Fundamentals of Structural analysis – Second Edition

Part One: Orientation 1
Chapter 1: Introduction 3
1.1 Structure 4
1.2 Structural Engineering 6
1.3 History of Structural Engineering 6
1.4 The Engineering Design Process 10
1.5 Structural Analysis 13
1.6 Structural Form 14
1.7 Simplifications for Purposes of Analysis 22
1.8 Loading Conditions 25
1.9 Building Materials 39
1.10 Systems of Units 41
1.11 References 43
1.12 Suggested Problems 43
Chapter 2: Basic Concepts of Structural Analysis 47
2.1 Forces 48
2.2 Specification of a Force 48
2.3 Free-Body Diagrams 50
2.4 Equations of Equilibrium 51
2.5 Condition Equations 53
2.6 Displacements 54
2.7 Compatibility 55
2.8 Boundary Conditions 56
2.9 Principle of Superposition 57
2.10 Stiffness and Flexibility 59
2.11 Work 61
2.12 Complementary Work 63
2.13 Principle of Virtual Displacements 64
2.14 Virtual Work for a Deformable Body 66
2.15 Complementary Virtual Work for a Deformable Body 68
2.16 Application of Virtual Methods 69
2.17 Principle of Stationary Total Potential Energy 70
2.18 Principle of Stationary Total Complementary Potential Energy 71
2.19 Maxwell’s and Betti’s Laws 73
Part Two: Analysis of Statically Determinate Structures 75
Chapter 3: Reactions 77
3.1 Reaction Forces for Planar Structures 78
3.2 Support Conditions: Real versus Idealized 80
3.3 External Statical Determinacy and Stability for Planar Structures 80
3.4 Computation of Reactions Using Equations of Equilibrium 83
3.5 Condition Equations for Planar Structures 90
3.6 Reaction Forces for Nonplanar Structures 94
3.7 External Statical Determinacy and Stability for Nonplanar Structures 95
3.8 Computation of Reactions for Nonplanar Structures 97
3.9 Variations in Boundary Conditions 101
3.10 Suggested Problems 103
Chapter 4: Member Forces in Planar Trusses and Space Frameworks 112
4.1 Planar Truss Structures 113
4.2 Idealizations for Planar Trusses 114
4.3 Variations in Planar Truss Configuration 115
4.4 Truss Joint Identification and Member Force Representation 116
4.5 Sign Convention and Member Force Representation 118
4.6 Strategy for Planar Truss Analysis 119
4.7 Condition Equations for Determining Reactions 120
4.8 Statical Determinacy and Stability of Planar Trusses 120
4.9 Numerical Truss Analysis Problems 124
4.10 Complex Planar Trusses 130
4.11 Nonplanar Truss-Type Space Frameworks 131
4.12 Variations in Framework Configurations 132
4.13 Joint Identification, Member Force Notation, and Sign Convention 134
4.14 Overall Statical Determinacy and Stability of Space Frameworks 135
4.15 Analysis of Truss-Type Space Frameworks 136
4.16 Complex Frameworks 142
4.17 References 142
4.18 Suggested Problems 143
Chapter 5: Member Forces in Beams and Frames 151
5.1 Beam and Frame Structures 152
5.2 Internal Forces for Flexural Members 152
5.3 Notation and Sign Convention 153
5.4 Statical Determinacy and Stability of Beam and Frame Structures 155
5.5 Determination of Internal Forces 157
5.6 Relationships Between Load, Shear, and Bending Moment 159
5.7 Shear and Bending Moment Diagrams 161
5.8 Qualitative Deflected Structures 166
5.9 Detailed Construction of V and M Diagrams 167
5.10 Example Shear and Moment Diagram Problems 169
5.11 Shear and Moment Diagrams for Statically Indeterminate Structures 178
5.12 Internal Forces in Nonplanar Structures 182
5.13 Member Force Notation and Sign Convention 183
5.14 Internal Force Diagrams for Nonplanar Structures 184
5.15 Suggested Problems 186
Chapter 6: Influence Lines and Maximum Load Effects 192
6.1 Variable Loadings 193
6.2 Variation in Response Function with Position of Load: Influence Line 193
6.3 Influence Lines by Equilibrium Methods 194
6.4 Influence Lines by Virtual Work: Müller-Breslau Principle 205
6.5 Use of Influence Lines 210
6.6 Maximum Response Functions in Beams 214
6.7 Suggested Problems 224
Part Three: Elastic Deflections of Structures 231
Chapter 7: Elastic Deflections of Trusses and Frameworks 233
7.1 Description of Truss Deflection Problem 234
7.2 Axial Force-Deformation Relationships 234
7.3 Geometry of Truss Deflections 237
7.4 Truss Deflections by Complementary Virtual Work 238
7.5 Application of the Complementary Virtual Work Method 239
7.6 Deflections of Space Frameworks 246
