## Description

This book is specially designed for the course on “Strength of Materials I” for Civil engineering and Mechanical engineering. All the concepts have been explained in a simple manner and problems are solved in a step-by-step procedure. A large number of illustrative examples have been solved, for better understanding of basic principles and fundamental concepts. This book is written in a simple and logical sequence.

## Table of Content

**Chapter 1 Stress, Strain and Deformation of Solids**

1.1 Introduction to Mechanics

1.2 Review of Statics and Dynamics

1.3 Mechanical Properties of Materials

1.4 Mechanics of Deformable Bodies

1.4.1 Stress and Strain

1.4.2 Simple and Compound Stresses

1.4.3 Types of Stresses

1.4.4 Shear Stress

1.4.5 Volumetric Strain

1.4.6 Longitudinal Strain

1.4.7 Lateral Strain

1.4.8 Poisson’s Ratio

1.5 Hooke’s Law

1.6 Relationship between Stress and Strain

1.6.1 One-dimensional Stress System

1.6.2 Two-dimensional Stress System

1.6.3 Three-dimensional Stress System

1.7 Elastic Constants

1.7.1 Relation between Young’s Modulus and Rigidity Modulus

1.7.2 Relation between Young’s Modulus and Bulk Modulus

1.7.3 Relation between Young’s Modulus, Rigidity Modulus and Bulk Modulus

1.8 Stress-strain Diagram

1.8.1 Stress-strain Diagram for Mild Steel

1.8.2 Stress-strain Diagram for TOR Steel

1.8.3 Stress-strain Diagram for Concrete

1.9 Deformation of a Body due to Self Weight

1.10 Analysis of Bars of Varying Sections

1.11 Principle of Superposition

1.12 Deformation in a Uniformly Tapering Round Bar

1.13 Deformation in a Uniformly Tapering Rectangular Bar

1.14 Stresses in Composite/Compound Bar

1.15 Thermal Stress

1.15.1 Stresses and Strain when the Supports Yield

1.15.2 Thermal Stresses in Composite Bars of Varying Cross Sections Fixed at

Both Ends

1.15.3 Thermal Stress in Composite Bar

1.16 Introduction to Complex Stresses

1.17 Principal Planes and Principal Stresses

1.18 Analytical Method for Determining Stresses on Oblique Section

1.18.1 A Member Subjected to a Direct Stress in One Plane

1.18.2 A Member Subjected to Like Direct Stresses in Two Mutually Perpendicular

Directions

1.18.3 A Member Subjected to Simple Shear Stress

1.18.4 A Member Subjected to Direct Stresses in Two Mutually Perpendicular

Directions, Accompanied by a Simple Shear Stress

1.19 Graphical Method for Determining Stresses on Oblique Section

1.19.1 Mohr’s Circle

1.19.2 Mohr’s Circle, when a Body is Subjected to Two Mutual Perpendicular

Principal Tensile Stresses of Unequal Intensities

1.19.3 Mohr’s Circle when a Body is Subjected to Two Mutually Perpendicular

Principal Stresses, which are Unequal and Unlike

1.19.4 Mohr’s Circle when a Body is Subjected to Two Mutually Perpendicular

Principal Tensile Stresses Accompanied by a Simple Shear Stress

1.20 Thin Cylindrical and Spherical Shells

1.20.1 Stresses in Thin Cylinder

1.20.2 Change in Dimension of a Thin Cylinder Subjected to Internal Pressure

1.20.3 Maximum ShearStress

1.20.4 A Thin Cylinder Subjected to Internal Fluid Pressure and Torque

1.20.5 Efficiency of a Joint

1.21 Thin Spherical Shells

1.21.1 Change in Dimensions of a Thin Spherical Shell Subjected to Internal

Pressure

1.22 Wire Wound Thin Cylindrical Shells

1.23 Strain Energy

1.23.1 Resilience

1.23.2 Proof Resilience

1.23.3 Modulus of Resilience

1.24 Stresses due to Different Types of Loads

1.24.1 Expression for Strain Energy Stored in a Body, when the Load is Applied

Gradually

1.24.2 Expression for Strain Energy Stored in the Body, when the Load is Applied

Suddenly

1.24.3 Expression for Strain Energy Stored in the Body, when the Load is Applied

With Impact

1.25 Strain Energy due to Shear

1.26 Strain Energy due to Torsion

**Chapter 2 Shear and Bending in Beams**

2.1 Introduction

2.2 Classification of Beams

2.2.1 Statically Determinate Beams

2.2.2 Statically Indeterminate Beams

2.3 Types of Supports

2.4 Types of Loading

2.5 Shear Force and Bending Moment

2.5.1 Shear Force

2.5.2 Bending Moment

2.5.3 Bending Moment and Shear Force Diagram

2.5.4 Relationship between Intensity of Load, Shear Force and Bending

Moment

2.6 Shear Force and Bending Moment Diagrams for Cantilever Beams

2.6.1 Cantilever Beam with Point Load at Free End

2.6.2 Cantilever Beam with UDL

2.6.3 Cantilever Beam with UDL and Point Load

2.6.4 Cantilever Beam with UDL for a Part of its Length

2.6.5 Cantilever Beam with UVL

2.7 Shear Force and Bending Moment Diagrams for Simply Supported Beams

2.7.1 Simply Supported Beam with a Point Load W at the Centre

2.7.2 Simply Supported Beam with an Eccentric Point Load

2.7.3 Simply Supported Beam with Uniformly Distributed Load

2.7.4 Simply Supported Beam with Uniformly Varying Load from Zero at

Each End to w Per Unit Length at the Centre

2.7.5 Simply Supported Beam with Uniformly Varying Load from Zero at One

End to w Per Unit Length at the Other End

2.7.6 Simply Supported Beam with a Concentrated Moment

