In this revised and augmented third edition, many new solved problems have been added especially in the chapters l, 2, 5, 6, 7, 10 and 13. Simultaneously, a large number of model objective questions have also been added to test the understanding of the students from the viewpoints of competitive examinations. The biggest advantage of this book is its simplicity in expressing the subject matter in the most simplified manner. The material covered is so designed that any beginner can follow it easily, and get a complete picture of the subject after having gone through the material covered in the text.
I deeply appreciate the many comments and suggestions that I received from the users of the previous editions of this book. I may be contacted on my email for any further suggestion, comment.

1. Simple Stresses and Strains 1-44

1.1 Introduction 1

1.2 Stress-Strain Curves in Tension 1

1.3 True Stress-Strain Curve 3

1.4 Poisson's Ratio 5

1.5 Ductility 5

1.6 Elongation produced in a Test Specimen 6

1.7 Shear Stress and Strain 6

1.8 Volumetric Strain 7

1.9 Bulk Modulus of Elasticity 8

1.10 Elastic Constants Relationship 8

1.10 Thermal Stress and Strain

1.11 Thermal Stress and Strain in a Simple Bar 27

1.12 Thermal Stress and Strain in a Compound Bar 28

Multiple Choice Questions 39

Exercises 41

2. Principal Stresses 45-78

2.1 Introduction 45

2.2 Stresses on an Inclined Plane (Principal Planes and Principal Stresses) 45

2.3 Mohr's Circle of Plane Stress 64

Multiple Choice Questions 74

Exercises 76

3. Centroid and Moment of Inertia 79-116

3.1 Centre of Gravity 79

3.2 Centroid 79

3.3 Moment of Inertia 92

      3.3.1 Moment of Inertia of Mass 92

      3.3.2 Radius of Gyration w.r.t. Mass Moment of Inertia 93

      3.3.3 Moment of Inertia of Area 93

      3.3.4 Radius of Gyration w.r.t. Second Moment of Area 94

3.4 Parallel-Axes Theorem 94

3.5 Moment of Inertia of a Rectangular Section 95

3.6 Moment of Inertia of a Solid Circular Section 97

3.7 Moment of Inertia of a Hollow Circular Section 99

3.8 Moment of Inertia of a Semi-Circle 99

3.9 Moment of Inertia of a Quarter-Circle 100

Multiple Choice Questions 112

Exercises 113

      Shear Forces and Bending Moments in Beams 117-178

4.1 What is a Beam ? 117

4.2 Classification of Beams 117

4.3 Types of Loadings 118

4.4 Calculation of Beam Reactions 119

4.5 Shear Forces in a Beam 119

4.6 Bending Moments in a Beam 120

4.7 Sign Conventions for Shear Force and Bending Moment 120

4.8 Shear Force and Bending Moment Diagrams (SFD and BMD) 121

4.9 SFD and BMD for Cantilever Beams 121

      4.9.1 Cantilever Beam carrying a Point Load at its Free End 121

      4.9.2 Cantilever Beam carrying Uniformly Distributed Load (udl) throughout the Span 122

      4.9.3 Cantilever Beam carrying Uniformly Distributed Load Over a Certain Length from Free End 124

      4.9.4 Cantilever Beam carrying Uniformly Distributed Load Over a Certain Length from Fixed End 125

      4.9.5 Cantilever Beam carrying Uniformly Distributed Load Over its Entire Span and a Point Load at its Free End 126

      4.9.6 Cantilever Beam carrying several Point Loads 127

      4.9.7 Cantilever Beam carrying Uniformly Varying Load 129

4.10 SFD and BMD for Simply Supported Beams 134

      4.10.1 Simply Supported Beam carrying a Central Point Load 134

      4.10.2 Simply Supported Beam carrying an Eccentric Point Load 136

      4.10.3 Simply Supported Beam carrying Uniformly Distributed Load (udl) Over its Entire Span 138

      4.10.4 Simply Supported Beam carrying Uniformly Varying Load which varies from Zero at Each End to w per unit Length at the Mid-Point 139

      4.10.5 Simply Supported Beam carrying Uniformly Varying Load which varies from Zero at One End to w per unit Length at Other End 142

