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Chapter 1 Introduction to Structural Engineering1

1.1 Description of Structural Analysis and Structural Design2

Proof of Performance3

Value of Analysis of Simple Structures4

1.2 Idealization of a Structure5

Types of Structures6

Mathematical Model of a Single Member7

Mathematical Model of an Assembly of Members9

1.3 Types of Loads on Structures12

1.4 Specification of Loading13

1.5 Internal Stresses14

1.6 Free-Body Diagrams19

1.7 Equilibrium Conditions for Planar Structures20

1.8 Superposition of Forces in Statically Determinate Structures23

1.9 Superposition of Deformations25

1.10 Symmetric and Antisymmetric Loading of Symmetric Structures27

Symmetrically Loaded Symmetric Structures28

Antisymmetrically Loaded Symmetric Structures30

General Loading of Symmetric Structures32

1.11 Summary and Limitations35

Chapter 2 Computation of Reactions for Planar Statically Determinate Structures39

2.1 Static Determinacy of Reactions and Equations of Condition40

Equations of Condition for Plane Frames41

Equations of Condition for Plane Trusses43

Examples of Statically Determinate Reactions45

2.2 Geometric Stability48

2.3 Computation of Reactions for Structures with Concentrated Loads56

2.4 Computation of Reactions for Structures with Distributed Loads60

2.5 Reactions for Symmetric Structures62

2.6 Summary and Limitations70

Problems72

Computer Problems76

Chapter 3 Analysis of Plane Trusses79

3.1 Truss Action80

3.2 Unknowns and Assumptions in Truss Analysis83

3.3 Determinacy and Geometric Stability86

3.4 Plane Truss Analysis by the Method of Joints91

3.5 Special Considerations at Truss Joints99

3.6 Truss Analysis by the Method of Sections104

3.7 Summary and Limitations112

Problems116

Computer Problems121

Chapter 4 Analysis of Beams： Shear， Moment， and Axial Force Diagrams123

4.1 Sign Convention124

4.2 Differential Equations of Equilibrium for a Transversely Loaded Beam125

4.3 Drawing Shear and Moment Diagrams Using Direct Integration126

4.4 Drawing Shear and Moment Diagrams Using Equilibrium Directly131

4.5 Relationships Between Loading， Shear，and Moment Diagrams134

4.6 Incremental Techniques for Obtaining Shear and Moment Diagrams136

4.7 Shear and Moment Diagrams in Girders of Beam-and-Girder Systems143

4.8 Differential Equation of Equilibrium for Axially Loaded Member145

4.9 Loading and Internal Axial Force Diagrams148

4.10 Summary and Limitations149

Problems153

Chapter 5 Analysis of Statically Determinate Plane Frames157

5.1 Frame Action158

5.2 Equations of Equilibrium159

5.3 Determinacy and Geometric Stability161

Number of Unknowns and Number of Equations of Solution161

Geometric Instability164

5.4 Analysis of Plane Frames for the Distribution of Internal Moments by Method of Sections166

5.5 Moment Variation by Superposition167

5.6 Summary and Limitations179

Problems182

Computer Problems186

Chapter 6 Simple Bending Theory and Deformation Analysis of Beams189

6.1 Relationship Between Bending and Curvature190

6.2 Assumptions and Limitations of Simple Bending Theory195

6.3 Determination of Beam Displacements by Direct Integration201

6.4 Curvature-Area or Moment-Area Theorem203

6.5 Elastic Load and Conjugate Beam Analysis217

6.6 Axial Deformations of Beams223

6.7 Axial Deformations Due to Curvature227

6.8 Summary and Limitations233

Problems236

Chapter 7 Deformation of Structures： Virtual Work241

7.1 Structural Deformations242

7.2 Principle of Virtual Work for Rigid Bodies242

7.3 Reactions of Structures Using Virtual Work243

7.4 Principle of Virtual Work for Deformable Bodies246

Conservation of Energy249

Equations of the Virtual Work Principles250

7.5 Internal Virtual Work for Prismatic Members253

7.6 Application of the Complementary Virtual Work Principle to Deflection Analysis of Trusses257

7.7 Application of the Complementary Virtual Work Principle to Deflection Analysis of Beams and Frames266

7.8 Use of Integration Charts to Compute Internal Work271

