Strength of Materials

1313 Pages·2018·35.955 MB·English

by  R. K. Rajput

AA TTeexxttbbooookk ooff
SSttrreennggtthh ooff
MMaatteerriiaallss
In
SI Units
[A Textbook for students of B.E., B.Tech. as per the 2018 AICTE
Curriculum, AMIE, GATE, UPSC and Other Competitive Examinations]
Er. R.K. Rajput
M.E. (Hons.) Gold Medallist; Grad.-Mech. Engg. & Elect. Engg.; MIE (India);
MSESI; MISTE; CE (India)
Recipient of :
“Best Teacher (Academic) Award”
“Distinguished Author Award”
“Jawahar Lal Nehru Memorial Gold Medal”
for an Outstanding Research Paper
(Institution of Engineers—India)
Principal (Formerly)
 Thapar Polytechnic College;
 Punjab College of Information Technology;
PATIALA
S Chand And Company Limited
(ISO 9001 Certified Company)
RAM NAGAR, NEW DELHI - 110 055
S Chand And Company Limited
(ISO 9001 Certified Company)
Head Office: 7361, RAM NAGAR, QUTAB ROAD, NEW DELHI - 110 055
Phone: [phone] Fax: [phone]
www.schandpublishing.com; e-mail: [email protected]
Branches:
Ahmedabad : Ph: 27541965, 27542369, [email protected]
Bengaluru : Ph: 22268048, 22354008, [email protected]
Bhopal : Ph: 4209587, [email protected]
Chandigarh : Ph: 2625356, 2625546, 4025418, [email protected]
Chennai : Ph: 28410027, 28410058, [email protected]
Coimbatore : Ph: 2323620, 4217136, [email protected] (Marketing Office)
Cuttack : Ph: 2332580, 2332581, [email protected]
Dehradun : Ph: 2711101, 2710861, [email protected]
Guwahati : Ph: 2738811, 2735640, [email protected]
Hyderabad : Ph: 27550194, 27550195, [email protected]
Jaipur : Ph: 2219175, 2219176, [email protected]
Jalandhar : Ph: 2401630, [email protected]
Kochi : Ph: 2809208, 2808207, [email protected]
Kolkata : Ph: 23353914, 23357458, [email protected]
Lucknow : Ph: 4065646, [email protected]
Mumbai : Ph: 22690881, 22610885, 22610886, [email protected]
Nagpur : Ph: 2720523, 2777666, [email protected]
Patna : Ph: 2300489, 2260011, [email protected]
Pune : Ph: 64017298, [email protected]
Raipur : Ph: 2443142, [email protected] (Marketing Office)
Ranchi : Ph: 2361178, [email protected]
Sahibabad : Ph: 2771235, 2771238, [email protected]
© 1998, Er. R.K. Rajput
All rights reserved. No part of this publication may be reproduced or copied in any material form (including
photocopying or storing it in any medium in form of graphics, electronic or mechanical means and whether
or not transient or incidental to some other use of this publication) without written permission of the copyright
owner. Any breach of this will entail legal action and prosecution without further notice.
Jurisdiction : All disputes with respect to this publication shall be subject to the jurisdiction of the Courts,
Tribunals and Forums of New Delhi, India only.
First Edition 1998; Subsequent Editions and Reprints of the Main Textbook 1999, 2001, 2003 (Twice), 2004,
2006, 2007 (Twice), 2008, 2009, 2010, 2011, 2012 (Thrice), 2013, 2014 (Twice), 2015, 2016, 2017
Revised Edition 2018
ISBN : 978-93-525-3369-5
Dedicated
to
My Wife
Mrs. Ramesh Rajput
(iii)

PREFACE
I take the pleasure in presenting 7th revised edition of this book.
The warm reception which the previous editions and reprints have
received is a matter of much satisfaction to me.
Besides revising the other chapters, specifically in Chapter
22 and Chapter 23, Questions (both ‘Subjective’ and ‘Objective’)
selected from latest UPSC examinations, with solutions, have been
added to make this book a fresh unit in every respect.
The constructive suggestions for the improvement of this are
most welcome.
