Structural Analysis: Using Classical and Matrix Methods, 4th Edition

DEDICATION vii

PREFACE xiii

PART ONE: STATICALLY DETERMINATE STRUCTURES 1

CHAPTER 1 Introduction 3

1.1 Structural Analysis and Design 3

1.2 History of Structural Analysis 4

1.3 Basic Principles of Structural Analysis 7

1.4 Structural Components and Systems 8

1.5 Structural Forces 9

1.6 Structural Idealization (Line Diagrams) 11

1.7 Calculation Accuracy 13

1.8 Checks on Problems 13

1.9 Impact of Computers on Structural Analysis 14

CHAPTER 2 Structural Loads 16

2.1 Introduction 16

2.2 Structural Safety 17

2.3 Specifications and Building Codes 17

2.4 Types of Structural Loads 20

2.5 Dead Loads 20

2.6 Live Loads 21

2.7 Live Load Impact Factors 23

2.8 Live Loads on Roofs 23

2.9 Rain Loads 24

2.10 Wind Loads 26

2.11 Simplified ASCE Procedure for Estimating Wind Loads 29

2.12 Detailed ASCE Procedure for Estimating Wind Loads 31

2.13 Seismic Loads 32

2.14 Equivalent Lateral Force Procedure for Estimating Seismic Loads 34

2.15 Snow Loads 37

2.16 Other Loads 40

2.17 Problems for Solution 41

CHAPTER 3 System Loading and Behavior 43

3.1 Introduction 43

3.2 Tributary Areas 44

3.3 Influence Areas 48

3.4 Live Load Reduction 48

3.5 Loading Conditions for Allowable Stress Design 50

3.6 Loading Conditions for Strength Design 52

3.7 Concept of the Force Envelope 55

3.8 Problems for Solution 56

CHAPTER 4 Reactions 57

4.1 Equilibrium 57

4.2 Moving Bodies 57

4.3 Calculation of Unknowns 58

4.4 Types of Support 59

4.5 Stability, Determinacy, and Indeterminacy 61

4.6 Unstable Equilibrium and Geometric Instability 64

4.7 Sign Convention 65

4.8 Free-Body Diagrams 66

4.9 Horizontal and Vertical Components 67

4.10 Reactions by Proportions 67

4.11 Reactions Calculated by Equations of Statics 68

4.12 Principle of Superposition 71

4.13 The Simple Cantilever 72

4.14 Cantilevered Structures 73

4.15 Reaction Calculations for Cantilevered Structures 75

4.16 Arches 77

4.17 Three-Hinged Arches 78

4.18 Uses of Arches and Cantilevered Structures 83

4.19 Cables 83

4.20 Problems for Solution 88

CHAPTER 5 Shearing Force and Bending Moment 95

5.1 Introduction 95

5.2 Shear Diagrams 97

5.3 Moment Diagrams 98

5.4 Relations Among Loads, Shearing Forces, and Bending Moments 98

5.5 Moment Diagrams Drawn from Shear Diagrams 99

5.6 Shear and Moment Diagrams for Statically Determinate Frames 106

5.7 Shearing Force and Bending Moment Equations 110

5.8 Problems for Solution 112

CHAPTER 6 Introduction to Plane Trusses 117

6.1 Introduction 117

6.2 Assumptions for Truss Analysis 118

6.3 Truss Notation 119

6.4 Roof Trusses 120

6.5 Bridge Trusses 121

6.6 Arrangement of Truss Members 122

6.7 Statical Determinacy of Trusses 123

6.8 Methods of Analysis and Conventions 127

6.9 Method of Joints 129

6.10 Computer Analysis of Statically Determinate Trusses 134

6.11 Example Computer Problem 135

6.12 Problems for Solution 138

CHAPTER 7 Plane Trusses, Continued 143

7.1 Analysis by the Method of Sections 143

7.2 Application of the Method of Sections 144

7.3 Method of Shears 151

7.4 Zero-Force Members 153

7.5 When Assumptions Are Not Correct 155

7.6 Simple, Compound, and Complex Trusses 156

7.7 The Zero-Load Test 157

7.8 Stability 159

7.9 Equations of Condition 161

7.10 Problems for Solution 162

CHAPTER 8 Three-Dimensional or Space Trusses 168

8.1 Introduction 168

8.2 Basic Principles 168

8.3 Equations of Static Equilibrium 169

8.4 Stability of Space Trusses 171

8.5 Special Theorems Applying to Space Trusses 171

8.6 Types of Support 172

