Statics of Deformable Solids

by Raymond L. Bisplinghoff, James W. Mar, Theodore H.H. Pian

Overview

Well-written, thoughtfully prepared, and profusely illustrated, this text is the work of a trio of prominent experts. The treatment builds on the mechanics background obtained from an engineering curriculum's first course in physics, providing the foundations for a study of such advanced topics in solid mechanics as the theory of elasticity, structural analysis, plasticity, and shell theory.
Divided into two parts, the book begins with an exposition of the fundamentals of solid mechanics and the principles of mechanics, statics, and simple statically indeterminate systems. The second half deals with strain and stress in three-dimensional solids, elementary elasticity, stress-strain relations for plastic solids, and energy principles in solid continuum. Each chapter concludes with a set of problems and a concise summary of important principles.

Product Details

ISBN-13:	9780486789934
Publisher:	Dover Publications
Publication date:	12/17/2014
Series:	Dover Books on Engineering
Pages:	336
Product dimensions:	6.10(w) x 9.10(h) x 0.80(d)

About the Author

Raymond L. Bisplinghoff (1917–85) was a Professor in the Department of Aeronautics and Astronautics at the Massachusetts Institute of Technology. His other Dover books include Aeroelasticity, co-authored with Holt Ashley and Robert L. Halfman, and Principles of Aeroelasticity, co-authored with Holt Ashley.

Table of Contents

Preface

Chapter 1 Foundations of Solid Mechanics

1.1 Introduction 1

1.2 Ways of thinking 2

1.3 Methodology in solid mechanics 2

Chapter 2 Principles of Mechanics

2.1 Introduction 6

2.2 The concept of force 6

2.3 Law of the parallelogram of forces-resultant of concurrent forces 9

2.4 Law of transmissibility of forces 10

2.5 Law of motion 10

2.8 Law of action and reaction 13

2.7 Equilibrium of a particle 13

2.8 Summary of the principles of mechanics 15

Chapter 3 Statics

3.1 Introduction 18

3.2 Properties of force and moments 18

3.3 Equilibrium of a particle 25

3.4 Equilibrium of a system of particles 28

3.5 Examples of the use of the free-body diagram 37

3.6 Systems of parallel forces-center of gravity 43

3.7 Plane and space trusses 46

3.8 Internal forces and moments in slender beams 50

3.9 Relations between load, shear, and bending moment 58

3.10 General beam theory 61

3.11 Torsion of a rod 63

3.12 Summary 64

Chapter 4 Simple Statically Indeterminate Systems

4.1 Introduction 75

4.2 Principles of analysis of statically indeterminate systems 77

4.3 Example: airplane landing gear 80

4.4 Examples of plane trusses 81

4.5 Example of thermal stresses in bolt-and-bushing assembly 84

4.6 Example of assembly stresses in bolt-and-nut assembly 86

4.7 Example of statically indeterminate beam 86

4.8 Summary 88

Chapter 5 Analysis of Strain

5.1 Introduction 93

5.2 The fundamental metric tensors 94

5.3 The strain tensor 97

5.4 The geometrical meaning of the strain tensor 98

5.5 Small strain 101

5.8 The strain transformation laws 104

5.7 Principal strains and principal directions 105

5.8 The strain-displacement relations 111

5.9 Linear strain 113

5.10 The change in volume 117

5.11 Two simple examples of strain 119

5.12 The deviator and spherical strain tensors 121

5.13 Compatibility relations for Linear strain 122

5.14 Summary 126

Chapter 6 Analysis of Stress

6.1 Introduction 141

6.2 The concept of stress at a point 141

6.3 The stress tensor 142

6.4 The transformation of stress 146

6.5 The symmetry of the stress tensor: moment equilibrium 149

6.6 The differential equations of equilibrium 151

6.7 The equations of equilibrium on the surface of a body 152

6.8 Principal stresses and principal directions 153

8.1 The extreme shear stresses 157

6.10 The deviator and spherical stress tensors 160

6.11 Summary 160

Chapter 7 Elasticity

7.1 Introduction 168

7.2 The generalized Hooke's Law-anisotropy 168

7.3 Monoclinic material: thirteen constants 175

7.4 Orthotropic material: nine constants 177

7.5 Tetragonal material: six constants 178

7.8 Cubic material: three constants 179

7.7 Isotropic material: two constants 180

7.8 Thermoelastic stress-strain relation 183

7.9 Elastic constants for some materials of engineering interest 185

7.10 Strain energy 187

7.11 Summary: isotropic stress-strain law and energy relations 190

7.12 Summary: the equations of linear elasticity 192

7.13 Simple examples of solutions for equations of elasticity 194

7.14 Engineering beam theory 198

7.15 Summary: engineering beam theory 199

Chapter 8 Plastic Behavior of Solids

8.1 Introduction 206

8.2 Stress-strain relations under uniaxial loading conditions 206

8.3 Yield condition under general state of stress for isotropic materials 210

8.4 Plastic stress-strain relations 218

8.5 Summary 225

Chapter 9 Energy Principles in Solid Continuum

9.1 Introduction 231

9.2 Work and internal energy 232

9.3 Relations for linearly elastic systems 234

9.4 Principle of Virtual Work 239

9.5 Betti's Law and Maxwell's Law 247

9.6 Principle of Minimum Potential Energy 248

9.7 Castigliano's First Theorem 251

9.8 Principle of Virtual Complementary Work 256

9.9 Principle of Minimum Complementary Energy 258

9.10 Castigliano's Second Theorem 259

9.11 Theorem of Least Work 263

9.12 Summary 266

Appendix: Mathematical Themes

A.1 Introduction 273

A.2 The summation and indicial notation 273

A.3 The e-symbol and the Kronecker δ 274

A.4 Coordinate transformations and determinants 275

A.5 Curvilinear coordinates 276

A.6 Invariants, vectors, and tensors 277

A.7 Vector analysis 279

A.8 Vector addition 280

A.9 Scalar multiplication 280

A.10 Unit vectors 281

A.11 Cartesian representation of a vector 281

A.12 The scalar product 282

A.13 The vector product 283

A.14 The triple scalar product 285

A.15 Extreme-value problems in differential calculus 286

A.16 Some examples of extreme-value problems with simple constraints 287

A.17 The Lagrange multiplier method 288

A.18 Elements of the calculus of variations 291

A.19 The Divergence Theorem 297

A.20 Matrix algebra 299

A.21 Equality 301

A.22 Addition and subtraction 301

A.23 Scalar multiplication 301

A.24 Matrix multiplication 301

A.25 Unit matrix 302

A.26 Inversion of matrices 302

Bibliography 304

Symbols 310

Index 315