      4.10.6 Simply Supported Beam Subjected to a Couple 144

4.11 Relations among Load, Shear Force and Bending Moment 159

4.12 SFD and BMD for Overhanging Beams 160

      4.12.1 Overhanging Beam with Equal Overhangs on Each Side and Loaded with Point Loads at the Ends 160

      4.12.2 Overhanging Beam with Equal Overhangs on Each Side and Loaded with a Uniformly Distributed Load Over its Entire Span 162

Multiple Choice Questions 171

Exercises 174

5. Stresses in Beams 179-220

5.1 Pure Bending in Beams 179

5.2 Simple Bending Theory 179

5.3 Position of Neutral Axis 181

5.4 Section Modulus 182

5.5 Composite Beam 182

5.6 Beams of Uniform Strength 184

5.7 Shear Stresses in Beams 198

5.8 Shear Stress Distribution (General Case) 198

5.9 Shear Stress Distribution in a Rectangular Cross-Section 200

5.10 Shear Stress Distribution in a Circular Cross-Section 202

5.11 Shear Stress Distribution in an I-Section 204

Multiple Choice Questions 215

Exercises 218

6. Deflection of Beams 221-286

6.1 Introduction 221

6.2 Differential Equation of Flexure 221

6.3 Sign Convention 2Z3

6.4 Double Integration Method 223

      6.4.1 Cantilever Beam carrying a Point Load at its Free End 223

      6.4.2 Cantilever Beam carrying zidl over its Entire Span 225

      6.4.3 Cantilever Beam subjected to a Pure Couple at its Free End 226

      6.4.4 Cantilever Beam carrying a Point Load anywhere on its Span 227

      6.4.5 Cantilever Beam carrying Gradually Varying Load 229

      6.4.6 Simple Beam carrying a Central Point Load 231

      6.4.7 Simple Beam carrying udl over its Entire Span 232

6.5 Macaulay's Method 241

6.6 Moment Area Method 250

      6.6.1 Cantilever Beam carrying a Point Load at its Free End 752

      6.6.2 Cantilever Beam carrying a udl over its Entire Span 254

      6.6.3 Simple Beam carrying a Central Point Load 255

      6.6.4 Simple Beam carrying a udl over its Entire Span 256

6.7 Conjugate Beam Method 263

      6.7.1 Simple Beam carrying a Point Load at its Centre 263

      6.7.2 Simple Beam carrying a Point Load not at the Centre 265

6.8 Method of Superposition 279

Multiple Choice Questions 281

Exercises 283

7.Torsion of Circular Members 287-334

7.1 Introduction 287

7.2 Torsion Equation 287

7.3 Torsional Rigidity 290

7.4 Polar Modulus 290

7.5 Power Transmitted by a Shaft 291

7.6 Effect of Stress Concentration 318

7.7 Torsion of a Tapered Shaft 321

7.8 Torsion of a Thin Circular Tube 322

7.9 Effect of End Thrust 323

7.10 Strain energy Due to Torsion 327

Multiple Choice Questions 329

Exercises 332

8.Springs 335-376

8.1 Introduction 335

8.2 Spring Terminology 335

8.3 Classification of Springs 335

8.4 Load-deflection Curve 337

8.5 Leaf Spring 337

8.6 Quarter-elliptic Leaf Spring 343

8.7 Spiral Spring 346

8.8 Helical Spring 349

      8.8.1 Close Coiled Helical Spring Subjected to an Axial Load 349

      8.8.2 Close Coiled Helical Spring Subjected to an Axial Twist 351

      8.8.3 Open Coiled Helical Spring Subjected to an Axial Load 353

      8.8.4 Open Coiled Helical Spring Subjected to an Axial Twist 355

8.9. Combination of Springs 366

      8.9.1 Series Combination 366

      8.9.2 Parallel Combination 367

Multiple Choice Questions 372

Exercises 375

9. Strain Energy 377-400

9.1 Introduction 377

9.2 Strain Energy due to Direct Loads 377

      9.2.1 Strain Energy due to Gradually Applied Load 377

      9.2.2 Strain Energy due to Suddenly Applied Load 379

      9.2.3 Strain Energy due to Impact or Shock Load 380

9.3 Strain Energy due to Shear 382

9.4 Strain Energy due to Pure Bending 383

9.5 Strain Energy due to Principal Stresses 385

9.6 Strain Energy due to Volumetric Strain 386

