This rigorous, well-organized textbook examines computer-oriented structural analysis, with a strong emphasis on current applications. The book features coverage of both framed structures (trusses, beams, plane and space frames) and continuous structures (plates and shells).
In an easy-to-read style, the authors define the terminology, coordinate systems, and fundamental concepts and procedures of computerized structural analysis, laying the foundation for more advanced treatments, such as finite element analysis. The book covers the stiffness analysis of frames, the equation of statics and kinematics, the flexibility method, virtual work principles, many special analysis procedures (such as substructuring and condensation), the finite element method, and more. Featuring many worked-out examples, an introduction giving an overview of structural analysis while relating it to other subjects, and a text that is fully SI Metric, this text is the most complete available source on up-to-date methodologies of matrix structural analysis.
Contents
SYMBOLS xv
Ch. 1. INTRODUCTION
1.1 A Brief History of Structural Analysis 2
1.2 Computer Programs 4
1.3 Illustrations 7
References 13
Ch. 2. DEFINITIONS AND CONCEPTS
2.1 Degrees of Freedom 15
2.2 Coordinate Systems and Conditions of Analysis 17
2.3 Structure Idealization 22
2.4 Axial Force Member: Force-Displacement Relationships 24
2.4.1 Element Stiffness Equations 24
2.4.2 Element Flexibility Equations 26
2.4.3 Mixed Force-Displacement Equations 27
2.5 Axial Force Member: Global Stiffness Equation 28
2.6 Examples 29
2.7 Problems 36
Ch. 3. FORMATION OF THE GLOBAL ANALYSIS EQUATIONS
3.1 Direct Stiffness Method—The Basic Equations 41
3.2 Direct Stiffness Method—The General Procedure 50
3.3 Some Features of the Stiffness Equations 59
3.4 Indeterminacy 60
3.5 Problems 62
References 68
Ch. 4. STIFFNESS ANALYSIS OF FRAMES—I
4.1 Stress-Strain Relationships 69
4.2 Work and Energy 72
4.3 Reciprocity 74
4.4 Flexibility-Stiffness Transformations 76
4.5 The Framework Element Stiffness Matrix 81
4.5.1 Axial force member 82
4.5.2 Pure torsional member 83
4.5.3 Beam bent about its z axis 84
4.5.4 Beam bent about its y axis 89
4.5.5 Complete element stiffness matrix 90
4.6 Commentary on Neglected Deformations 90
4.7 Examples 92
4.8 Problems 106
References 111
Ch. 5. STIFFNESS ANALYSIS OF FRAMES—II
5.1 Coordinate Transformations 112
5.1.1 Transformation Matrices 114
5.1.2 Transformation of Degrees of Freedom 118
5.1.3 Transformations and Energy 118
5.1.4 Rectangular Transformation Matrices 120
5.2 Loads Between Nodal Points 132
5.3 Self-Straining Problems—Initial and Thermal Strain Conditions 146
5.4 Problems 158
Ch. 6. THE EQUATIONS OF STATICS AND KINEMATICS
6.1 Static Equilibrium Equations for Statically Determinate Structures 166
6.2 Static Equilibrium Equations for Statically Indeterminate Structures 174
6.3 Identification of Redundant Forces 180
6.4 Kinematic Instability 186
6.5 Reaction Elements, Force Releases, Displacement Constraints 192
6.6 Kinematic Equations 197
6.7 Relationship Between Statics and Kinematics Equations 205
6.8 Static Versus Kinematic Indeterminacy 207
6.9 Problems 211
References 214
Ch. 7. THE FLEXIBILITY METHOD
7.1 Flexibility Method—Basic Equations for 216 Truss Analysis 224
7.2 Flexibility Method—The General Procedure
7.3 Flexibility Analysis—Basic Equations for Continuous Beam Analysis 224
7.4 Flexibility Method Analysis for Initial Strains, Support Settlements, and Distributed Loads 229
7.5 The Framework Element Flexibility Matrix 239
7.6 Problems 241
References 243
Ch. 8. VIRTUAL WORK PRINCIPLES
8.1 Principle of Virtual Displacements. Rigid Bodies 245
8.2 Principle of Virtual Displacements. Deformable Bodies 250
8.3 Virtual Displacements Analysis Procedure and Detailed Expressions 252
8.3.1 General Procedure 252
8.3.2 Virtual Strain Energy 254
8.3.3 External Virtual Work 257
8.4 Construction of Analytical Solutions by Use of the Principle of Virtual Displacements 259
8.4.1 Exact Solutions 259
8.4.2 Approximate Solutions and the Significance of the Chosen Virtual Displacements 263
8.4.3 Illustrative Examples 264
8.5 Principle of Virtual Forces 269
8.5.1 Equations of Equilibrium 269
8.5.2 Characteristics of Virtual Force Systems 272
8.5.3 Formulation of the Virtual Forces Principle 274
8.5.4 Construction of Analytical Solutions by Virtual Forces Principle 276
8.6 Energy Theorems 281
8.7 Problems 285
References 290
Ch. 9. VIRTUAL WORK PRINCIPLES IN FRAMEWORK ANALYSIS
9.1 Description of the Displaced State of Elements 292
9.1.1 Definition of the Shape Function Mode of Description 292
9.1.2 Formulation of Shape Functions 293
9.1.3 Characteristics of Shape Functions 299
9.2 Virtual Displacements in the Formulation of Element Stiffness Equations 300
9.2.1 Construction of Expressions for Real and Virtual Displacements 300
9.2.2 Virtual Displacements Formula for an Element Stiffness Matrix 301
9.2.3 Application to Standard Axial, Torsional, and Flexural Elements 302
9.3 Nonuniform Elements 303
9.4 Loads Between Nodal Points and Initial Strain Effects; A General Approach 306
9.5 Virtual Forces in the Formulation of Element Force-Displacement Equations 311
9.6 Virtual Forces in the Formulation of Global Flexibility Equations 319
9.7 Problems 322
References 327
Ch. 10. SPECIAL ANALYSIS PROCEDURES
10.1 Condensation 329
10.2 Substructuring 331
10.3 Constraints 340
10.4 Joint Coordinates 344
10.5 Reanalysis Techniques 348
10.6 Symmetry and Antisymmetry 355
10.7 Transfer Matrix Method 362
10.8 Problems 369
References 372
Ch. 11. SOLUTION OF LINEAR ALGEBRAIC EQUATIONS
11.1 The Basic Choice—Direct Inversion Versus
Decomposition 375
11.2 Elimination Methods 378
11.2.1 Gaussian Elimination 378
11.2.2 The Cholesky Method 382
11.2.3 Variations 384
11.3 Solution of Banded Equations 385
11.4 Frontal Solvers 390
11.5 Accuracy and Errors 396
11.6 Elements of Error Analysis 398
11.6.1 Equation Condition 399
11.6.2 The Condition Number 404
11.6.3 Error Estimates, Artificial Ill-Conditioning, and Equilibration 407
11.6.4 Use of the Determinant 410
11.6.5 Corrective Procedures 413
11.7 Problems 417
References 420
Ch. 12. THE FINITE ELEMENT METHOD
12.1 The Finite Element Concept 421
12.2 Basic Relationships for Multiaxial Stress States 426
12.3 Formulation of a Triangular Plane Stress Element 431
12.4 Finite Element Global Analysis 436
12.5 Summary of Features and Other Aspects of Finite Element Analysis 443
12.6 Problems 448
References 451
AUTHOR INDEX 453
SUBJECT INDEX 455
