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PREFACE xv

PART 1 DETERMINATE STRUCTURES

1 INTRODUCTION 2

1.1 Structural Analysis and Design, 2

1.2 History of Structural Analysis, 3

1.3 Basic Principles of Structural Analysis, 6

1.4 Structural Components and Systems, 6

1.5 Structural Forces, 8

1.6 Calculation Accuracy, 8

1.7 Checks on Problems, 9

1.8 Using Computers for Structural Analysis, 10

1.9 Overview of this Textbook, 11

2 STRUCTURAL LOADS 12

2.1 Introduction, 12

2.2 Structural Safety, 13

2.3 Codes, Standards, and Specifications, 14

2.4 Types of Structural Loads, 15

2.5 Loading Conditions for Allowable Stress Design, 16

2.6 Loading Conditions for Strength Design, 17

2.7 Dead Loads, 19

2.8 Live Loads, 21

2.9 Live Load Impact Factors, 22

2.10 Live Loads on Roofs, 23

2.11 Rain Loads, 25

2.12 Snow Loads, 27

2.13 Wind Loads, 30

2.14 ASCE Envelope Procedure for Estimating Wind Loads, 32

2.15 Seismic Loads, 34

2.16 Equivalent Lateral Force Procedure for Seismic Loads, 36

2.17 Highway Bridge Loads, 40

2.18 Railway Bridge Loads, 41

2.19 Other Loads, 42

2.20 Examples with Video Solutions, 43

2.21 Problems for Solution, 43

3 VERTICAL SYSTEM LOADING AND BEHAVIOR 46

3.1 Introduction, 46

3.2 Structural Idealization, 47

3.3 Vertical Load Path, 48

3.4 Tributary Areas, 51

3.5 Influence Area, 57

3.6 Floor Live Load Reductions, 58

3.7 Columns in Multistory Buildings, 60

3.8 Examples with Video Solutions, 62

3.9 Problems for Solution, 62

4 LATERAL SYSTEM LOADING AND BEHAVIOR 65

4.1 Introduction, 65

4.2 Lateral Load Path, 66

4.3 Vertical Lateral Force Resisting Systems, 68

4.4 Diaphragms, 71

4.5 Tributary Approach, 73

4.6 Examples with Video Solutions, 80

4.7 Problems for Solution, 81

5 REACTIONS 83

5.1 Equilibrium, 83

5.2 Calculation of Unknowns, 84

5.3 Types of Supports, 84

5.4 Role and Analysis of Springs, 86

5.5 Internal Releases, 86

5.6 Stability and Statical Determinacy, 87

5.7 Unstable Equilibrium and Geometric Instability, 90

5.8 Free-Body Diagrams, 91

5.9 Reactions for Single Rigid-Body Systems, 92

5.10 Reactions for Multiple Connected Rigid-Body Systems, 97

5.11 Matrix Formulation for Reactions, 102

5.12 SAP2000 Computer Applications, 104

5.13 Examples with Video Solutions, 107

5.14 Problems for Solution, 107

6 AXIAL FORCE, SHEAR FORCE, AND BENDING MOMENT 115

6.1 Introduction, 115

6.2 Member Internal Forces, 115

6.3 Axial, Shear, and Bending Moment Equations, 118

6.4 Relation between Load, Shear, and Moment, 121

6.5 Shear and Bending Moment Diagrams for Beams, 123

6.6 Axial Diagrams, 129

6.7 Shear and Bending Moment Diagrams for Frames, 130

6.8 Moment Diagrams Using Superposition, 134

6.9 Structural System Consideration, 135

6.10 SAP2000 Computer Applications, 137

