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Nonlinear Analysis of Reinforced Concrete Xuehui AN

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

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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

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Q? Bridge Pier Seismic Movement How to do seismic design

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Pyramid Sunset on Nile Photo by An, 1996.1

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

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Seismic Damage

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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

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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

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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

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

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

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

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

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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

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

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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

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Reinforcement Seismic Design ： Coming Force Prediction Capacity Prediction

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

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

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

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

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

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Design and Evaluation

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

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

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Compression between experimental and analytical result

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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

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

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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

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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

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