## Description

This book is specially designed for the course on “Mechanics of Solids” for B.E Civil Engineering. All the concepts have been explained in a simple manner and problems are solved in a step-by-step manner for better understanding. Previous Anna University question papers with answers have been incorporated at the end, which gives an idea to the students from the examination point of view.

## Table of Content

**Chapter 1 Stress and Strain**

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 Stress in Uniformly Tapering Round Bar

1.13 Stress in Uniformly Tapering Rectangular Bar

1.14 Stresses in 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 Thin Cylinders and Shells

1.16.1 Stresses in Thin Cylinder

1.16.2 Change in Dimension of a Thin Cylinder Subjected to

Internal Pressure

1.16.3 Maximum Shear Stress

1.16.4 A Thin Cylinder Subjected to Internal Fluid Pressure and

Torque

1.16.5 Efficiency of a Joint

1.17 Thin Spherical Shells

1.17.1 Change in Dimensions of a Thin Spherical Shell Subjected

to Internal Pressure

1.18 Wire Wound Thin Cylindrical Shells

1.19 Strain Energy

1.19.1 Resilience

1.19.2 Proof Resilience

1.19.3 Modulus of Resilience

1.20 Stresses due to Different Types of Loads

1.20.1 Expression for Strain Energy Stored in a Body, when the

Load is Applied Gradually

1.20.2 Expression for Strain Energy Stored in the Body, when the

Load is Applied Suddenly

1.20.3 Expression for Strain Energy Stored in the Body, when the

Load is Applied with Impact

1.21 Strain Energy due to Shear

1.22 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 Relation between 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 Section

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**

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 Complex Stresses and Plane Trusses**

5.1 Introduction to Complex Stresses

5.2 Principal Planes and Principal Stresses

5.3 Analytical Method for Determining Stresses on Oblique Section

5.3.1 A Member Subjected to a Direct Stress in One Plane

5.3.2 A Member Subjected to Like Direct Stresses in Two

Mutually Perpendicular Directions

5.3.3 A Member Subjected to Simple Shear Stress

5.3.4 A Member Subjected to Direct Stresses in Two Mutually

Perpendicular Directions, Accompanied by a Simple Shear

Stress

5.4 Graphical Method for Determining Stresses on Oblique Section

5.4.1 Mohr’s Circle

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

Perpendicular Principal Tensile Stresses of Unequal

Intensities

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

Perpendicular Principal Stresses, which are Unequal and

Unlike

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

Perpendicular Principal Tensile Stresses Accompanied by a

Simple Shear Stress

5.5 Plane Trusses

5.5.1 Perfect Structure

5.5.2 Deficient Structure

5.5.3 Redundant Structure

5.6 Analysis of Plane Trusses

5.6.1 Assumptions

5.6.2 Determination of Forces in the Members

5.6.3 Analytical Methods

5.7 Method of Joints

5.8 Method of Sections

5.9 Method of Tension Coefficients

5.9.1 Tension Coefficient

**• Solved Question Papers**

• Index

• Reference

## About The Authors

**Dr. Binu Sukumar** is Professor & Head, Department of Civil Engineering, R.M.K. Engineering College, Chennai. She has more than 22 years of experience in teaching. She btained her B.Tech in Civil Engineering from Government College of Engineering, Trivandrum, Kerala University, M.Tech in Structural Engineering from Indian Institute of Technology, Madras and Ph.D. from Anna University, Chennai. She has also held various positions in industry as Trainee Engineer in Kerala State PWD and Site Engineer in Kerala State Nirmithi Kendra. She was awarded Ultra Tech Award 2015 and 2016 for Outstanding Student Chapter of ICI, Tamil Nadu, as Professor & Head Department of Civil Engineering, R.M.K Engineering College. 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. She is a life member of various professional societies like Indian Society for Technical Education (ISTE), Institution of Engineers (IEI) and Indian Concrete Institute (ICI).

**V Sherin **is Assistant Professor, Department of Civil Engineering, R.M.K. Engineering College, Chennai. She has nearly two years of experience in teaching. She obtained her Masters in Structural Engineering from Mepco Schlenk Engineering College (Autonomous), Sivakasi, Anna University, Chennai. She has secured the Gold Medal in her Master’s degree. She has attended several National and International Conferences, Workshops, Faculty Development and Training programs. She is a life member of Indian Concrete Institute (ICI).

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