ANALYSIS OF STRUCTURAL MEMBER SYSTEMSPDF电子书下载

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Ⅰ—MATHEMATICAL PRELIMINARIES 3

1 Introduction to Matrix Algebra 3

1-1 Definition of a Matrix 3

1-2 Equality， Addition， and Subtraction of Matrices 5

1-3 Matrix Multiplication 5

1-4 Transpose of a Matrix 8

1-5 Special Square Matrices 10

1-6 Operations on Partitioned Matrices 12

1-7 Definition and Properties of a Determinant 16

1-8 Cofactor Expansion Formula 19

1-9 Cramer’s Rule 21

1-10 Adjoint and Inverse Matrices 22

1-11 Elementary Operations on a Matrix 24

1-12 Rank of a Matrix 27

1-13 Solvability of Linear Algebraic Equations 30

2 Characteristic-Value Problems and Quadratic Forms 46

2-1 Introduction 46

2-2 Second-Order Characteristic-Value Problem 48

2-3 Similarity and Orthogonal Transformations 52

2-4 The nth-Order Symmetrical Characteristic-Value Problem 55

2-5 Quadratic Forms 57

3 Relative Extrema for a Function 66

3-1 Relative Extrema for a Function of One Variable 66

3-2 Relative Extrema for a Function of n Independent Variables 71

3-3 Lagrange Multipliers 75

4 Differential Geometry of a Member Element 81

4-1 Parametric Representation of a Space Curve 81

4-2 Arc Length 82

4-3 Unit Tangent Vector 85

4-4 Principal Normal and Binormal Vectors 86

4-5 Curvature， Torsion， and the Frenet Equations 88

4-6 Summary of the Geometrical Relations for a Space Curve 91

4-7 Local Reference Frame for a Member Element 92

4-8 Curvilinear Coordinates for a Member Element 94

5 Matrix Transformations for a Member Element 100

5-1 Rotation Transformation 100

5-2 Three-Dimensional Force Transformations 103

5-3 Three-Dimensional Displacement Transformations 109

Ⅱ—ANALYSIS OF AN IDEAL TRUSS 115

6 Governing Equations for an Ideal Truss 115

6-1 General 115

6-2 Elongation—Joint Displacement Relation for a Bar 116

6-3 General Elongation—Joint Displacement Relation 120

6-4 Force-Elongation Relation for a Bar 125

6-5 General Bar Force—Joint Displacement Relation 130

6-6 Joint Force-Equilibrium Equations 130

6-7 Introduction of Displacement Restraints； Governing Equations 132

6-8 Arbitrary Restraint Direction 134

6-9 Initial Instability 137

7 Variational Principles for an Ideal Truss 152

7-1 General 152

7-2 Principle of Virtual Displacements 153

7-3 Principle of Virtual Forces 159

7-4 Strain Energy； Principle of Stationary Potential Energy 162

7-5 Complementary Energy； Principle of Stationary Complementary Energy 165

7-6 Stability Criteria 169

8 Displacement Method—Ideal Truss 178

8-1 General 178

8-2 Operation on the Partitioned Equations 178

8-3 The Direct Stiffness Method 180

8-4 Incremental Formulation； Classical Stability Criterion 191

8-5 Linearized Stability Analysis 200

9 Force Method—Ideal Truss 210

9-1 General 210

9-2 Governing Equations—Algebraic Approach 211

9-3 Governing Equations—Variational Approach 216

9-4 Comparison of the Force and Mesh Methods 217

Ⅲ—ANALYSIS OF A MEMBER ELEMENT 229

10 Governing Equations for a Deformable Solid 229

10-1 General 229

10-2 Summation Convention； Cartesian Tensors 230

10-3 Analysis of Deformation； Cartesian Strains 232

10-4 Analysis of Stress’ 240

10-5 Elastic Stress-Strain Relations 248

10-6 Principle of Virtual Displacements； Principle of Stationary Potential Energy； Classical Stability Criteria 253