7.7 Truss Deflections by Energy Methods 248
7.8 Suggested Problems 252
Chapter 8: Elastic Deflections of Beam and Frame Structures 259
8.1 Description of Flexural Deformation Problem 260
8.2 Flexural Force-Deformation Relationships 260
8.3 Integration Method 265
8.4 Moment-Area Method 269
8.5 Application of Moment-Area Method 271
8.6 The Conjugate Beam Method 281
8.7 Beam and Frame Deflections by Complementary Virtual Work 288
8.8 Deflections for Nonplanar Beam and Frame Structures 297
8.9 Beam and Frame Deflections by Energy Methods 302
8.10 Reference 304
8.11 Suggested Problems 304
Part Four: Analysis of Statically Indeterminate Structures 315
Chapter 9: More Basic Concepts of Structural Analysis 317
9.1 Requirements and Limitations of Equilibrium 318
9.2 Static Indeterminacies; Redundancies 319
9.3 Requirements and Limitations of Compatibility 321
9.4 Kinematic Indeterminacies; Redundancies 322
9.5 Alternate Form of Analysis 323
9.6 Static versus Kinematic Indeterminacy 326
9.7 Compatibility Method of Analysis 326
9.8 Equilibrium Method of Analysis 328
9.9 Behavioral Characteristics of Statically Indeterminate Structures 329
Chapter 10: Method of Consistent Deformations (and Other
Compatibility Methods) 334
10.1 Nature of Compatibility Methods 335
10.2 Redundancies: External versus Internal 335
10.3 Determination of Redundant Reactions 335
10.4 Application of the Method of Consistent Deformations 339
10.5 Support Settlements and Elastic Supports 348
10.6 Selection of Internal Moments as Redundants 353
10.7 Self-Straining Problems 362
10.8 Determination of Redundant Member Forces for Truss Structures 367
10.9 Compatibility Equations by Energy Methods 372
10.10 Suggested Problems 378
Chapter 11: Slope Deflection Method (and Other Equilibrium Methods) 384
11.1 Nature of Equilibrium Methods 385
11.2 The Slope Deflection Equation 385
11.3 Interpretation of the Slope Deflection Equation 388
11.4 Slope Deflection Method for Beam Problems 389
11.5 Slope Deflection Method for Frame Problems 394
11.6 Temperature Change 400
11.7 Problem Variations 403
11.8 Equilibrium Equations by Energy Methods 404
11.9 Suggested Problems 408
Chapter 12: Moment Distribution Method 414
12.1 Solution Techniques for Equilibrium Methods 415
12.2 Iterative Methods 415
12.3 Physical Interpretation of Iterative Solutions 417
12.4 Moment Distribution Method for Beam Problems 418
12.5 Application of Moment Distribution Method to Beam Problems 420
12.6 Modifications in Moment Distribution Method 426
12.7 Application to Beam Problems Using Modifications 429
12.8 Moment Distribution Method for Frame Structures 431
12.9 Application of Moment Distribution Method to Frame Problems 434
12.10 Suggested Problems 441
Part Five: Matrix Methods of Analysis 445
Chapter 13: Member Force-Deformation Relations 447
13.1 Significance of Member Interactive Relationships 448
13.2 Structure and Member Coordinate Systems 448
13.3 Member Flexibility Matrix 450
13.4 Member Stiffness Matrix 453
13.5 Some Observations on the Flexibility and Stiffness Matrices 457
13.6 Flexibility-Stiffness Transformations 458
13.7 Alternative Member Coordinate Systems 462
13.8 Suggested Problems 463
Chapter 14: Stiffness Method 465
14.1 Fundamental Concepts of Stiffness Method 466
14.2 Overview of Stiffness Method 466
14.3 Generation of Structure Stiffness Matrix 469
14.4 Compatibility Matrices 471
14.5 Application of Stiffness Method 474
14.6 Loads Applied between Node Points – Equivalent Structure Forces 489
14.7 Self-Straining Problems 497
14.8 Direct Stiffness Method 505
14.9 Further Observations about Stiffness Equations 507
14.10 Suggested Problems 508
Chapter 15: Flexibility Method 519
15.1 Fundamentals of Flexibility Method 520
15.2 Overview of Flexibility Method 520
15.3 Equilibrium Matrices 522
15.4 Generation of Structure Flexibility Matrix 522
15.5 Application of the Flexibility Method 524
15.6 Internally Redundant Structures 535
15.7 Loads Applied Between Node Points 537
15.8 Self-Straining Problems 540
15.9 Choice of Redundants 541
15.10 Comparisons Between Flexibility and Stiffness Methods 543
15.11 Suggested Problems 543
Appendix 545
Answers to Selected Problems 546
Index 561