6.11 Examples with Video Solutions, 141

6.12 Problems for Solution, 142

7 PLANE TRUSSES 150

7.1 Introduction, 150

7.2 Assumptions for Truss Analysis, 151

7.3 Roof Trusses, 152

7.4 Bridge Trusses, 153

7.5 Arrangement of Truss Members, 154

7.6 Stability and Statical Determinacy of Trusses, 154

7.7 Methods of Analysis and Conventions, 158

7.8 Method of Joints, 159

7.9 Matrix Formulation for Reactions and Bar Forces, 162

7.10 Zero-Force Members, 164

7.11 Method of Sections, 166

7.12 Simple, Compound, and Complex Trusses, 172

7.13 Structural System Consideration, 173

7.14 SAP2000 Computer Applications, 175

7.15 Examples with Video Solutions, 178

7.16 Problems for Solution, 178

8 DEFLECTIONS AND ANGLE CHANGES IN STRUCTURES 187

8.1 Introduction, 187

8.2 Reasons for Computing Deflections, 188

8.3 Long Term Deflections, 189

8.4 Sketching Deformed Shapes of Structures, 189

8.5 Determining Sense of Reactions from Deformed Shape, 194

8.6 Elastic Beam Theory, 195

8.7 Deflection by Double Integration, 197

8.8 SAP2000 Computer Applications, 202

8.9 Examples with Video Solutions, 204

8.10 Problems for Solution, 205

9 DEFLECTION AND ANGLE CHANGES USING VIRTUALWORK 211

9.1 Introduction to Energy Methods, 211

9.2 Conservation of Energy Principle, 211

9.3 Virtual Work or Complementary Virtual Work Method, 212

9.4 Truss Deflections by Virtual Work, 213

9.5 Application of Virtual Work to Trusses, 214

9.6 Deflections and Angle Changes of Beams and Frames, 217

9.7 Application of Virtual Work Using Visual Integration, 221

9.8 Application of Virtual Work to Springs, 225

9.9 Consideration of Shear Deformations, 227

9.10 SAP2000 Computer Applications, 228

9.11 Examples with Video Solutions, 230

9.12 Problems for Solution, 230

PART 2 INDETERMINATE STRUCTURES

10 INTRODUCTION TO STATICALLY INDETERMINATE STRUCTURES 238

10.1 Introduction, 238

10.2 Continuous Structures, 239

10.3 Advantages of Statically Indeterminate Structures, 240

10.4 Disadvantages of Statically Indeterminate Structures, 241

10.5 Methods of Analyzing Statically Indeterminate Structures, 242

10.6 Looking Ahead, 243

11 FORCEMETHOD FOR STATICALLY INDETERMINATE STRUCTURES 244

11.1 Beams and Frames with One Redundant, 244

11.2 Maxwell’s Law of Reciprocal Deflections, 252

11.3 Beams and Frames with Two or More Redundants, 253

11.4 Support Settlement, 254

11.5 SAP2000 Computer Applications, 256

11.6 Examples with Video Solutions, 258

11.7 Problems for Solution, 259

12 FORCEMETHODFORSTATICALLY INDETERMINATESTRUCTURESCONTINUED 262

12.1 Analysis of Externally Redundant Trusses, 262

12.2 Analysis of Internally Redundant Trusses, 264

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12.3 Analysis of Composite Structures, 266

