Engineering mechanics of deformable solids : a presentation with exercises / Sanjay Govindjee.

Format:

Book

Author/Creator:

Govindjee, Sanjay.

Contributor:

Class of 1891 Department of Arts Fund.

UPSO (University Press Scholarship Online)

Language:

English

Subjects (All):

Deformations (Mechanics).

Solids--Mechanical properties.

Solids.

Mechanical engineering--Problems, exercises, etc.

Mechanical engineering.

Genre:

Problems and exercises.

Physical Description:

1 online resource (xiv, 334 pages) : illustrations

Edition:

First edition.

Place of Publication:

Oxford : Oxford University Press, 2013.

System Details:

text file

Summary:

This book covers the essential elements of engineering mechanics of deformable bodies, including mechanical elements in tension-compression, torsion, and bending. It emphasizes a fundamental bottom-up approach to the subject in a concise and uncluttered presentation. Of special interest are chapters dealing with potential energy as well as principle of virtual work methods for both exact and approximate solutions. The book places an emphasis on the underlying assumptions of the theories in order to encourage the reader to think more deeply about the subject matter. The book should be of special interest to undergraduate students looking for a streamlined presentation as well as those returning to the subject for a second time. Solutions to the end of chapter exercises are available on request for instructors. Book jacket.

Contents:

