# Strength of Materials, Third Edition

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## Book Description

**Strength of Materials, 3rd Edition** is ideal for students pursuing degrees in civil and mechanical engineering, as well as computer science, electronics, and instrumentation. Topics include combined stresses, centroid and the moment of inertia, shear forces and bending moments in beams, stresses in beams, the deflection of beams, torsion of circular members, springs, strain energy, the theory of elastic failure, buckling of columns, pressure vessels, and the analysis of framed structures.

The general arrangement of the new edition of the book remains unchanged however the text has been thoroughly revised. Also, several new solved problems in the chapters have been added. It continues to provide students with a sound understanding of the fundamental concepts of civil structures, machine elements, and other components. A large number of New Solved Examples** **(about 50) have been added in the chapters such as 1, 2, 5, 6, 7, 10, and 13. Model Multiple Choice Questions** **(about 250) have been added at the end to test the understanding of students and to provide and approach for competitive examinations. A new chapter (Chapter 14) on Mechanical Testing of Materials** **has been introduced. The entire text has been thoroughly revised and updated to eliminate the possible errors left out in the previous editions of the book. The Third Edition is augmented by more than 100 pages and the scope of the book has been further increased.

## Table of Contents

**Chapter 1: Simple Stresses and Strains **

1.1 Introduction

1.2 Stress-strain Curves in Tension

1.3 True Stress-strain Curve

1.4 Poisson’s Ratio

1.5 Ductility

1.6 Elongation Produced in A Test Specimen

1.7 Shear Stress and Strain

1.8 Volumetric Strain

1.9 Bulk Modulus of Elasticity

1.10 Elastic Constants Relationship

1.10 Thermal Stress and Strain

1.11 Thermal Stress and Strain in A Simple Bar

1.12 Thermal Stress and Strain in A Compound Bar

• *Multiple Choice Questions *

• *Exercises *

Chapter 2: Principal Stresses

2.1 Introduction

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

2.3 Mohr’s Circle of Plane Stress

• *Multiple Choice Questions *

• *Exercises *

Chapter 3: Centroid and Moment of Inertia

3.1 Centre of Gravity

3.2 Centroid

3.3 Moment of Inertia

3.3.1 Moment of Inertia of Mass

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

3.3.3 Moment of Inertia of Area

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

3.4 Parallel-axes theorem

3.5 Moment of Inertia of A Rectangular Section

3.6 Moment of Inertia of A Solid Circular Section

3.7 Moment of Inertia of A Hollow Circular Section

3.8 Moment of Inertia of A Semi-Circle

3.9 Moment of Inertia of A Quarter-Circle

• *Multiple Choice Questions *

• *Exercises *

Chapter 4: Shear Forces and Bending Moments in Beams

4.1 What is a Beam?

4.2 Classification of Beams

4.3 Types of loadings

4.4 Calculation of Beam Reactions

4.5 Shear Forces in a Beam

4.6 Bending Moments in a Beam

4.7 Sign Conventions for Shear Force and Bending Moment

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

4.9 FD and BMD for Cantilever Beams

4.9.1 Cantilever Beam with a Point Load at its Free end

Second method (for bending moment)