8.7 Illustrative Examples 173

8.8 Solution Using Simultaneous Equations 178

8.9 Example Problem with SABLE32 180

8.10 Problems for Solution 182

CHAPTER 9 Influence Lines for Beams 185

9.1 Introduction 185

9.2 The Influence Line Defined 185

9.3 Influence Lines for Simple Beam Reactions 186

9.4 Influence Lines for Simple Beam Shearing Forces 187

9.5 Influence Lines for Simple Beam Moments 188

9.6 Qualitative Influence Lines 189

9.7 Uses of Influence Lines; Concentrated Loads 194

9.8 Uses of Influence Lines; Uniform Loads 195

9.9 Common Simple Beam Formulas from Influence Lines 196

9.10 Determining Maximum Loading Effects Using Influence Lines 197

9.11 Maximum Loading Effects Using Beam Curvature 198

9.12 Impact Loading 199

9.13 Problems for Solution 201

CHAPTER 10 Truss Influence Lines and Moving Loads 204

10.1 Influence Lines for Trusses 204

10.2 Arrangement of Bridge Floor Systems 204

10.3 Influence Lines for Truss Reactions 206

10.4 Influence Lines for Member Forces of Parallel-Chord Trusses 206

10.5 Influence Lines for Members Forces of Nonparallel Chord Trusses 208

10.6 Influence Lines for K Truss 210

10.7 Determination of Maximum Forces 211

10.8 Counters in Bridge Trusses 213

10.9 Live Loads for Highway Bridges 215

10.10 Live Loads for Railway Bridges 219

10.11 Maximum Values for Moving Loads 220

10.12 Problems for Solution 223

CHAPTER 11 Deflections and Angle Changes Using Geometric Methods 225

11.1 Introduction 225

11.2 Sketching Deformed Shapes of Structures 225

11.3 Reasons for Computing Deflections 230

11.4 The Moment-Area Theorems 232

11.5 Application of the Moment-Area Theorems 234

11.6 Analysis of Fixed-End Beams 241

11.7 Maxwell’s Law of Reciprocal Deflections 243

11.8 Problems for Solution 245

CHAPTER 12 Deflections and Angle Changes Using Geometric Methods Continued 248

12.1 The Method of Elastic Weights 248

12.2 Application of the Method of Elastic Weights 249

12.3 Limitations of the Elastic-Weight Method 254

12.4 Conjugate-Beam Method 255

12.5 Summary of Conjugate Beams 257

12.6 Equilibrium 257

12.7 Summary of Beam Relations 258

12.8 Application of the Conjugate Method to Beams 258

12.9 Long Term Deflections 260

12.10 Application of the Conjugate Method to Frames 261

12.11 Problems for Solution 261

CHAPTER 13 Deflection and Angle Changes Using Energy Methods 264

13.1 Introduction to Energy Methods 264

13.2 Conservation of Energy Principle 264

13.3 Virtual Work or Complementary Virtual Work Method 265

13.4 Truss Deflections by Virtual Work 267

13.5 Application of Virtual Work to Trusses 269

13.6 Deflections of Beams and Frames by Virtual Work 273

13.7 Example Problems for Beams and Frames 274

13.8 Rotations or Angle Changes by Virtual Work 281

13.9 Introduction to Castigliano’s Theorems 283

13.10 Castigliano’s Second Theorem 284

13.11 Problems for Solution 289

PART TWO: STATICALLY INDETERMINATE STRUCTURES

Classical Methods

CHAPTER 14 Introduction to Statically Indeterminate Structures 297

14.1 Introduction 297

14.2 Continuous Structures 298

14.3 Advantages of Statically Indeterminate Structures 300

14.4 Disadvantages of Statically Indeterminate Structures 302

14.5 Methods of Analyzing Statically Indeterminate Structures 302

14.6 Looking Ahead 304

CHAPTER 15 Force Methods of Analyzing Statically Indeterminate Structures 305

15.1 Beams and Frames with One Redundant 305

15.2 Beams and Frames with Two or More Redundants 314

15.3 Support Settlement 316

15.4 Problems for Solution 320

CHAPTER 16 Force Methods for Analyzing Statically Indeterminate StructuresContinued 322

