Nonlinear Analysis of Reinforced Concrete Xuehui AN

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

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

Q? Bridge Pier Seismic Movement How to do seismic design

Pyramid Sunset on Nile Photo by An,

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

Seismic Damage

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

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× /C

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

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

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

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

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

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

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

Compression strength ： 300 ～ 700kg/cm 2 Concrete ： Tensile strength ： 10 ～ 30kg/cm 2 Compression strength ： 3000 ～ 7000kg/cm 2 Steel ： Tensile strength ： 3000 ～ 7000kg/cm 2 Compression ： concrete RC Tension ： steel Crack Steel

Reinforcement Seismic Design ： Coming Force Prediction Capacity Prediction

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

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

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

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

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

Design and Evaluation

Performance Design Process Design Evaluation Engineering Judgment Computer Simulation Design Nonlinear FEM DataAnalysisOutput Yes/No Example:

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

Compression between experimental and analytical result

General Methods Constitutive ModelsExperimental 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

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

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

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 Chapter 2