4.9.2 Cantilever Beam with Uniformly Distributed Load (*udl*)

Throughout the Span Second method

4.9.3 Cantilever Beam with Uniformly Distributed Load Over a

Certain Length from Free End

4.9.4 Cantilever Beam with Uniformly Distributed Load Over a

Certain Length from Fixed End

4.9.5 Cantilever Beam with Uniformly Distributed Load Over its

Entire Span and a Point Load at its Free End

4.9.6 Cantilever Beam with Several Point Loads

4.9.7 Cantilever Beam with Uniformly Varying Load

4.10 SFD and BMD for simply supported beams

4.10.1 Simply Supported Beam with a Point Load at Its Mid-Point

4.10.2 Simply Supported Beam with a Point Load not at its Mid-Point

4.10.3 Simply Supported Beam with Uniformly Distributed Load (udl)

Over its Entire Span

4.10.4 Simply Supported Beam with Uniformly Varying Load Which Varies from

Zero at Each End to w per Unit Length at the Mid-Point

4.10.5 Simply Supported Beam with Uniformly Varying Load Which

Varies from Zero at One End to w Per Unit Length at Other End

4.10.6 Simply Supported Beam Subjected to a Couple

4.11 Relations among Load, Shear Force and Bending Moment

4.12 SFD and BMD for Overhanging Beams

4.12.1 Overhanging Beam with Equal Overhangs on Each Side

and Loaded with Point Loads at the Ends

4.12.2 Overhanging Beam with Equal Overhangs on Each Side and

Loaded with a Uniformly Distributed Load Over its Entire Span

• *Multiple Choice Questions *

• *Exercises *

Chapter 5: Stresses in Beams

5.1 Pure Bending in Beams

5.2 Simple Bending Theory

5.3 Position of Neutral Axis

5.4 Section Modulus

5.5 Composite Beam

5.6 Beams of Uniform Strength

5.7 Shear Stresses in Beams

5.8 Shear Stress Distribution (General Case)

5.9 Shear Stress Distribution in A Rectangular Cross-Section

5.10 Shear Stress Distribution in A Circular Cross-Section

5.11 Shear Stress Distribution in an I-Section

• *Multiple Choice Questions *

• *Exercises *

Chapter 6: Deflection of Beams

6.1 Introduction

6.2 Differential Equation of Flexure

6.3 Sign Convention

6.4 Double Integration Method

6.4.1 Cantilever Beam Carrying a Point Load at its Free End

6.4.2 Cantilever Beam Carrying *udl *Over Its Entire Span

6.4.3 Cantilever Beam Subjected to a Pure Couple at its Free End

6.4.4 Cantilever Beam Carrying a Point Load anywhere on its Span

6.4.5 Cantilever Beam Carrying Gradually Varying Load

6.4.6 Simple Beam Carrying a Point Load at its Centre

6.4.7 Simple Beam Carrying *udl *Over Its Entire Span

6.5 Macaulay’s Method

6.7 Moment Area Method

6.6.1 Cantilever Beam Carrying a Point Load at its Free End

6.6.2 Cantilever Beam Carrying a *udl *Over its Entire Span

6.6.3 Simple Beam carrying a Point Load at its Centre

6.6.4 Simple Beam Carrying a *udl *Cver its Entire Span

6.7 Conjugate Beam Method

6.7.1 Simple Beam Carrying a Point Load at its Centre

6.7.2 Simple Beam Carrying a Point Load not at the Centre

6.8 Method of Superposition

• *Multiple Choice Questions *

• *Exercises *

Chapter 7: Torsion of Circular Members

7.1 Introduction

7.2 Torsion Equation

7.3 Torsional Rigidity

7.4 Polar Modulus

7.5 Power Transmitted by a Shaft

7.6 Effect of Stress Concentration

7.7 Combined Bending and Torsion

7.8 Torsion of a Tapered Shaft

7.9 Torsion of a Thin Circular Tube

7.10 Effect of End Thrust

7.11 Strain Energy Due to Torsion

• *Multiple Choice Questions *

• *Exercises *

Chapter 8: Springs

8.1 Introduction

8.2 Spring Terminology

8.3 Classification of Springs

8.4 Load-deflection Curve

8.5 Leaf Spring

8.6 Quarter-elliptic Leaf Spring

8.7 Spiral Spring

8.8 Helical Spring