Er. R. K. Rajput
(Author)
Disclaimer : While the authors of this book have made every effort to avoid any mistakes or omission and have used their
skill, expertise and knowledge to the best of their capacity to provide accurate and updated information. The author and
S. Chand does not give any representation or warranty with respect to the accuracy or completeness of the contents of this
publication and are selling this publication on the condition and understanding that they shall not be made liable in any manner
whatsoever. S. Chand and the author expressly disclaim all and any liability/responsibility to any person, whether a purchaser
or reader of this publication or not, in respect of anything and everything forming part of the contents of this publication.
S. Chand shall not be responsible for any errors, omissions or damages arising out of the use of the information contained in
this publication.
Further, the appearance of the personal name, location, place and incidence, if any; in the illustrations used herein is purely
coincidental and work of imagination. Thus the same should in no manner be termed as defamatory to any individual.
(v)
PREFACE TO THE FIRST EDITION
The primary purpose of writing this book is to make available
to the student community, a book which deals with the various
topics in the subject of Strength of Materials exhaustively.
I have taken special care to present the subject-matter in a lucid,
direct and easily understandable style. A large number of worked out
simple, moderate and difficult problems are arranged in a systematic
manner to enable the students to grasp the subject effectively, from
examination point of view.
The book comprises of 18 chapters (including advance topics)
covering the syllabi in the subject of “Strength of Materials” of all
the Indian Universities and Competitive Examinations as well. The
other important feature of the book is that it contains Experiments at
the end of the chapters to enable the students to have an access to
the practical aspects of the subject.
Besides the above features, the book contains Typical Examples
(useful for students appearing in competitive examinations in
particular and other students in general), Highlights, Objective Type
Questions and a large number of Unsolved Examples. All these
features go to make this treatise a complete and comprehensive
book on the subject. It can be candidly said that this book will prove
a boon to the students appearing for Engineering Undergraduate
Examinations as well as for Competitive Examinations.
The author’s thanks are due to his wife Ramesh Rajput without
whose cooperation and encouragement this book would have never
been materialised.
In the end the author wishes to express his gratitude to Shri
Ravindra Kumar Gupta, Managing Director, S. Chand & Company
Ltd., New Delhi for taking pains in bringing out this book in a short
span of time.
Although every care has been taken to make the book free of
errors, yet the author shall be obliged, if errors present are brought
to his notice.
Constructive criticism will be warmly received.
(Author)
(vi)
CONTENTS
1. Simple Stresses and Strains 1–83
1.1 Classification of loads ... 1
1.2 Stress ... 2
1.3 Simple stress ... 2
1.4 Strain ... 3
1.4.1 Tensile strain ... 3
1.4.2 Compressive strain ... 3
1.4.3 Shear strain ... 3
1.4.4 Volumetric strain ... 4
1.5 Stress and Elongation Produced in a bar due to its self-weight ... 17
1.6 Tie Bar of Uniform Strength ... 17
1.7 Stress in a Bar due to Rotation ... 18
1.8 Elongation in Case of a Taper Rod ... 19
1.9 Elongation of a Conical Bar due to its Self-weight ... 22
1.10 Poisson’s Ratio ... 23
1.11 Rotation Between the Elastic Modulii ... 24
1.11.1 Relation between E and C ... 24
1.11.2 Relation between E and K ... 25
1.12 Stresses Induced in Compound Ties or Struts ... 31
1.13 Thermal Stress and Strain ... 46
1.14 Hoop Stress ... 63
Typical Examples (For Competitive Examinations) ... 64
Highlights ... 75
Objective Type Questions ... 76
Unsolved Examples ... 79
2. Principal Stresses and Strains 84–135
2.1 Stresses in a Tensile Member ... 84
2.2 Stresses due to Pure Shearing ... 85
2.3 Two Mutually Perpendicular Direct Stresses ... 86
2.4 Principal Planes and Principal Stresses ... 87