9.7 Shear Strain Energy due to Principal Stresses 388

9.8 Castigliano's Theorem 389

Multiple Choice Questions 396

Exercises 398

10. Theory of Elastic Failure401-424

10.1 Introduction 401

10.2 Maximum Normal Stress Theory 401

10.3 Maximum Normal Strain Theory 402

10.4 Maximum Total Strain Energy Theory 403

10.5 Maximum Shear Stress Theory 403

10.6 Maximum Distortion Energy Theory 404

Multiple Choice Questions 421

Exercises 424

11. Buckling of Columns 425-460

11.1 Introduction 425

11.2 Important Terminology 425

11.3 Classification of Columns 425

11.4 Euler's Theory 426

      11.4.1 Euler's Formula (When Both Ends of the Column are Hinged or Pinned) 426

      11.4.2 Euler's Formula (When Both Ends of the Column are Fixed) 428

      11.4.3 Euler's Formula (When One End of the Column is Fixed and Other End Hinged) 430

      11.4.4 Euler's Formula (When One End of the Column is Fixed and Other End Free) 432

      11.4.5 Crippling Stress 434

      11.4.6 Limitations of Euler's Formula 435

      11.5 Empirical Formulae 440

      11.5.1 Rankine-Gordon Formula 441

      11.5.2 Johnson's Parabolic Formula 442

      11.5.3 Straight-Line Formula 443

11.6 IS Code Formula (IS: 800-1962) 444

11.7 Secant Formula (for Eccentric Loading) 444

Multiple Choice Questions 455

Exercises 457

12. Pressure Vessels 461-530

12.1 Introduction 461

12.2 Stresses in a Thin Cylindrical Shell 46I

12.3 Volumetric Strain for a Thin Cylindrical Shell 463

12.4 Wire Wound Thin Cylinders 465

12.5 Stresses in a Thin Spherical Shell 475

12.6 Volumetric Strain for a thin Spherical Shell 477

12.7 Cylindrical Shell with Hemispherical Ends 480

12.8 Stresses in Thick Cylinders (Lame's Theory) 482

      12.8.1 General Case (When Internal and External Pressures both are acting) 485

      12.8.2 When only Internal Pressure is acting 485

      12.8.3 When only External Pressure is acting 487

      12.8.4 When a Solid Circular Shaft is Subjected to External Pressure 488

12.9 Longitudinal Stress 488

12.10 Strains in Thick Cylinders 495

12.11 Compound Cylinders 499

      12.11.1 Stress due to Shrinkage 500

      12.11.2 Stresses due to Fluid Pressure 502

      12.11.3 Resultant Stresses 504

      12.11.4 Shrinkage Allowance 505

12.12 Stresses in a Thick Spherical Shell 518

Multiple Choice Questions 523

Exercises 527

13. Plane Trusses 531-578

13.1 Introduction 531

13.2 Types of Trusses 531

13.3 Forces in the Truss 533

13.4 Analysis of Trusses 533

13.4.1 Analysis of Trusses by Method of Joints 533

13.4.2 Analysis of Trusses by Method of Sections 559

13.5 Zero-Force Members 571

Multiple Choice Questions 572

Exercises 573

14. Mechanical Testing of Materials 579-588

14.1 Introduction 579

14.2 Hardness Test 579

      14.2.1 Brinell Test 579

      14.2.2 Rockwell Test 580

      14.2.3 Vickers Test 580

14.3 Fatigue 580

14.4 Creep 581

14.5 Tension Test 582

14.6 Compression Test 582

14.7 Stiffness Test 583

14.8 Torsion Test 583

14.9 Bend Test 584

14.10 Impact Test 584

Multiple Choice Questions 586

Model Multiple Choice Questions for Competitive Examinations 589-612

Appendix A 613-620

Appendix B 621-622

Subject Index 623-624

D. K. Singh is associate professor in the Division of Manufacturing Processes and Automation Engineering at Netaji Subhas Institute of Technology, University of Delhi, New Delhi. He has contributed over 35 papers to various national and international journals, and conferences. He has also authored 11 books. His books are published by Ane Books Pvt. Ltd. (co-published with CRC Press /Taylor & Francis Group, USA) and Pearson Education, Singapore.

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