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Chapter 1 Introduction to Structural Engineering 1

1.1 Description of Structural Analysis and Structural Design 2

Proof of Performance 3

Value of Analysis of Simple Structures 4

1.2 Idealization of a Structure 5

Types of Structures 6

Mathematical Model of a Single Member 7

Mathematical Model of an Assembly of Members 9

1.3 Types of Loads on Structures 12

1.4 Specification of Loading 13

1.5 Internal Stresses 14

1.6 Free-Body Diagrams 19

1.7 Equilibrium Conditions for Planar Structures 20

1.8 Superposition of Forces in Statically Determinate Structures 23

1.9 Superposition of Deformations 25

1.10 Symmetric and Antisymmetric Loading of Symmetric Structures 27

Symmetrically Loaded Symmetric Structures 28

Antisymmetrically Loaded Symmetric Structures 30

General Loading of Symmetric Structures 32

1.11 Summary and Limitations 35

Chapter 2 Computation of Reactions for Planar Statically Determinate Structures 39

2.1 Static Determinacy of Reactions and Equations of Condition 40

Equations of Condition for Plane Frames 41

Equations of Condition for Plane Trusses 43

Examples of Statically Determinate Reactions 45

2.2 Geometric Stability 48

2.3 Computation of Reactions for Structures with Concentrated Loads 56

2.4 Computation of Reactions for Structures with Distributed Loads 60

2.5 Reactions for Symmetric Structures 62

2.6 Summary and Limitations 70

Problems 72

Computer Problems 76

Chapter 3 Analysis of Plane Trusses 79

3.1 Truss Action 80

3.2 Unknowns and Assumptions in Truss Analysis 83

3.3 Determinacy and Geometric Stability 86

3.4 Plane Truss Analysis by the Method of Joints 91

3.5 Special Considerations at Truss Joints 99

3.6 Truss Analysis by the Method of Sections 104

3.7 Summary and Limitations 112

Problems 116

Computer Problems 121

Chapter 4 Analysis of Beams： Shear， Moment， and Axial Force Diagrams 123

4.1 Sign Convention 124

4.2 Differential Equations of Equilibrium for a Transversely Loaded Beam 125

4.3 Drawing Shear and Moment Diagrams Using Direct Integration 126

4.4 Drawing Shear and Moment Diagrams Using Equilibrium Directly 131

4.5 Relationships Between Loading， Shear，and Moment Diagrams 134

4.6 Incremental Techniques for Obtaining Shear and Moment Diagrams 136

4.7 Shear and Moment Diagrams in Girders of Beam-and-Girder Systems 143

4.8 Differential Equation of Equilibrium for Axially Loaded Member 145

4.9 Loading and Internal Axial Force Diagrams 148

4.10 Summary and Limitations 149

Problems 153

Chapter 5 Analysis of Statically Determinate Plane Frames 157

5.1 Frame Action 158

5.2 Equations of Equilibrium 159

5.3 Determinacy and Geometric Stability 161

Number of Unknowns and Number of Equations of Solution 161

Geometric Instability 164

5.4 Analysis of Plane Frames for the Distribution of Internal Moments by Method of Sections 166

5.5 Moment Variation by Superposition 167

5.6 Summary and Limitations 179

Problems 182

Computer Problems 186

Chapter 6 Simple Bending Theory and Deformation Analysis of Beams 189

6.1 Relationship Between Bending and Curvature 190

6.2 Assumptions and Limitations of Simple Bending Theory 195

6.3 Determination of Beam Displacements by Direct Integration 201

6.4 Curvature-Area or Moment-Area Theorem 203

6.5 Elastic Load and Conjugate Beam Analysis 217

6.6 Axial Deformations of Beams 223

6.7 Axial Deformations Due to Curvature 227

6.8 Summary and Limitations 233

Problems 236

Chapter 7 Deformation of Structures： Virtual Work 241

7.1 Structural Deformations 242

7.2 Principle of Virtual Work for Rigid Bodies 242

7.3 Reactions of Structures Using Virtual Work 243

7.4 Principle of Virtual Work for Deformable Bodies 246

Conservation of Energy 249

Equations of the Virtual Work Principles 250

7.5 Internal Virtual Work for Prismatic Members 253

7.6 Application of the Complementary Virtual Work Principle to Deflection Analysis of Trusses 257

7.7 Application of the Complementary Virtual Work Principle to Deflection Analysis of Beams and Frames 266

7.8 Use of Integration Charts to Compute Internal Work 271

