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Chapter 1 Analysis of Framed Structures 1

1.1 Introduction 1

1.2 Force Analysis 2

1.3 Principle of Superposition 2

1.4 Terminology 2

1.5 Stability and Determinacy 3

1.6 Practical Application When n ＝ m 5

1.7 Statically Determinate Structures 6

1.8 Plane Framed Structures 7

Problems 10

Chapter 2 Trusses 15

2.1 Stability and Determinacy 16

2.2 Forces of Interaction／Internal Force Resultants 17

2.3 Force Analysis of Statically Determinate Trusses 19

2.4 Method of Joints 19

2.5 Method of Sections 19

2.6 Conventions and Practice 19

Problems 27

Chapter 3 Internal Force Resultants 37

3.1 Internal and External Force Functions and Diagrams 38

3.2 Shear and Bending Moment Functions and Diagrams for Beams 39

3.3 Relationships Between Internal and External Loads 43

3.4 Shear and Bending Moment Diagrams for Frames 47

Problems 49

Chapter 4 Moveable Loads／Influence Functions and Lines 57

4.1 Influence Functions／Influence Lines 58

4.2 Application of Influence Line Concept 63

4.3 Generalized Application 64

4.4 Floor Girders 67

4.5 Bridge Trusses 69

4.6 Extreme Effects Due to Fixed Loads of Variable Placement 72

Problems 80

Chapter 5 Energy Methods （Part 1） 93

5.1 Introduction 93

5.2 Basic Concepts 93

5.3 Virtual Displacement／Virtual Work 95

5.4 Contacting Surfaces and Forces 96

5.5 Forces 97

5.6 Rigid Displacements 97

5.7 Small Displacements 98

5.8 Rectangular Components 99

5.9 Instantaneous Center 99

5.10 Principle of Virtual Work 100

5.11 Virtual Work of Forces on a Rigid Virtual Displacement 100

5.12 Vector Representations and Work Formulations 102

5.13 Example Problems 103

5.14 Influence Lines 108

Problems 115

Chapter 6 Displacement-Deformation Analysis of Structures 126

6.1 Trusses 128

6.2 Beams 129

6.3 Moment-Area Theorems 130

6.4 Notes for Application of the Moment-Area Theorems 134

6.5 Procedures for Application of the M-A Theorems to Deflection Analysis 135

6.6 Frames 143

6.7 Procedures 144

6.8 Combination Approach 156

Problems 158

Chapter 7 Energy Methods （Part 2） 173

7.1 Introduction 173

7.2 Displacements by Virtual Work 173

7.3 Procedure 175

7.4 Evaluation of δWσ 175

7.5 Basic Applications 178

7.6 Beam 179

7.7 Truss 180

7.8 Displacements Due to Applied Loads 181

7.9 Beams and Frames 182

7.10 Trusses 187

7.11 Combined Loads 191

7.12 Strain Energy and Internal Force-Deformation Relations 194

7.13 Conservative Applied Forces 195

7.14 Principle of Stationary Potential Energy 196

7.15 Principle of Minimum Potential Energy 197

7.16 Complementary Strain Energy and Force-Deformation Relations 198

7.17 The Special Case of Hooke's Law 199

7.18 Betti's Theorem 200

7.19 Maxwell's Reciprocal Theorem 201

7.20 Castigliano's Theorems 203

7.21 Theorem on Deflections 204

7.22 Theorem on Deflections Specialized for Hooke's Law 206

7.23 The Theorem of Least Work 207

7.24 Application of Castigliano's Theorems 209

Problems 211

Chapter 8 Statically Indeterminate Structures 231

8.1 Introduction 231

8.2 General Procedure of Analysis 233

8.3 Member Rigidity 233

8.4 Solution Strategies 233

8.5 Force Method 234

8.6 Displacement Method and Kinematic Indeterminacy 234

8.7 Flexibility and Stiffness： Flexibility Coefficients 235

8.8 Stiffness Coefficients 237

Chapter 9 Force Methods 239

9.1 Method of Consistent Deformation 239

9.2 Use of Superposition 241

9.3 Example Problems 241

9.4 Prescribed Displacements 257

9.5 The Three-Moment Equation 261

9.6 Application Procedure 267

9.7 Combined Methods 271

9.8 Method of Least Work 273

Problems 280

Chapter 10 Displacement Methods of Analysis 308

10.1 Slope-Deflection Equations 310

10.2 Applications 314

10.3 Note on the Equations of Equilibrium 315

10.4 Restatement of the Slope-Deflection Equations 315

10.5 End-Rotations 316

10.6 Examples of Beams and Frames with Prescribed Joint Displacements 316

10.7 Frames with Sidesway 326

10.8 Modified Slope-Deflection Equations 330

10.9 Applications 330

10.10 Sidesway Problems and Superposition 333

10.11 Moment Distribution 339

10.12 One Independent Joint Rotation 343

10.13 Two Independent Joint Rotations 344

10.14 Several Independent Joint Rotations 346

10.15 Non-Zero Prescribed Displacements and Moment Distribution 354

10.16 Sidesway Analysis and Moment Distribution 356

10.17 Equations of Equilibrium by Virtual Work： Matrix Methods 359

10.18 Hooke's Law 366

10.19 Reactions and Virtual Work 369

10.20 Strain Energy of Bending 373

10.21 Potential Energy of Prescribed Loads 376

10.22 Principle of Stationary Potential Energy： Equations of Equilibrium 378

10.23 Matrix Formulations—Summary 379

10.24 Application Procedure 380

Problems 387

Chapter 11 Influence Lines 415

11.1 Introduction 415

11.2 Muller-Breslau Principle 415

11.3 Influence Lines for Deflection 417

11.4 Practical Application 417

Problems 421

Appendix A 424

A.1 Supplemental Notes on the Principle of Virtual Work 424

Appendix B Sidesway Analysis 428

B.1 General Formulation and Superposition 428

B.2 General Formulation 428

B.3 Superposition 430

Answers 432

References 451

Index 453