Nonlinear Analysis of Reinforced Concrete Xuehui AN

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

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

(1) Modeling of Concrete under Tensile Stress

Fracture energy based stress-strain model for concrete

From real crack band to finite element

Fracture energy based stress-strain model for concrete Applied in FEM Analysis

Concrete Stress Strain Steel Stress Strain micro micro

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

Deformed Bar

Concrete Stress Strain Steel Stress Strain micro micro As Ac +

Concrete Steel CrackingFEM Model One Element Fine Elements

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)

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 ?

Concrete Steel Stress Strain micro micro Stress Strain Total Force - Steel Force ( x ) = Concrete Force ( x )

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

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

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

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

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

Stress-Strain Relationship of Concrete in Tension by Vecchio and Collins

Stress-strain relationship of concrete in tension by Okamura et al.

Todays Topic English Ability