1 Introduction 1

1.1 Force systems 2

1.1.1 Units 2

1.2 Characterization of force systems 3

1.2.1 Distributed forces 3

1.2.2 Equivalent forces systems 5

1.3 Work and power 6

1.3.1 Conservative forces 7

1.3.2 Conservative systems 8

1.4 Static equilibrium 8

1.4.1 Equilibrium of a body 8

1.4.2 Virtual work and virtual power 8

1.5 Equilibrium of subsets: Free-body diagrams 9

1.5.1 Internal force diagram 9

1.6 Dimensional homogeneity 11

Exercises 11

2 Tension-Compression Bars: The One-Dimensional Case 13

2.1 Displacement field and strain 13

2.1.1 Units 14

2.1.2 Strain at a point 15

2.2 Stress 17

2.2.1 Units 17

2.2.2 Pointwise equilibrium 17

2.3 Constitutive relations 18

2.3.1 One-dimensional Hooke's Law 18

2.3.2 Additional constitutive behaviors 19

2.4 A one-dimensional theory of mechanical response 19

2.4.1 Axial deformation of bars: Examples 19

2.4.2 Differential equation approach 26

2.5 Energy methods 31

2.6 Stress-based design 34

Chapter summary 35

Exercises 36

3 Stress 41

3.1 Average normal and shear- stress 41

3.1.1 Average stresses for a bar under axial load 42

3.1.2 Design with average stresses 43

3.2 Stress at a point 46

3.2.1 Nomenclature 47

3.2.2 Internal reactions in terms of stresses 48

3.2.3 Equilibrium in terms of stresses 50

3.3 Polar and spherical coordinates 53

3.3.1 Cylindrical/polar stresses 54

3.3.2 Spherical stresses 55

Chapter summary 56

Exercises 56

4 Strain 59

4.1 Shear strain 59

4.2 Pointwise strain 59

4.2.1 Normal strain at a point 60

4.2.2 Shear strain at a point 61

4.2.3 Two-dimensional strains 62

4.2.4 Three-dimensional strain 63

4.3 Polar/cylindrical and spherical strain 64

4.4 Number of unknowns and equations 64

Chapter summary 65

Exercises 65

5 Constitutive Response 67

5.1 Three-dimensional Hooke's Law 67

5.1.1 Pressure 69

5.1.2 Strain energy in three dimensions 70

5.2 Two-dimensional Hooke's Law 70

5.2.1 Two-dimensional plane stress 70

5.2.2 Two-dimensional plane strain 71

5.3 One-dimensional Hooke's Law: Uniaxial state of stress 72

5.4 Polar/cylindrical and spherical coordinates 72

Chapter summary 72

Exercises 73

6 Basic Techniques of Strength of Materials 75

6.1 One-dimensional axially loaded rod revisited 75

6.2 Thinness 79

6.2.1 Cylindrical thin-walled pressure vessels 79

6.2.2 Spherical thin-walled pressure vessels 81

6.3 Saint-Venant's principle 82

Chapter summary 85

Exercises 86

7 Circular and Thin-Wall Torsion 89

7.1 Circular bars: Kinematic assumption 89

7.2 Circular bars: Equilibrium 92

7.2.1 Internal torque-stress relation 93

7.3 Circular bars: Elastic response 94

7.3.1 Elastic examples 94

7.3.2 Differential equation approach 103

7.4 Energy methods 107

7.5 Torsional failure: Brittle materials 108

7.6 Torsional failure: Ductile materials 110

7.6.1 Twist-rate at and beyond yield 110

7.6.2 Stresses beyond yield 111

7.6.3 Torque beyond yield 112

7.6.4 Unloading after yield 113

7.7 Thin-walled tubes 116

7.7.1 Equilibrium 117

7.7.2 Shear flow 117

7.7.3 Internal torque-stress relation 118

7.7.4 Kinematics of thin-walled tubes 119

Chapter summary 121

Exercises 122

8 Bending of Beams 128

8.1 Symmetric bending: Kinematics 128

8.2 Symmetric bending: Equilibrium 131

8.2.1 Internal resultant definitions 132

8.3 Symmetric bending: Elastic response 136

8.3.1 Neutral axis 136

8.3.2 Elastic examples: Symmetric bending stresses 138

8.4 Symmetric bending: Elastic deflections by differential equations 144

8.5 Symmetric multi-axis bending 148

8.5.1 Symmetric multi-axis bending: Kinematics 149

8.5.2 Symmetric multi-axis bending: Equilibrium 149

8.5.3 Symmetric multi-axis bending: Elastic 150

8.6 Shear stresses 152

8.6.1 Equilibrium construction for shear stresses 153

8.6.2 Energy methods: Shear deformation of beams 158

8.7 Plastic bending 158

8.7.1 Limit cases 159

8.7.2 Bending at and beyond yield: Rectangular cross-section 161

8.7.3 Stresses beyond yield: Rectangular cross-section 163

8.7.4 Moment beyond yield: Rectangular cross-section 163

8.7.5 Unloading after yield: Rectangular cross-section 164

Chapter summary 167

Exercises 168

9 Analysis of Multi-Axial Stress and Strain 179

9.1 Transformation of vectors 179

9.2 Transformation of stress 180

9.2.1 Traction vector method 181

9.2.2 Maximum normal and shear stresses 184

9.2.3 Eigenvalues and eigenvectors 185

9.2.4 Mohr's circle of stress 187

9.2.5 Three-dimensional Mohr's circles of stress 190

9.3 Transformation of strains 192

9.3.1 Maximum normal and shear strains 193

9.4 Multi-axial failure criteria 197

9.4.1 Tresca's yield condition 198

9.4.2 Henky-von Mises condition 200

Chapter summary 204

Exercises 205

10 Virtual Work Methods: Virtual Forces 209

10.1 The virtual work theorem: Virtual force version 209

10.2 Virtual work expressions 211

10.2.1 Determination of displacements 211

10.2.2 Determination of rotations 211

10.2.3 Axial rods 212

10.2.4 Torsion rods 213

10.2.5 Bending of beams 214

10.2.6 Direct shear in beams (elastic only) 215

10.3 Principle of virtual forces: Proof 217

10.3.1 Axial bar: Proof 217

10.3.2 Beam bending: Proof 218

10.4 Applications: Method of virtual forces 220

Chapter summary 225

Exercises 226

11 Potential-Energy Methods 230

11.1 Potential energy: Spring-mass system 230

11.2 Stored elastic energy: Continuous systems 232

11.3 Castigliano's first theorem 235

11.4 Stationary complementary potential energy 236

11.5 Stored complementary energy: Continuous systems 237

11.6 Castigliano's second theorem 240

11.7 Stationary potential energy: Approximate methods 246

11.8 Ritz's method 250

11.9 Approximation errors 254

11.9.1 Types of error 254

11.9.2 Estimating error in Ritz's method 255

11.9.3 Selecting functions for Ritz's method 257

Chapter summary 258

Exercises 259

12 Geometric Instability 263

12.1 Point-mass pendulum: Stability 263

12.2 Instability: Rigid links 264

12.2.1 Potential energy: Stability 265

12.2.2 Small deformation assumption 267

12.3 Euler buckling of beam-columns 270

12.3.1 Equilibrium 270

12.3.2 Applications 271

12.3.3 Limitations to the buckling formulae 274

12.4 Eccentric loads 275

12.4.1 Rigid links 275

12.4.2 Euler columns 277

12.5 Approximate solutions 278

12.5.1 Buckling with distributed loads 282

12.5.2 Deflection behavior for beam-columns with combined axial and transverse loads 285

Chapter summary 286

Exercises 287

13 Virtual Work Methods: Virtual Displacements 291

13.1 The virtual work theorem: Virtual displacement version 291

13.2 The virtual work expressions 293

13.2.1 External work expressions 293

13.2.2 Axial rods 294

13.2.3 Torsion rods 296

13.2.4 Bending of beams 297

13.3 Principle of virtual displacements: Proof 298

13.3.1 Axial bar: Proof 299

13.3.2 Beam bending: Proof 300

13.4 Approximate methods 301

Chapter summary 307

Exercises 308.

Notes:

Includes index.

Electronic reproduction. Oxford Available via World Wide Web.

Description based on print version record.

Local Notes:

Acquired for the Penn Libraries with assistance from the Class of 1891 Department of Arts Fund.

ISBN:

0191649937

9780191649936

Publisher Number:

99977312948

Access Restriction:

Restricted for use by site license.