7.9 Summary and Limitations 275

Problems 280

Computer Problems 284

Chapter 8 Influence Lines for Statically Determinate Structures 287

8.1 Definition of an Influence Line 288

8.2 Influence Lines for Beams 289

8.3 Use of the Influence Line to Obtain the Magnitude of a Force or Moment Action for a General Loading 296

8.4 Influence Lines for Trusses 300

8.5 Influence Lines for Beam-and-Girder Structures 304

8.6 Influence Lines Using Virtual Work and the Muller-Breslau Principle 307

8.7 Absolute Maximum Moment and Shear 314

8.8 Summary and Limitations 318

Problems 320

Chapter 9 Deformation Analysis of Nonprismatic Beams and Beams of Nonlinear Material 325

9.1 Analysis of Bending Deformations of Piecewise Nonprismatic Members 326

9.2 Use of Numerical Integration in Deformation Calculations 332

9.3 Axial Deformations of Nonprismatic Members 337

9.4 Axial Deformations of Members of Nonlinear Materials 340

9.5 Bending Deformations of Members of Nonlinear Materials 349

9.6 Summary and Limitations 360

Problems 363

Computer Problems 367

Chapter 10 Analysis of Statically Indeterminate Structures 369

10.1 Statically Indeterminate Structures 370

10.2 Analysis by Superposition 372

10.3 Selection of Redundant Restraints 382

10.4 Method of Consistent Deformations 383

10.5 Analysis of Symmetric Structures 400

10.6 Deformation Analysis of Indeterminate Structures 404

10.7 Analysis of Indeterminate Structures with Nonlinear Materials 416

10.8 Summary and Limitations 423

Problems 426

Computer Problems 432

Chapter 11 Slope-Deflection Method 435

11.1 Slope-Deflection Method 436

11.2 Slope-Deflection Equations 436

Slope-Deflection Equations for End Moments 437

Slope-Deflection Equations for End Shears 441

Fixed End Moments and Fixed End Forces 442

11.3 Application of the Slope-Deflection Equations to the Solution of Structures with No Joint Translation 446

11.4 Application of the Slope-Deflection Equations to the Solution of Structures with Joint Translation 454

11.5 Analysis of Symmetric Structures 461

11.6 Summary and Limitations 469

Problems 472

Chapter 12 Moment Distribution Method of Analysis 477

12.1 Moment Distribution Method 478

12.2 Moment Distribution Without Joint Translation 478

12.3 Reduced Stiffness for Members with Ends Free to Rotate 485

12.4 Structures with Joint Displacements 492

12.5 Modified Relative Stiffness for Symmetric Structures 503

12.6 Summary and Limitations 509

Problems 512

Chapter 13 Influence Lines for Statically Indeterminate Structures 517

13.1 Development of Influence Lines by Direct Computation and Their Use 518

13.2 Betti’s Law and Maxwell’s Law of Reciprocal Deflections 531

13.3 Muller-Breslau Principle 534

13.4 Influence Lines Using the Muller-Breslau Principle 536

Quantitative Influence Lines for Beams 536

Influence Lines for Trusses 541

Construction of Qualitative Influence Lines for Frames 541

13.5 Summary and Limitations 543

Problems 550

Chapter 14 Approximate Analysis Using Force-Based Assumptions 553

14.1 Need for Approximate Methods of Analysis 553

14.2 Vertical Loading of Beams in a Frame 554

14.3 Moments and Forces in Simple Frames with Lateral Loads 556

14.4 Portal Method of Analysis 560

14.5 Cantilever Method of Analysis 568

14.6 Estimating Lateral Displacements Due to Lateral Loads 578

14.7 Approximate Analysis of Indeterminate Trusses 581

14.8 Summary and Limitations 588

Problems 591

Chapter 15 Approximate Analysis Using Assumed Deformations 595

15.1 Strain， Complementary Strain， Potential， and Complementary Potential Energy 596

Strain and Complementary Strain Energy 596

Total Potential and Total Complementary Potential Energy 601

Principle of Minimum Potential Energy and Virtual Work 602

Principle of Minimum Total Complementary Energy and Complementary Virtual Work 603

15.2 Castigliano’s and Engesser’s Theorems 604

15.3 Approximate Analysis of Nonprismatic Members 606

15.4 Approximate Analysis of Single-Story Frames 615

15.5 Shear Building Approximation 617

15.6 Single-Bay Building Approximation 622

15.7 Summary and Limitations 627

Problems 633