16.1 Analysis of Externally Redundant Trusses 322

16.2 Analysis of Internally Redundant Trusses 326

16.3 Analysis of Trusses Redundant Internally and Externally 329

16.4 Temperature Changes, Shrinkage, Fabrication Errors, and So On 330

16.5 Castigliano’s First Theorem 332

16.6 Analysis Using Computers 341

16.7 Problems for Solution 342

CHAPTER 17 Influence Lines for Statically Indeterminate Structures 347

17.1 Influence Lines for Statically Indeterminate Beams 347

17.2 Qualitative Influence Lines 353

17.3 Influence Lines for Statically Indeterminate Trusses 356

17.4 Problems for Solution 360

CHAPTER 18 Slope Deflection: A Displacement Method of Analysis 363

18.1 Introduction 363

18.2 Derivation of Slope-Deflection Equations 363

18.3 Application of Slope Deflection to Continuous Beams 366

18.4 Continuous Beams with Simple Ends 369

18.5 Miscellaneous Items Concerning Continuous Beams 371

18.6 Analysis of Beams with Support Settlement 372

18.7 Analysis of Frames—No Sidesway 374

18.8 Analysis of Frames with Sidesway 376

18.9 Analysis of Frames with Sloping Legs 382

18.10 Problems for Solution 382

PART THREE: STATICALLY INDETERMINATE STRUCTURES

Common Methods in Current Practice

CHAPTER 19 Approximate Analysis of Statically Indeterminate Structures 389

19.1 Introduction 389

19.2 Trusses with Two Diagonals in Each Panel 390

19.3 Continuous Beams 391

19.4 Analysis of Building Frames for Vertical Loads 395

19.5 Analysis of Portal Frames 398

19.6 Analysis of Building Frames for Lateral Loads 400

19.7 Approximate Analyses of Frame Compared to ‘‘Exact’’ Analysis by SABLE32 407

19.8 Moment Distribution 408

19.9 Analysis of Vierendeel ‘‘Trusses’’ 408

19.10 Problems for Solution 410

CHAPTER 20 Moment Distribution for Beams 413

20.1 Introduction 413

20.2 Basic Relations 415

20.3 Definitions 417

20.4 Sign Convention 419

20.5 Application of Moment Distribution 419

20.6 Modification of Stiffness for Simple Ends 424

20.7 Shearing Force and Bending Moment Diagrams 425

20.8 Computer Solution with SABLE32 428

20.9 Problems for Solution 430

CHAPTER 21 Moment Distribution for Frames 433

21.1 Frames with Sidesway Prevented 433

21.2 Frames with Sidesway 435

21.3 Sidesway Moments 437

21.4 Frames with Sloping Legs 447

21.5 Multistory Frames 451

21.6 Computer Analysis of Frame 455

21.7 Problems for Solution 457

CHAPTER 22 Introduction to Matrix Methods 461

22.1 Structural Analysis Using the Computer 461

22.2 Matrix Methods 461

22.3 Review of Matrix Algebra 462

22.4 Force and Displacement Methods of Analysis 462

22.5 Introduction to the Force or Flexibility Method 463

22.6 Problems for Solution 468

CHAPTER 23 Fundamentals of the Displacement or Stiffness Method 470

23.1 Introduction 470

23.2 General Relationships 470

23.3 Stiffness Equations for Axial Force Members 472

23.4 Stiffness Equations for Flexural Members 478

23.5 Stiffness Matrix for Combined Axial and Flexural Members 487

23.6 Characteristics of Stiffness Matrices 489

23.7 Relation Between Stiffness and Flexibility Matrices 490

23.8 Problems for Solution 492

CHAPTER 24 Stiffness Matrices for Inclined Members 494

24.1 General 494

24.2 Axial Force Members 494

24.3 Flexural Members 500

24.4 Loading Between Nodes 510

24.5 Problems for Solution 515

CHAPTER 25 Additional Matrix Procedures 518

25.1 General 518

25.2 Addition of Stiffness Equations 518

25.3 Stiffness Matrices for Inclined Members 520

25.4 Stiffness Equations for Structures with Enforced Displacements 523

25.5 Stiffness Equations for Structures with Members Experiencing Temperature Changes 524

25.6 Stiffness Equations for Structures Whose Members Have Incorrect Lengths 526

25.7 Applications of Matrix Partitioning 526

25.8 Condensation 527

25.9 Band Width of Stiffness Matrices for General Structures 528

25.10 Problems for Solution 531

APPENDICES

APPENDIX A The Catenary Equation 533

APPENDIX B Matrix Algebra 538

B.1 Introduction 538

B.2 Matrix Definitions and Properties 538

B.3 Special Matrix Types 539

B.4 Determinant of a Square Matrix 540

B.5 Adjoint Matrix 541

B.6 Matrix Arithmetic 542

B.7 Gauss’s Method for Solving Simultaneous Equations 547

B.8 Special Topics 548

APPENDIX C Wind, Seismic, and Snow Load Tables and Figures 553

APPENDIX D Computer Analysis of Various Structures Using SAP2000 565

D.1 Introduction 565

D.2 Analysis of Plane Trusses 565

D.3 Analysis of Space Trusses 567

D.4 Analysis of Statically Indeterminate Plane Trusses 568

D.5 Analysis of Composite Structures 570

D.6 Analysis of Continuous Beams and Frames 571

Glossary 573

Index 579