Nonlinear Analysis of Reinforced Concrete

1. Nonlinear Analysis of Reinforced Concrete Xuehui AN

2. Today’s Agenda • Review of last week’s lecture • Constitutive Models for RC (3) • Today’s Topic

3. 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

4. (1) Modeling of Concrete under Tensile Stress

5. (1) Modeling of Concrete under Tensile Stress

6. (1) Modeling of Concrete under Tensile Stress

7. Fracture energy based stress-strain model for concrete

8. Fracture energy based stress-strain model for concrete From real crack band to finite element

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

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

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

12. Deformed Bar

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

20. Concrete Steel FEM Model Cracking Fine Elements One Element

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

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

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

25. Concrete Steel Total Force Steel Force Average Concrete Force Average Steel Force Average Strain Total Force – Average Steel Force = Average Concrete Force

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

27. 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

28. 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

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

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

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

50. Today’s Topic • English Ability