12.4 Temperature Changes, Shrinkage, Fabrication Errors, and So On, 270

12.5 SAP2000 Computer Applications, 271

12.6 Examples with Video Solutions, 274

12.7 Problems for Solution, 274

13 MOMENT DISTRIBUTION FOR BEAMS 278

13.1 Introduction, 278

13.2 Sign Convention, 279

13.3 Basic Concepts and Definitions, 280

13.4 Distribution Factors, 282

13.5 Application of Moment Distribution, 284

13.6 Modification of Stiffness and FEM for Simple Ends, 288

13.7 Shearing Force and Bending Moment Diagrams, 289

13.8 Spreadsheet Computer Applications, 291

13.9 Examples with Video Solutions, 292

13.10 Problems for Solution, 292

14 MOMENT DISTRIBUTION FOR FRAMES 295

14.1 Frames with Sidesway Prevented, 295

14.2 Sway Frames with Point Loads at Joints, 298

14.3 General Frames with Sidesway, 303

14.4 Frames with Sloping Legs, 308

14.5 Multistory Frames, 311

14.6 Examples with Video Solutions, 312

14.7 Problems for Solution, 312

15 APPROXIMATE ANALYSIS OF STATICALLY INDETERMINATE STRUCTURES 316

15.1 Introduction, 316

15.2 Trusses with Two Diagonals in Each Panel, 317

15.3 Continuous Beams, 318

15.4 Analysis of Building Frames for Vertical Loads, 320

15.5 Analysis of Portal Frames, 323

15.6 Analysis of Building Frames for Lateral Loads, 325

15.7 Exact and Approximate Analysis Results Comparison, 329

15.8 Analysis of Vierendeel Trusses, 330

15.9 Examples with Video Solutions, 331

15.10 Problems for Solution, 331

PART 3 IINFLUENCE LINES

16 INFLUENCE LINES FOR DETERMINATE STRUCTURES 336

16.1 Introduction, 336

16.2 The Influence Line Defined, 336

16.3 Influence Lines for Simple Beam Reactions, 337

16.4 Influence Lines for Simple Beam Shear Forces, 337

16.5 Influence Lines for Simple Beam Moments, 338

16.6 Influence Lines Using Quantitative Approach, 339

16.7 Qualitative Influence Lines, 341

16.8 Uses of Influence Lines: Concentrated Loads, 346

16.9 Uses of Influence Lines: Uniform Loads, 347

16.10 Determining Maximum Loading Effects Using Influence Lines, 348

16.11 Maximum Loading Effects Using Beam Curvature, 349

16.12 Maximum Values for Moving Loads, 350

16.13 Influence Lines for Trusses, 352

16.14 Examples with Video Solutions, 360

16.15 Problems for Solution, 360

17 INFLUENCE LINES FOR STATICALLY INDETERMINATE STRUCTURES 365

17.1 Influence Lines for Statically Indeterminate Beams, 365

17.2 Qualitative Influence Lines for Indeterminate Beams and Frames, 370

17.3 Influence Lines for Determining Loading Scenarios for Continuous Systems, 374

17.4 Examples with Video Solutions, 375

17.5 Problems for Solution, 375

PART 4 MATRIX METHODS FOR STRUCTURAL ANALYSIS

18 INTRODUCTION TOMATRIX METHODS 380

18.1 Structural Analysis Using the Computer, 380

18.2 Matrix Methods, 381

18.3 Force and Displacement Methods of Analysis, 382

18.4 Introduction to the Force or Flexibility Method, 382

18.5 Examples with Video Solutions, 387

18.6 Problems for Solution, 387

19 DIRECT STIFFNESS METHOD FOR TRUSSES 389

19.1 Introduction, 389

19.2 Definitions and Concepts, 390

19.3 Kinematic Determinacy, 392

19.4 Stiffness Method, 394

19.5 Stiffness Matrix for Axial Force Members, 400

19.6 Stiffness Matrix for Inclined Axial Force Members, 401

19.7 Assemblage of Structure-Level Stiffness Matrix for Planar Trusses, 405

19.8 Solving for Member End Forces, 408

19.9 Characteristics of Stiffness Matrices, 412

19.10 Spreadsheet Computer Applications, 412

19.11 Examples with Video Solutions, 417

19.12 Problems for Solution, 417

20 DIRECT STIFFNESS METHOD FOR BEAMS AND FRAMES 421

20.1 Introduction, 421

20.2 Stiffness Matrix for Flexural (Beam) Elements, 421

20.3 Matrix Stiffness Method Applied to Beams, 423

20.4 Solving for Member End Forces, 428

20.5 Plotting Deflections Using Beam Shape Functions, 431

20.6 Loading Between Nodes (Statical Equivalency), 434

20.7 Superposition to Obtain Shear, Moment, and Deflection Diagrams, 438

20.8 Stiffness Matrix for Combined Axial and Flexural (Frame) Elements, 441

20.9 Transformation Matrix for Inclined Frame Element, 442

20.10 Matrix Stiffness Method Applied to Frames, 443

20.11 Spreadsheet Computer Applications, 448

20.12 SAP2000 Computer Applications, 450

20.13 Examples with Video Solutions, 452

20.14 Problems for Solution, 452

21 ADDITIONAL TOPICS FOR THE DIRECT STIFFNESS METHOD 459

21.1 Introduction, 459

21.2 Stiffness Formulation for Structures with Enforced Displacements, 459

21.3 Stiffness Formulation for Structures Subjected to Temperature Changes, 462

21.4 Stiffness Formulation for Structures with Misfit Members, 468

21.5 Static Condensation, 470

21.6 Partially Restrained Connections, 474

21.7 Releases, 478

21.8 Inclined Supports, 481

21.9 SAP2000 Computer Applications, 485

21.10 Examples with Video Solutions, 488

21.11 Problems for Solution, 489

A ASCE 7-16 Information 494
B Introduction to SAP2000 499
B.1 Introduction, 499
B.2 Slides, 500
C Matrix Algebra 520
C.1 Introduction, 520
C.2 Matrix Definitions and Properties, 520
C.3 Special Matrix Types, 521
C.4 Determinant of a Square Matrix, 522
C.5 Adjoint Matrix, 523
C.6 Matrix Arithmetic, 524
C.7 Matrix Partitioning, 528
D Reference Charts 531
D.1 Introduction, 531