Engineering structures considered include bars, columns, struts, tubes, vessels, beams, springs and frames. The loadings imposed upon them are, typically, tension, compression and shear, bending, torsion and pressure, separately and in combination. The mechanics of such structures examine the manner in which they each bear their respective loading in a safe predictable way. This aids design considerations upon choice of material and its physical shape when seeking, say, a safe design with low weight.
The presentation of chapters is intended to guide the reader from a basic to more advanced understanding of common engineering structures. Thus, the consideration of stress and strain under elastic and plastic conditions is required for a full understanding of a structure that may bend, twist and buckle as it is deflected by its loading. The approach adopted is to intersperse theory with examples and exercises that emphasise practical application. Standard analytical techniques including stress transformation, energy methods and yield criteria precede a final chapter on finite element analysis.
Worked examples and exercises have been devised and compiled by the author to support the topics within each chapter. Some have been derived, with a conversion to SI units, from past examination papers set by institutions with which the author has been associated, namely: Brunel, Kingston and Surrey Universities and the Council of Engineering Institutions.
The contents should serve most courses in mechanical, civil, aeronautical and materials engineering.
Readership: Undergraduate and postgraduate engineering students from intermediary to advanced levels.

PREFACE IX

HISTORICAL OVERVIEW

I Introduction 1

II Units and Conventions 1

III Elasticity 3

IV Structures 4

V Yielding 5

VI Concl uding Remarks 6

References 6

C H A P T E R 1 PROPERTIES OF AREAS

1.1 Centroid and Moments of Area 7

1.2 Parallel and Perpendicular Axes 8

1.3 Principal Second Moments of Area 15

1.4 Graphical Solution to I and I 21

1.5 Matrix Method 24

Exercises 27

C H A P T E R 2 STATIC EQUILIBRIUM

2.1 Co-Planar, Concurrent Forces 31

2.2 Co-Planar, Non-Concurrent Forces 34

2.3 The Free-Body Diagram 40

2.4 Bar Forces in Plane Frames 43

2.5 Forces and Moments in Beams 47

Exercises 53

C H A P T E R 3 BASIC STRESS AND STRAIN

3.1 Direct Stress and Strain 61

3.2 Shear Stress and Strain 66

3.3 Compound Bars 75

3.4 Temperature Effects 83

3.5 Combined Mechanical and Thermal Effects 87

Exercises 91

C H A P T E R 4 LINEAR ELASTICITY

4.1 Elastic Constants 97

4.2 Analysis of Pure Shear 1 14

4.3 Relationships Between Elastic Constants 1 17

4.4 Extended Hooke’s Law 120

4.5 Thin-Walled Pressure Vessels 123

4.6 Thick-Walled Cylinder 130

4.7 Thick-Walled Sphere 139

Exercises 145

C H A P T E R 5 BENDING AND SHEAR IN BEAMS

5.1 Direct Stress in Bending 149

5.2 Combined Bending and Direct Stress 154

5.3 Bending of Composite Beams 1 60

5.4 Shear Stress Due to Shear Force 17 1

5.5 Shear Flow in Thin-Walled Sections 177

References 187

Exercises 187

C H A P T E R 6 SLOPE AND DEFLECTION OF BEA如'IS

6.1 Differential Equation of Flexure 195

6.2 Mohr’s Theorems 199

6.3 Telescopic Cantilever 2 15

6.4 Macaulay’s Method 223

6.5 Superposition Principle 228

Exercises 237

C H A P T E R 7 THEORIES OF TORSION vii

7.1 Torsion of Circular Bars 243

7.2 Torsion of Thin Strips 253

7.3 Bredt-Batho Torsion Theory 263

Exercises 280

C H A P T E R 8 BUCKLING OF STRUTS

8.1 Euler Buckl ing Theory 287

8.2 Imperfect Euler Struts 291

8.3 Empirical Buckling Formulae 306

8.4 inelastic Buckling of Struts 318

Exercises 323

C H A P T E R 9 BUCKLING OF PLATES AND TUBES

9.1 Buckling Modes 329

9.2 Unsupported Plate Under Axial Compression 330

9.3 Supported Plate Under Axial Compression 332

9.4 inelastic Buckling of Plates Under Axial Compression 336

9.5 Post-Buckling of Plates Under Axial Compression 340

9.6 Plate Under Biaxial Compression 342

9.7 Plate Under In-Plane Shear 344

9.8 Tension Field Beam 353

9.9 Secondary Buckling of Plate Elements 365

9.10 Torsional Buckling of Thin Circular Tubes 365

9.11 Torsional and Shear Buckling of Non-Circular Tubes 368

References 370

Exercises 371

C H A P T E R 10 ENERGY METHODS

10.1 Internal Energy and External Work 373

10.2 Strain Energy Expressions 376

10.3 Application to Springs 388

10.4 Impact Loading 406

10.5 Castigliano ’s Theorems 409

10.6 Stationary Potential Energy 423

Exercises 427

C H A P T E R 11 PLANE STRESSAND STRAIN

11.1 Plane Stress Analysis 433

11.2 Mohr’s Circle 444

11.3 Matrix Method 448

11.4 Plane Strain Analyses 450

11.5 Wheatstone Bridge Theory 465

Exercises 481

CHA PT E R 12 YIELD, STRENGTH AND FAILURE CRITERIA

12.1 Yielding of Ductile Metals 487

12.2 Principal Biaxial Stress 501

12.3 Combined Axial and Shear Stresses 505

12.4 Failure Criteria for Brittle Solids 516

12.5 Failure Criteria for Fibrous Materials 524

References 534

Exercises 534

C H A P T E R 13 FINITE ELEMENTS

13.1 Stiffness Matrix 543

13.2 Energy Methods 544

13.3 Bar Element Under Axial Stress 548

13.4 Plane Frame 553

13.5 Torsion Element 560

13.6 Beam Element 564

13.7 Plane Triangular Element 580

Exercises 593

INDEX 599

中科院文献情报中心