7.9 Summary and Limitations275

Problems280

Computer Problems284

Chapter 8 Influence Lines for Statically Determinate Structures287

8.1 Definition of an Influence Line288

8.2 Influence Lines for Beams289

8.3 Use of the Influence Line to Obtain the Magnitude of a Force or Moment Action for a General Loading296

8.4 Influence Lines for Trusses300

8.5 Influence Lines for Beam-and-Girder Structures304

8.6 Influence Lines Using Virtual Work and the Muller-Breslau Principle307

8.7 Absolute Maximum Moment and Shear314

8.8 Summary and Limitations318

Problems320

Chapter 9 Deformation Analysis of Nonprismatic Beams and Beams of Nonlinear Material325

9.1 Analysis of Bending Deformations of Piecewise Nonprismatic Members326

9.2 Use of Numerical Integration in Deformation Calculations332

9.3 Axial Deformations of Nonprismatic Members337

9.4 Axial Deformations of Members of Nonlinear Materials340

9.5 Bending Deformations of Members of Nonlinear Materials349

9.6 Summary and Limitations360

Problems363

Computer Problems367

Chapter 10 Analysis of Statically Indeterminate Structures369

10.1 Statically Indeterminate Structures370

10.2 Analysis by Superposition372

10.3 Selection of Redundant Restraints382

10.4 Method of Consistent Deformations383

10.5 Analysis of Symmetric Structures400

10.6 Deformation Analysis of Indeterminate Structures404

10.7 Analysis of Indeterminate Structures with Nonlinear Materials416

10.8 Summary and Limitations423

Problems426

Computer Problems432

Chapter 11 Slope-Deflection Method435

11.1 Slope-Deflection Method436

11.2 Slope-Deflection Equations436

Slope-Deflection Equations for End Moments437

Slope-Deflection Equations for End Shears441

Fixed End Moments and Fixed End Forces442

11.3 Application of the Slope-Deflection Equations to the Solution of Structures with No Joint Translation446

11.4 Application of the Slope-Deflection Equations to the Solution of Structures with Joint Translation454

11.5 Analysis of Symmetric Structures461

11.6 Summary and Limitations469

Problems472

Chapter 12 Moment Distribution Method of Analysis477

12.1 Moment Distribution Method478

12.2 Moment Distribution Without Joint Translation478

12.3 Reduced Stiffness for Members with Ends Free to Rotate485

12.4 Structures with Joint Displacements492

12.5 Modified Relative Stiffness for Symmetric Structures503

12.6 Summary and Limitations509

Problems512

Chapter 13 Influence Lines for Statically Indeterminate Structures517

13.1 Development of Influence Lines by Direct Computation and Their Use518

13.2 Betti’s Law and Maxwell’s Law of Reciprocal Deflections531

13.3 Muller-Breslau Principle534

13.4 Influence Lines Using the Muller-Breslau Principle536

Quantitative Influence Lines for Beams536

Influence Lines for Trusses541

Construction of Qualitative Influence Lines for Frames541

13.5 Summary and Limitations543

Problems550

Chapter 14 Approximate Analysis Using Force-Based Assumptions553

14.1 Need for Approximate Methods of Analysis553

14.2 Vertical Loading of Beams in a Frame554

14.3 Moments and Forces in Simple Frames with Lateral Loads556

14.4 Portal Method of Analysis560

14.5 Cantilever Method of Analysis568

14.6 Estimating Lateral Displacements Due to Lateral Loads578

14.7 Approximate Analysis of Indeterminate Trusses581

14.8 Summary and Limitations588

Problems591

Chapter 15 Approximate Analysis Using Assumed Deformations595

15.1 Strain， Complementary Strain， Potential， and Complementary Potential Energy596

Strain and Complementary Strain Energy596

Total Potential and Total Complementary Potential Energy601

Principle of Minimum Potential Energy and Virtual Work602

Principle of Minimum Total Complementary Energy and Complementary Virtual Work603

15.2 Castigliano’s and Engesser’s Theorems604

15.3 Approximate Analysis of Nonprismatic Members606

15.4 Approximate Analysis of Single-Story Frames615

15.5 Shear Building Approximation617

15.6 Single-Bay Building Approximation622

15.7 Summary and Limitations627

Problems633