2.5 Two-dimensional Stress System (General) ... 87
2.6 Graphical Methods ... 89
2.6.1 Mohr’s circle ... 89
2.6.1.1 Mohr’s circle construction for like stresses ... 90
2.6.1.2 Mohr’s circle construction for unlike stresses ... 91
2.6.1.3 Mohr’s circle construction for two perpendicular direct stresses ... 91
as the state of simple shear
2.6.1.4 Mohr’s circle construction for principal stresses ... 93
(vii)
2.6.2 Ellipse of stress ... 117
2.7 Combined Bending and Torsion ... 118
2.8 Analysis of Strain ... 121
2.8.1 Direct strain on oblique plane due to a direct pull on a plane ... 121
2.8.2 Direct strain on a oblique plane due to shear stress. ... 122
2.8.3 Direct strain on an oblique plane due to two normal pulls ... 123
and a shear force
2.8.4 Strain on an inclined section due to two perpendicular ... 125
normal strains
2.8.5 Ellipse of strains ... 126
2.8.6 Mohr’s circle of strains ... 127
2.8.7 Principal strains and strain energy due to principal stresses ... 127
2.8.7.1 Principal strains due to principal stresses ... 127
2.8.7.2 Strain energy due to principal stresses ... 127
Highlights ... 132
Unsolved Examples ... 133
3. Bending Moments and Shearing Forces 136–185
3.1 Introduction ... 136
3.2 Some Basic Definitions ... 136
3.3 Classification of Beams ... 137
3.4 Shear Force (S.F.) and Bending Moment (B.M.) ... 138
3.5 Sign conventions ... 138
3.6 Cantilever with an End Load ... 138
3.7 Cantilever with Uniformly Distributed Load ... 139
3.8 Cantilever with Uniformly Distributed load and a
Concentrated Load at the Free End ... 139
3.9 Cantilever Carrying Uniformly Distributed Load for a Part of its ... 140
Length from the Free End
3.10 Cantilever Carrying Load Whose Intensity Varies Uniformly from ... 142
Zero at the Free End to the Per unit Run at the Fixed End
3.11 Cantilever Carrying load Whose Intensity varies Uniformly from ... 144
Zero at the Fixed Point End to w Per Unit Run at the Free End
3.12 Simply Supported Beam Carrying Concentrated Load at the Mid Span ... 147
3.13 Simply Supported Beam Carrying Concentrated Load not at Mid Span ... 147
3.14 Simply Supported Beam Carrying a Uniformly Distributed Load ... 148
of w Per unit Run over the Whole Span
3.15 General Relation between the Load, the Shearing Force and the ... 149
Bending Moment
3.16 Simply Supported Beam Carrying a Load whose Intensity varies ... 153
Uniformly from Zero at each End to w per Unit Run at the Mid Span
3.17 Simply Supported Beam carrying a Load whose Intensity varies ... 154
Uniformly from Zero at one end to w per unit Run at the other End
(viii)
3.18 Simply Supported Beam with Equal Overhangs and carrying a ... 161
Uniformly Distributed Load of per w Unit Run over the Whole Length
3.19 The Points of Contraflexure ... 162
3.20 Loading and B.M. diagrams from S.F. Diagrams ... 172
Typical Examples (For Competitive Examinations) ... 174
Highlights ... 181
Objective Type Questions ... 181
Unsolved Examples ... 182
4. Bending Stresses in Beams 186–248
4.1 Theory of Simple Bending (Bending equation) ... 186
4.2 Position of Neutral Axis ... 188
4.3 Section Modulus ... 188
4.4 Practical Application of Bending Equation ... 190
4.5 Beam of Heterogeneous Materials (Flitched beam) ... 211
4.6 Beams of Uniform Strength ... 218
4.7 Bimetallic Strip ... 223
4.8 Reinforced Cement Concrete (R.C.C.) ... 225
Typical Examples (For Competitive Examinations) ... 230
Highlights ... 244
Objective Type Questions ... 245
Unsolved Examples ... 245
5. Combined Direct and Bending Stresses 249–282
5.1 Introduction ... 249
5.2 Load acting Eccentrically to One Axis ... 249
5.3 Condition for No Tension in the Section ... 251
5.4 Wind Pressure on Chimneys ... 261
5.5 Earth Pressure on retaining Walls ... 266
5.5.1 Angle of repose ... 266
5.5.2 Earth pressure ... 267
Typical Examples (For Competitive Examinations) ... 273
Highlights ... 280
Objective Type questions ... 280
Theoretical Questions ... 281
Unsolved Examples ... 281
6. Shearing Stresses 283–313
6.1 Introduction ... 283
6.2 Shearing Stress Variation ... 284
6.3 Variation of Shear Stress in Beam Cross-section ... 285
6.4 Shear Stress Distribution for Typical Sections ... 288
Typical Examples (For Competitive Examinations) ... 298
Highlights ... 311
(ix)