10-7 Principle of Virtual Forces； Principle of Stationary Complementary Energy 257

11 St. Venant Theory of Torsion-Flexure of Prismatic Members 271

11-1 introduction and Notation 271

11-2 The Pure-Torsion Problem 273

11-3 Approximate Solution of the Torsion Problem for Thin-Walled Open CrossSections 281

11-4 Approximate Solution of the Torsion Problem for Thin-Walled Closed Cross Sections 286

11-5 Torsion-Flexure with Unrestrained Warping 293

11-6 Exact Flexural Shear Stress Distribution for a Rectangular Cross Section 303

11-7 Engineering Theory of Flexural Shear Stress Distribution in Thin-Walled Cross Sections 306

12 Engineering Theory of Prismatic Members 330

12-1 Introduction 330

12-2 Force-Equilibrium Equations 331

12-3 Force-Displacement Relations； Principle of Virtual Forces 333

12-4 Summary of the Governing Equations 339

12-5 Displacement Method of Solution—Prismatic Member 340

12-6 Force Method of Solution 349

13 Restrained Torsion-Flexure of a Prismatic Member 371

13-1 Introduction 371

13-2 Displacement Expansions； Equilibrium Equations 372

13-3 Force-Displacement Relations—Displacement Model 375

13-4 Solution for Restrained Torsion—Displacement Model 379

13-5 Force-Displacement Relations—Mixed Formulation 383

13-6 Solution for Restrained Torsion—Mixed Formulation 389

13-7 Application to Thin-Walled Open Cross Sections 395

13-8 Application to Thin-Walled Closed Cross Sections 405

13-9 Governing Equations--Geometrically Nonlinear Restrained Torsion 414

14 Planar Deformation of a Planar Member 425

14-1 Introduction； Geometrical Relations 425

14-2 Force-Equilibrium Equations 427

14-3 Force-Displacement Relations； Principle of Virtual Forces 429

14-4 Force-Displacement Relations—Displacement Expansion Approach； Principle of Virtual Displacements 435

14-5 Cartesian Formulation 445

14-6 Displacement Method of Solution—Circular Member 449

14-7 Force Method of Solution 458

14-8 Numerical Integration Procedures 473

15 Engineering Theory of an Arbitrary Member 485

15-1 Introduction； Geometrical Relations 485

15-2 Force-Equilibrium Equations 488

15-3 Force-Displacement Relations—Negligible Warping Restraint； Principle of Virtual Forces 490

15-4 Displacement Method—Circular Planar Member 493

15-5 Force Method—Examples 499

15-6 Restrained Warping Formulation 507

15-7 Member Force-Displacement Relations—Complete End Restraint 511

15-8 Generation of Member Matrices 517

15-9 Member Matrices—Prismatic Member 520

15-10 Member Matrices—Thin Planar Circular Member 524

15-11 Flexibility Matrix—Circular Helix 531

15-12 Member Force-Displacement Relations—Partial End Restraint 535

Ⅳ—ANALYSIS OF A MEMBER SYSTEM 545

16 Direct Stiffness Method—Linear System 545

16-1 Introduction 545

16-2 Member Force-Displacement Relations 546

16-3 System Equilibrium Equations 547

16-4 Introduction of Joint Displacement Restraints 548

17 General Formulation—Linear System 554

17-1 Introduction 554

17-2 Member Equations 555

17-3 System Force-Displacement Relations 557

17-4 System Equilibrium Equations 559

17-5 Introduction of Joint Displacement Restraints； Governing Equations 560

17-6 Network Formulation 562

17-7 Displacement Method 565

17-8 Force Method 567

17-9 Variational Principles 570

17-10 Introduction of Member Deformation Constraints 573

18 Analysis of Geometrically Nonlinear Systems 585

18-1 Introduction 585

18-2 Member Equations—Planar Deformation 585

18-3 Member Equations—Arbitrary Deformation 591

18-4 Solution Techniques； Stability Analysis 597

Index 605

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