Preface ix
Acknowledgments xi
Acronyms xiii
About the Companion Website xix
Part I Linear Analysis 1
1 A Primer on Matrix Structural Analysis 3
1.1 The Force Method 4
1.2 The Displacement Method 7
1.3 Matrix Structural Analysis 9
1.4 Formulation of the 1D Bar Element 12
1.5 Partitioning and the Solution of Matrix Equations 13
1.6 Computer Code 17
1.7 Summary 23
1.8 Practice Problems 24
2 Plane Trusses 27
2.1 Derivation of the Local Stiffness: Direct Stiffness Method 27
2.2 Derivation of the Local Stiffness: Flexibility Method 29
2.3 Coordinate Transformation and Global Stiffness 32
2.4 Calculating Internal Forces 37
2.5 Temperature Change 43
2.6 Inclined Supports 48
2.7 Computer Code 50
2.8 Summary 52
2.9 Practice Problems 53
Reference 55
3 Plane Beams 57
3.1 Elastic Beam Theory 57
3.2 Derivation of the Stiffness Matrix: Direct Stiffness Method 59
3.3 Derivation of the Stiffness Matrix: Flexibility Method 64
3.4 Member Loads 67
3.5 Releases (Hinges) 71
3.6 Shear Deformations 75
3.7 Computer Code 77
3.8 Summary 80
3.9 Practice Problems 82
Reference 84
4 Plane Frames 85
4.1 Derivation of the Local Stiffness Matrix: Direct Stiffness Method 85
4.2 Derivation of the Local Stiffness Matrix: Flexibility Method 86
4.3 Coordinate Transformations 89
4.4 Releases (Hinges) 96
4.5 Constraints 101
4.6 Computer Code 105
4.7 Summary 107
4.8 Practice Problems 108
Reference 110
5 Space Trusses and Frames 111
5.1 Overview of 3D Elements 111
5.2 Torsion 112
5.3 Combined Flexure and Torsion 114
5.4 3D Elements in Local Coordinates 115
5.5 Coordinate Transformations 118
5.6 Calculation of the Direction Cosines 120
5.7 Element Stiffness in Global Coordinates 124
5.8 Computer Code 129
5.9 Summary 129
5.10 Practice Problems 129
References 131
Part II Nonlinear Analysis 133
6 Introduction to Nonlinear Analysis 135
6.1 Overview 135
6.2 Material Nonlinear Analysis 137
6.3 Geometric Nonlinear Analysis 145
6.4 Levels of Analysis 150
6.5 Summary 153
6.6 Practice Problems 153
References 155
7 Solving Nonlinear Systems of Equations 157
7.1 Newtonâ"Raphson Method 157
7.2 Modified Newtonâ"Raphson Method 164
7.3 Hardening Curves 165
7.4 Limitations 168
7.5 Summary 168
7.6 Practice Problems 169
References 170
8 Geometric Nonlinear Analysis 171
8.1 Total Lagrangian Formulation 172
8.2 Determining Critical Loads Using Eigenvalue Analysis 181
8.3 Corotational Formulation 186
8.4 Determining Critical Loads Using Incremental, Iterative Analysis 190
8.5 Summary 192
8.6 Practice Problems 193
References 196
9 Nonlinear Material and Section Responses for Steel and Concrete 197
9.1 Fundamentals of Material Behavior 198
9.2 Uniaxial Plasticity Models 201
9.3 Loading, Unloading, Reloading, and Reversed Loading 204
9.4 Plasticity in 2D and 3D 212
9.5 Computer Code for Nonlinear Stressâ"Strain Models 213
9.6 Section Forceâ"Deformation Relationships 214
9.7 Interaction Diagrams 216
9.8 Summary 218
9.9 Practice Problems 219
References 219
10 Material Nonlinear Analysis 221
10.1 Virtual Work Formulation 221
10.2 Lumped Plasticity Frame Element 225
10.3 Distributed Plasticity Frame Element 232
10.4 Combined Geometric and Material Nonlinear Analysis 249
10.5 Summary 250
10.6 Practice Problems 250
References 253
Part III Advanced Topics 255
11 Joints and Connections 257
11.1 Rigid Offsets 257
11.2 Panel Zone Deformations 261
11.3 Connections and the Component Model 263
11.4 Summary 267
References 267
12 Slabs and Shear Walls 269
12.1 Shell Elements 270
12.2 Compatibility Between Shell and Frame Elements 273
12.3 Slabs 274
12.4 Composite Beams 276
12.5 Shear Walls 277
12.6 Summary 279
References 279
13 Nonlinear Static Pushover Analysis 281
13.1 Analysis Procedure 282
13.2 Leaning Columns 283
13.3 Steel Concentrically Braced Frame 285
13.4 Reinforced Concrete Moment Frame 290
13.5 Summary 293
References 294
A Linear Algebra 295
A. 1 Matrix Properties 295
A. 2 Matrix Operations 296
A. 3 Gauss Elimination 300
A. 4 Ill-conditioning in Matrix Structural Analysis 305
A. 5 Banded Matrices and Sparse Matrix Storage 306
Reference 307
B Error Analysis 309
B. 1 Sources of Error 309
B. 2 Quantification of Error 310
B. 3 Verification and Validation 310
Index 313
