Theory of Nonlinear Structural Analysis

Gang Li, Dalian University of Technology, ChinaKevin K.F. Wong, Ph.D., University of California Los Angeles, USA

• Preface ixAbout the Authors xi1 Introduction 11.1 History of the Force Analogy Method 11.2 Applications of the Force Analogy Method 41.2.1 Structural Vibration Control 41.2.2 Modal Dynamic Analysis Method 61.2.3 Other Design and Analysis Areas 61.3 Background of the Force Analogy Method 6References 142 Nonlinear Static Analysis 172.1 Plastic Rotation 172.2 Force Analogy Method for Static Single-Degree-of-Freedom Systems 192.2.1 Inelastic Displacement 192.2.2 Application of the FAM on SDOF System 202.2.3 Nonlinear Analysis Using FAM 222.3 Nonlinear Structural Analysis of Moment-Resisting Frames 262.4 Force Analogy Method for Static Multi-Degree-of-Freedom Systems 312.5 Nonlinear Static Examples 362.6 Static Condensation 52References 613 Nonlinear Dynamic Analysis 633.1 State Space Method for Linear Dynamic Analysis 633.1.1 Equation of Motion 643.1.2 State Space Solution 663.1.3 Solution Procedure 683.2 Dynamic Analysis with Material Nonlinearity 723.2.1 Force Analogy Method 723.2.2 State Space Analysis with the Force Analogy Method 743.2.3 Solution Procedure 763.3 Nonlinear Dynamic Analysis with Static Condensation 873.4 Nonlinear Dynamic Examples 99References 1094 Flexural Member 1114.1 Bending and Shear Behaviors 1114.1.1 Hysteretic Models 1114.1.2 Displacement Decomposition 1134.1.3 Local Plastic Mechanisms 1154.2 Inelastic Mechanisms of Flexural Members 1154.2.1 Elastic Displacement X’ 1164.2.2 Plastic Bending Displacement X1’’ 1174.2.3 Plastic Shear Displacement X2’’ 1174.2.4 Combination of the Bending and Shear Behaviors 1174.3 Nonlinear Static Analysis of Structures with Flexural Members 1184.3.1 Force Analogy Method for Static Single-Degree-of-Freedom Systems 1184.3.2 Force Analogy Method for Static Multi-Degree-of-Freedom Systems 1294.4 Nonlinear Dynamic Analysis of Structures with Flexural Members 1434.4.1 Hysteretic Behaviors of the Flexural Members 1434.4.2 Solution Procedure of the FAM 146References 1595 Axial Deformation Member 1615.1 Physical Theory Models for Axial Members 1615.1.1 General Parameters 1625.1.2 Displacement Decomposition 1635.2 Sliding Hinge Mechanisms 1645.3 Force Analogy Method for Static Axial Members 1665.3.1 Regions O–Aa and O–F 1665.3.2 Region F–G 1665.3.3 Regions Aa–A and A–B 1675.4 Force Analogy Method for Cycling Response Analysis of Axial Members 1705.4.1 Region B–C 1705.4.2 Region C–D 1715.4.3 Region D’–A2 1725.4.4 Region D–E 1735.4.5 Region E–F 1745.4.6 Region Aa2–A2 1745.5 Application of the Force Analogy Method in Concentrically Braced Frames 1785.5.1 Force Analogy Method for Static SDOF CBFs 1785.5.2 Force Analogy Method for Static MDOF CBFs 1825.5.3 Force Analogy Method for Dynamical CBFs under Earthquake Loads 188References 1946 Shear Member 1956.1 Physical Theory Models of Shear Members 1956.1.1 Flexural Behavior 1956.1.2 Axial Behavior 1976.1.3 Shear Behavior 1976.2 Local Plastic Mechanisms in the FAM 1986.2.1 Displacement Decomposition 1986.2.2 Behavior of VSH 1996.2.3 Behavior of HSH 2006.3 Nonlinear Static Analysis of the Shear Wall Structures 2016.4 Nonlinear Dynamic Analysis of RC Frame-Shear Wall Structures 2226.4.1 Hysteretic Behaviors of the RC Shear Wall Members 2226.4.2 Solution Procedure of the FAM 224References 2347 Geometric Nonlinearity 2357.1 Classical Stiffness Matrices with Geometric Nonlinearity 2367.1.1 The P-Δ Approach 2377.1.2 The Geometric Stiffness Approach 2387.2 Stability Functions 2397.2.1 Stiffness Matrix [ki] 2407.2.2 Stiffness Matrix [ki’ ] 2447.2.3 Stiffness Matrix [Ki’’] 2467.3 Force Analogy Method with Stability Functions 2507.4 Nonlinear Dynamic Analysis Using Stability Functions 2617.4.1 Force Analogy Method 2617.4.2 Nonlinear Dynamic Analysis with the Force Analogy Method 2627.4.3 State Space Analysis with Geometric and Material Nonlinearities 2637.5 Nonlinear Dynamic Analysis with Static Condensation Using Stability Functions 2727.6 Nonlinear Dynamic Examples 283References 2948 Application of the Force Analogy Method in Modal Superposition 2978.1 Nonlinear Static Pushover Analysis in the FAM 2988.1.1 NSPA for Mass-Normalized SDOF Systems 2998.1.2 NSPA for Multi-Degree-of-Freedom Systems 3038.2 Modal Decomposition in the FAM 3128.3 Modal Response Summation 3188.4 Nonlinear Modal Superposition Method Example 319References 3299 Application: Structural Vibration Control 3319.1 Passive Control Technique 3319.1.1 Model of Passive Energy-Dissipation Devices 3319.1.2 Model of Framed Structures with PEDDs 3339.1.3 Force Analogy Method for Dynamical Analysis of Multi-Degree-Freedom Systems 3349.2 Application of the FAM in Active or Semi-Active Structural Control 3369.2.1 Background of MBC 3369.2.2 Force Analogy Method in Market-Based Control 342References 349Index 351