8.8.1 Close Coiled Helical Spring Subjected to an Axial Load

8.8.2 Close Coiled Helical Spring Subjected to an Axial Twist

8.8.3 Open Coiled Helical Spring Subjected to an Axial Load

8.8.4 Open Coiled Helical Spring Subjected to an Axial Twist

8.9 Combination of springs

8.9.1 Series Combination

8.9.2 Parallel Combination

• *Multiple Choice Questions *

• *Exercises *

Chapter 9: Strain Energy

9.1 Introduction

9.2 Strain Energy Due to Direct Loads

9.2.1 Strain Energy Due to Gradually Applied Load

9.2.2 Strain Energy Due to Suddenly Applied Load

9.2.3 Strain Energy Due to Impact or Shock Load

9.3 Strain Energy Due to Shear

9.4 Strain Energy Due to Torsion

9.5 Strain Energy Due to Pure Bending

9.6 Strain Energy Due to Principal Stresses

9.7 Strain Energy Due to Volumetric Strain

9.8 Shear Strain Energy Due to Principal Stresses

9.9 Castigliano’s Theorem

• *Multiple Choice Questions *

• *Exercises *

Chapter 10: Theory of Elastic Failure

10.1 Introduction

10.2 Maximum Principal Stress Theory

10.3 Maximum Principal Strain Theory

10.4 Total Strain Energy Theory

10.5 Maximum Shear Stress Theory

10.6 Shear Strain Energy Theory

• *Multiple Choice Questions *

• *Exercises *

Chapter 11: Buckling of Columns

11.1 Introduction

11.2 Important Terminology

11.3 Classification of Columns

11.4 Euler’s Theory

11.4.1 Euler’s Formula (When both ends of the Column are Hinged/Pinned)

11.4.2 Euler’s Formula (When both ends of the Column are Fixed)

11.4.3 Euler’s Gormula (When One end of the Column is

Fixed and Other End Hinged)

11.4.4 Euler’s Gormula (When One End of the Column is

Fixed and Other End Free)

11.4.5 Crippling Stress

11.4.6 Limitations of Euler’s Formula

11.5 Empirical Formulae

11.5.1 Rankine-Gordon Formula

11.5.2 Johnson’s Parabolic Formula

11.5.3 Straight-line Formula

11.6 IS Code formula (IS: 800-1962)

11.7 Secant formula (for Eccentric Loading)

• *Multiple Choice Questions *

• *Exercises *

Chapter 12: Pressure Vessels

12.1 Introduction

12.2 Stresses in A Thin Cylindrical Shell

12.3 Volumetric Strain for A Thin Cylindrical Shell

12.4 Wire Wound Thin Cylinders

12.5 Stresses in A Thin Spherical Shell

12.6 Volumetric Strain for A Thin Spherical Shell

12.7 Cylindrical Shell With Hemispherical Ends

12.8 Stresses in Thick Cylinders (Lame’s Theory)

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

12.8.2 When Only Internal Pressure is Acting

12.8.3 When Only External Pressure is Acting

12.8.4 When A Solid Circular Shaft is Subjected to External Pressure

12.9 Longitudinal Stress

12.10 trains in Thick Cylinders

12.11 Compound Cylinders

12.11.1 Stress Due to Shrinkage

12.11.2 Stresses Due to Fluid Pressure

12.11.3 Resultant Stresses

12.11.4 Shrinkage Allowance

12.12 Stresses in A Thick Spherical Shell

• *Multiple Choice Questions *

• *Exercises *

Chapter 13: Analysis of Framed Structures

13.1 Introduction

13.2 Types of Trusses

13.3 Forces in the Truss

13.4 Analysis of Trusses

13.4.1 Analysis of Trusses by Method of Joints

13.4.2 Analysis of Trusses by Method of Sections

13.5 Zero-force members

• *Multiple Choice Questions *

• *Exercises *

Chapter 14: Mechanical Testing of Materials

14.1 Introduction

14.2 Hardness Test

14.2.1 Brinell Test

14.2.2 Rockwell Test

14.2.3 Vickers Test

14.3 Fatigue

14.4 Creep

14.5 Tension Test

14.6 Compression Test

14.7 Stiffness Test

14.8 Torsion Test

14.9 Bend Test

14.10 Impact Test

• *Multiple Choice Questions *

Model Multiple Choice Questions for Competitive Examinations

Index

## Author(s)

### Biography

**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.