribution strain stress Strain distribution Average Local 1 4 3 2

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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

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