A comprehensive book focusing on the Force Analogy Method, a novel method for nonlinear dynamic analysis and simulation This book focusses on the Force Analogy Method, a novel method for nonlinear dynamic analysis and simulation.

Preface ix About the Authors xi 1 Introduction 1 1.1 History of the Force Analogy Method 1 1.2 Applications of the Force Analogy Method 4 1.2.1 Structural Vibration Control 4 1.2.2 Modal Dynamic Analysis Method 6 1.2.3 Other Design and Analysis Areas 6 1.3 Background of the Force Analogy Method 6 References 14 2 Nonlinear Static Analysis 17 2.1 Plastic Rotation 17 2.2 Force Analogy Method for Static Single-Degree-of-Freedom Systems 19 2.2.1 Inelastic Displacement 19 2.2.2 Application of the FAM on SDOF System 20 2.2.3 Nonlinear Analysis Using FAM 22 2.3 Nonlinear Structural Analysis of Moment-Resisting Frames 26 2.4 Force Analogy Method for Static Multi-Degree-of-Freedom Systems 31 2.5 Nonlinear Static Examples 36 2.6 Static Condensation 52 References 61 3 Nonlinear Dynamic Analysis 63 3.1 State Space Method for Linear Dynamic Analysis 63 3.1.1 Equation of Motion 64 3.1.2 State Space Solution 66 3.1.3 Solution Procedure 68 3.2 Dynamic Analysis with Material Nonlinearity 72 3.2.1 Force Analogy Method 72 3.2.2 State Space Analysis with the Force Analogy Method 74 3.2.3 Solution Procedure 76 3.3 Nonlinear Dynamic Analysis with Static Condensation 87 3.4 Nonlinear Dynamic Examples 99 References 109 4 Flexural Member 111 4.1 Bending and Shear Behaviors 111 4.1.1 Hysteretic Models 111 4.1.2 Displacement Decomposition 113 4.1.3 Local Plastic Mechanisms 115 4.2 Inelastic Mechanisms of Flexural Members 115 4.2.1 Elastic Displacement X’ 116 4.2.2 Plastic Bending Displacement X1’’ 117 4.2.3 Plastic Shear Displacement X2’’ 117 4.2.4 Combination of the Bending and Shear Behaviors 117 4.3 Nonlinear Static Analysis of Structures with Flexural Members 118 4.3.1 Force Analogy Method for Static Single-Degree-of-Freedom Systems 118 4.3.2 Force Analogy Method for Static Multi-Degree-of-Freedom Systems 129 4.4 Nonlinear Dynamic Analysis of Structures with Flexural Members 143 4.4.1 Hysteretic Behaviors of the Flexural Members 143 4.4.2 Solution Procedure of the FAM 146 References 159 5 Axial Deformation Member 161 5.1 Physical Theory Models for Axial Members 161 5.1.1 General Parameters 162 5.1.2 Displacement Decomposition 163 5.2 Sliding Hinge Mechanisms 164 5.3 Force Analogy Method for Static Axial Members 166 5.3.1 Regions O–Aa and O–F 166 5.3.2 Region F–G 166 5.3.3 Regions Aa–A and A–B 167 5.4 Force Analogy Method for Cycling Response Analysis of Axial Members 170 5.4.1 Region B–C 170 5.4.2 Region C–D 171 5.4.3 Region D’–A2 172 5.4.4 Region D–E 173 5.4.5 Region E–F 174 5.4.6 Region Aa2–A2 174 5.5 Application of the Force Analogy Method in Concentrically Braced Frames 178 5.5.1 Force Analogy Method for Static SDOF CBFs 178 5.5.2 Force Analogy Method for Static MDOF CBFs 182 5.5.3 Force Analogy Method for Dynamical CBFs under Earthquake Loads 188 References 194 6 Shear Member 195 6.1 Physical Theory Models of Shear Members 195 6.1.1 Flexural Behavior 195 6.1.2 Axial Behavior 197 6.1.3 Shear Behavior 197 6.2 Local Plastic Mechanisms in the FAM 198 6.2.1 Displacement Decomposition 198 6.2.2 Behavior of VSH 199 6.2.3 Behavior of HSH 200 6.3 Nonlinear Static Analysis of the Shear Wall Structures 201 6.4 Nonlinear Dynamic Analysis of RC Frame-Shear Wall Structures 222 6.4.1 Hysteretic Behaviors of the RC Shear Wall Members 222 6.4.2 Solution Procedure of the FAM 224 References 234 7 Geometric Nonlinearity 235 7.1 Classical Stiffness Matrices with Geometric Nonlinearity 236 7.1.1 The P-Δ Approach 237 7.1.2 The Geometric Stiffness Approach 238 7.2 Stability Functions 239 7.2.1 Stiffness Matrix [ki] 240 7.2.2 Stiffness Matrix [ki’ ] 244 7.2.3 Stiffness Matrix [Ki’’] 246 7.3 Force Analogy Method with Stability Functions 250 7.4 Nonlinear Dynamic Analysis Using Stability Functions 261 7.4.1 Force Analogy Method 261 7.4.2 Nonlinear Dynamic Analysis with the Force Analogy Method 262 7.4.3 State Space Analysis with Geometric and Material Nonlinearities 263 7.5 Nonlinear Dynamic Analysis with Static Condensation Using Stability Functions 272 7.6 Nonlinear Dynamic Examples 283 References 294 8 Application of the Force Analogy Method in Modal Superposition 297 8.1 Nonlinear Static Pushover Analysis in the FAM 298 8.1.1 NSPA for Mass-Normalized SDOF Systems 299 8.1.2 NSPA for Multi-Degree-of-Freedom Systems 303 8.2 Modal Decomposition in the FAM 312 8.3 Modal Response Summation 318 8.4 Nonlinear Modal Superposition Method Example 319 References 329 9 Application: Structural Vibration Control 331 9.1 Passive Control Technique 331 9.1.1 Model of Passive Energy-Dissipation Devices 331 9.1.2 Model of Framed Structures with PEDDs 333 9.1.3 Force Analogy Method for Dynamical Analysis of Multi-Degree-Freedom Systems 334 9.2 Application of the FAM in Active or Semi-Active Structural Control 336 9.2.1 Background of MBC 336 9.2.2 Force Analogy Method in Market-Based Control 342 References 349 Index 351

Nonlinear structural analysis in civil engineering is not a new topic. The Force Analogy Method as a relatively new algorithm was first developed in 1999 for solving nonlinear dynamic analysis problems. Conventional methods for calculating the nonlinear behavior of civil engineering structures use the analysis procedure of changing the structural member stiffness, while structural dynamics is incorporated into the procedure through implicit time integration of the varying stiffness matrices. Examples of these conventional methods include the Wilson-and Newmark- methods. In these conventional methods, the major problem is that significant iterative computations in updating the time-varying stiffness matrices have to be performed to ensure numerical convergence once the structure experiences yielding and nonlinear deformation. As a result, the iterative operation is time consuming and the entire dynamic analysis process becomes practically uneconomical. By using the force analogy method, on the other hand, the state-transition matrix needs to be computed only once due to the constant use of the initial stiffness of the structure, and this greatly simplifi es the overall computation and makes the nonlinear analysis readily available for solving various practical problems. The book: Introduces an analytical/computational method of nonlinear analysis of structure –the Force Analogy MethodCovers both the theoretical background and practical applications in seismic analysis of structuresNew topic, not currently covered in any books, authored by experts in the area This book is essential reading for professional scientists, engineers and researchers in structural engineering. Graduate and undergraduate students in civil engineering, software developers will also find it helpful.