Nonlinear Analysis of Reinforced Concrete

1. Nonlinear Analysis of Reinforced Concrete Xuehui AN

2. Today’s Agenda • Review of last week’s lecture • Seismic Design Concept • Basic Knowledge of RC • Constitutive Models for RC

3. Life-Cycle-Cost Life-Cycle-Management Construction Material study Structural performance study Lease Resale Management Insurance Cost Management Information Technology Environment Society Design Serving Geographic Geological Study Investigation Structural performance evaluation Recycle Maintaining / Repair Material study A Sustainable World

4. Q? How to do seismic design Seismic Movement Bridge Pier

5. Pyramid Sunset on Nile Photo by An, 1996.1

6. Presenting my first paper in the International Conference on Seismic Design, Cairo University, Egypt

7. Seismic Damage

8. Failure： Limited state design method Load (Force) ＞Capacity Local damage Stress＞strength Allowable stress design method Tensile stress＞Tensile strength Compression stress＞Compression strength Shear stress＞Shear strength Experiment Elastic Mechanics

9. Structure using material of concrete • Concrete: • Good at compression • Weak in tension • Free shape • Heavy • Easy to get • Using of cement • Strong in fire Steel: Good to work with concrete, Similar thermal expansion coefficient with concrete Expensive 10×10-6 1/C

10. Structure using material of RC • Concrete: • Good at compression • Weak in tension • Free shape • Heavy • Easy to get • Using of cement • Strong in fire Steel: Good to work with concrete, Similar thermal expansion coefficient with concrete Expensive Main reinforcement Web reinforcement

11. Collapse of RC structures • Reinforced Concrete (Main reinforcement, Web reinforcement) • Shear failure：diagonal crack • Flexure failure：bending crack, compression failure

12. Collapse of RC structures • Reinforced Concrete (Main reinforcement, Web reinforcement) • Flexure failure：bending crack, compression failure

13. Collapse of RC structures • Reinforced Concrete (Main reinforcement, Web reinforcement) • Shear failure：diagonal crack

14. Collapse of RC structures • Reinforced Concrete (Main reinforcement, Web reinforcement) • Shear failure：diagonal crack

15. Failure： Limited state design method Load (Force) ＞Capacity Local damage Stress＞strength Allowable stress design method Tensile stress＞Tensile strength Steel Compression stress＞Compression strength Concrete Shear stress＞Shear strength Experiment Elastic Mechanics

16. ②Material： Concrete + Steel (reinforcement) Main reinforcement Web reinforcement

17. Compression strength：300～700kg/cm2 Concrete： Tensile strength：10～30kg/cm2 Compression strength：3000～7000kg/cm2 Steel： Tensile strength：3000～7000kg/cm2 Compression：concrete RC Tension：steel Crack Steel

18. Seismic Design： Coming Force Prediction Capacity Prediction Reinforcement

19. Seismic Performance: Design and Evaluation Bidding Performance Requirement Design Evaluation Performance Design Construction Serving

20. Seismic Performance: Design and Evaluation Performance Requirement Small Earthquake: No damage Big Earthquake: No collapse

21. Performance Design Concept Ductility Capacity Yield of main reinforcement Force Force Deformation Flexural failure Collapse Shear failure Collapse Shear Bending cracking Bending Deformation Area of Section

22. shear bending Performance Design Concept Ductility Capacity Absorb Seismic Energy Damage Control Flexible Design

23. Seismic Performance: Design and Evaluation Bidding Performance Requirement Design Evaluation Performance Design Construction Experiment Analysis Analysis + Experiment Serving

24. Design and Evaluation

25. Performance Design Process Engineering Judgment Design Computer Simulation Evaluation Example: Nonlinear FEM Yes/No Design Data Analysis Output

26. EFM ANALYSIS Assemble Element Structure Element Behavior by experiment Structure Behavior Prediction

27. Compression between experimental and analytical result

28. General Methods Constitutive Models Experimental Results constitutive adj. Making a thing what it is; essential. 本质的；基本的 Having power to institute, establish, or enact. 有设立权的有创建、建立或制订权力的 Stress-Strain relationship Digital experiment

29. EFM ANALYSIS Assemble Element Structure Element Behavior by experiment Structure Behavior Prediction

33. General Methods Constitutive Models Experimental Results Modeling Concrete, Reinforcement, Bond, Crack Microstructure, bond Level 0 Modeling Modeling 1-D RC stress-strain Bond 1-D Stress RC Level 1 Modeling Modeling 2-D RC stress-strain 2-D Stress RC Plates Level 2 Modeling Modeling 2-D RC Members Force-Deformation 2-D RC Members Level 3

34. Chapter 2 Reinforced Concrete Plate Element Model 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