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CHAPTER 1 CONCEPTS OF STRUCTURAL ANALYSIS 1
1.1 Introduction 1
1.2 Solution Methods 4
1.3 Classification of Structures 8
1.4 Comparison of Classical, Matrix, and Approximate Methods of Structural Analysis 9
1.5 Summary 10
CHAPTER 2 EQUILIBRIUM AND COMPATIBILITY 12
2.1 Introduction 12
2.2 Truss-Member Coordinate Systems 12
2.3 Truss-Member Coordinate Transformations 14
2.4 Truss Supports 18
2.5 Solution for Unknown Internal Forces in Statically Determinate Trusses—Equilibrium Equations 20
2.6 Solution for Unknown Nodal Displacements for Statically Determinate Structures—Compatibility Equations 34
2.7 Beam Member 38
2.8 Beam Supports 43
2.9 Frame Member 45
2.10 Frame Supports 47
2.11 Frame Example 48
2.12 Concluding Remarks 58
2.13 Summary—Equilibrium Relationships 66
2.14 Summary—Compatibility Relationships 66
CHAPTER 3 MEMBER BASIC FORCE-DISPLACEMENT RELATIONSHIPS 73
3.1 Introduction 73
3.2 Truss-Member Basic Flexibility and Stiffness Relationships 74
3.3 Beam-Member Basic Flexibility and Stiffness Relationships 76
3.4 Frame-Member Basic Flexibility and Stiffness Relationships 78
3.5 Support Basic Force-Displacement Relationships 79
3.6 Flexibility and Stiffness Coefficient Symmetry Conditions 80
3.7 Obtaining Flexibility and Stiffness Coefficients by Energy Methods 81
3.8 Summary—Member Basic Flexibility and Stiffness Relationships 87
CHAPTER 4 DISPLACEMENT METHOD 89
4.1 Introduction 89
4.2 Transformation of the Member Basic Stiffness Relationships to Global Coordinates 90
4.3 Assembly and Solution of Structure Stiffness Relationships for Statically Determinate Structures 98
4.4 Statically Indeterminate Structures 119
4.5 Alternative Forms of the Structure Stiffness Relationships 141
4.6 Structural Symmetry 173
4.7 Summary—Displacement Method 193
CHAPTER 5 DISPLACEMENT METHOD—SPECIAL CONSIDERATIONS 203
5.1 Introduction 203
5.2 Initially Strained Members 203
5.3 Special Members 230
5.4 Skewed Supports 254
5.5 Summary 267
CHAPTER 6 FORCE METHOD 275
6.1 Introduction 275
6.2 Statically Determinate Structures 275
6.3 Statically Indeterminate Structures 296
6.4 Summary—Force Method 336
CHAPTER 7 SOLUTION OF EQUATIONS 341
7.1 Introduction 341
7.2 Gaussian Elimination 342
7.3 Data Handling Techniques 350
7.4 Other Solution Algorithms 375
7.5 Errors and Conditioning 388
7.6 Summary 394
CHAPTER 8 SPACE STRUCTURES AND GRIDWORKS—DISPLACEMENT METHOD 398
8.1 Introduction 398
8.2 Member Stiffness Relationships 398
8.3 Space Truss Example 410
8.4 Gridwork Example 414
8.5 Space Frame Example 420
8.6 Summary 431
APPENDIX 1 MATRIX ALGEBRA REVIEW 435
A1.1 Introduction 435
A1.2 Structural Example 435
A1.3 Structural Example—Alternative Coordinate System 441
A1.4 Alternate Structural Example 444
A1.5 Summary 444
APPENDIX 2 SMIS3: AN ADVANCED SYMBOLIC MATRIX INTERPRETIVE SYSTEM 446
A2.1 Introduction 446
A2.2 Restrictions on Use 447
A2.3 Procedures for Use 447
A2.4 Operation Code Words 448
A2.5 SMIS3 Structural Elements and Stiffness Matrices 466
A2.6 Subroutine Documentation 472
ANSWERS TO PROBLEMS 488
INDEX 493