2.7.7 Point of Contraflexure

2.8 Shear Force and Bending Moment Diagrams for Overhanging Beams

2.9 Bending Stresses in Beams

2.9.1 Pure Bending or Simple Bending

2.9.2 Theory of Simple Bending (Classic Flexure Formula)

2.9.3 Expression for Bending Stress

2.9.4 Bending Stresses in Symmetrical Sections

2.9.5 Bending Stresses in Unsymmetrical Sections

2.9.6 Section Modulus

2.9.7 Section Modulus for Various Shapes or Beam Sections

2.10 Shear Stresses in Beams

2.10.1 Shear Stress at a Section

2.10.2 Shear Stress Distribution for Different Sections

2.11 Flitched Beams or Composite Beams

**Chapter 3 Deflection of Beams**

3.1 Introduction

3.2 Differential Equation of Deflected Beam

3.3 Slope and Deflection at a Point

3.4 Double Integration Method

3.4.1 Cantilever Beam with Point Load at Free End

3.4.2 Cantilever Beam with Concentrated Load at a Distance a from the Fixed

End

3.4.3 Cantilever Beam with Uniformly Distributed Load w Per Unit Run Over

The Whole Length

3.4.4 Cantilever Beam with Uniformly Distributed Load of w Per Unit Run for

a Distance a from the Fixed End

3.4.5 Cantilever Beam with Uniformly Distributed Load of w Per Unit Run on

A Part of Span from the Free End

3.4.6 Cantilever Beam with Moment Applied at Free End

3.4.7 Cantilever Beam with Uniformly Varying Load, Zero at the Free End to

w Per Unit Run at the Fixed End

3.4.8 Cantilever Beam with Uniformly Varying Load, Zero at the Fixed End to

w Per Unit Run at the Free End

3.4.9 Simply Supported Beam with Point Load at Mid Span

3.4.10 Simply Supported Beam with Uniformly Distributed Load of w Per

Meter Run Over the Whole Span

3.5 Macaulay’s Method

3.5.1 Boundary Conditions for Statically Determinate Beams

3.5.2 Example: Simply Supported Beam with Point Load at Mid Span

3.6 Moment Area Method

3.6.1 Moment Area Theorems

3.6.2 Cantilever Beam with a Point Load at Free End

3.6.3 Cantilever Beam with Uniformly Distributed Load

3.6.4 Simply Supported Beam with Point Load

3.6.5 Simply Supported Beam with Uniformly Distributed Load

3.7 Conjugate Beam Method

3.7.1 Cantilever Beam with Point Load at Free End

3.7.2 Cantilever Beam with Uniformly Distributed Load

3.7.3 Simply Supported Beam with Point Load at Mid Span

3.7.4 Simply Supported Beam with Uniformly Distributed Load

**Chapter 4 Torsion**

4.1 Introduction

4.2 Torsion of Shafts

4.2.1 Shafts

4.2.2 Torsional Equation

4.2.3 Maximum Torque Transmitted by Solid Circular Shaft

4.2.4 Maximum Torque Transmitted by Hollow Circular Shafts

4.2.5 Torsional Rigidity

4.2.6 Power Transmitted by the Shaft

4.2.7 Stresses in Shafts

4.2.8 Modulus of Rupture

4.2.9 Comparison of Solid and Hollow Shafts

4.3 Combined Bending Moment and Torsion

4.4 Shafts in Series

4.5 Shafts in Parallel

4.6 Compound Shafts

4.7 Shaft of Varying Section or Stepped Shaft

4.8 Torsional Resilience

4.9 Springs

4.9.1 Types of Springs

4.10 Close Coiled Helical Springs

4.11 Open Coiled Helical Springs

4.11.1 Stress in the Spring Wire

4.11.2 Spring Index

4.12 Springs in Series and Parallel

4.13 Laminated Springs

4.13.1 Semi-elliptical Spring

4.13.2 Quarter-elliptical Spring

4.14 Buffer Spring

4.14.1 Design of Buffer Spring

**Chapter 5 Analysis of Trusses **

5.1 Introduction

5.2 Plane Trusses

5.2.1 Perfect Frame/Truss

5.2.2 Deficient Frame

5.2.3 Redundant Frame

5.3 Analysis of Plane Trusses

5.3.1 Assumptions

5.3.2 Determination of Forces in the Members

5.3.3 Analytical Methods

5.3.4 Method of Joints

5.3.5 Method of Sections

5.3.6 Method of Tension Coefficients

5.4 Space Trusses

5.4.1 Tension Coefficient Method for Space Truss

** Solved Question Papers**

References

Index

## About The Authors

**Dr. Binu Sukumar** is Professor & Head, Department of Civil Engineering, R.M.K. Engineering College, Chennai. She has more than 23 years of experience in teaching. She obtained her B.Tech in Civil Engineering from Government College of Engineering, Trivandrum, M.Tech in Structural Engineering from Indian Institute of Technology, Madras and Ph.D. from Anna University, Chennai. She is a member of the Editorial Board for International Journal of Advances in Engineering Research & International Journal of Research in Science and Technology and Reviewer for many international journals published by Elsevier and Springer. She is a recognized Research Supervisor of Anna University.

**P Joyson Silva **is Assistant Professor, Department of Civil Engineering, R.M.K. Engineering College, Chennai. He has obtained his M.Tech in Structural Engineering from NIT Trichy. He has published many papers in International and National Journals. He is currently pursuing Ph.D program at Anna University, Chennai.

**V Sherin **is Assistant Professor, Department of Civil Engineering, R.M.K. Engineering College, Chennai. She obtained her Masters in Structural Engineering securing the Gold Medal from Mepco Schlenk Engineering College (Autonomous), Tamil Nadu.

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