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A TEXTBOOK OF ( STRENGTH OF MATERIALS (In S.I. Units) [For Degree, U.P.S.C. (Engg. Services), Gate and other Competitive Examinations] By Dr. R.K. Bansal B.Sc. Engg. (Mech.), M. Tech., Hons. (I.LT., Delhi) Ph.D., M.I.E. (India) Formerly Professor and Head Department of Mechanical Engineering, (University of Delhi) Delhi College of Engineering, Delhi ,. ~ LAXMI PUBLICATIONS (P) LTD BANGALORE • JALANDHAR • CHENNAI KOLKATA e • COCHIN LUCKNOW • • GUWAHATI • MUMBAI • NEW DELHI • BOSTON, USA HYDERABAD RANCHI

i, Published by : LAXMI PUBLICATIONS (P) LTD 113, Golden House, Daryaganj, New Delhi-110002 Phone : 011-43 53 25 00 Fax : 011-43 53 25 28 www.laxmipublications.com info@laxmipublications.com Compiled by : Smt. Nirmal Bansal © All rights reserved with the Author and Publishers. No part of this publication may be reproduced, stored in a retrieual system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording or otherwise without the prior written permission of the publisher. Price : Rs. 450.00 Only. Third Edition : 1996 Reprint : 1998, 2000, 2001, 2002, 2003, 2004 Fourth Edition : 2007, 2008, 2009 OFFICES i! :: I! I! n ",, Ji jl Ii lI India © Bangalore (() Chennai © Cochin (() Guwahati (() Hyderabad © Jalandhar © Kolkata © Lucknow © Mumbai (() Ranchi USA 080-26 61 15 61 044-24 34 47 26 0484-239 70 04 0361-254 36 69, 251 38 81 040-24 65 23 33 0181-222 12 72 Boston 11, Leavitt Street, Hingham, MA 02043, USA 033-22 27 43 84 0522-220 95 78 022-24 91 54 15, 24 92 78 69 0651-22147 64 ESM-0598-450-STRENGTH OF MATERIALS Typeset at : Goswami Printers, Delhi. C-17030/09/01 Printed at : Giriraj Offset Printer, Delhi. J

., i Contents ) Chapter\ Chapter 1. Simple Stresses and Strains 1.1. 1.2. -l! 1.3. 1.4. 1.5. 1.6. 1.7. 1.8. 1.9. 1.10. Introduction Stress Strain Types of Stresses Elasticity and Elastic Limit Hooke's Law and Elastic Modulii Modulus of Elasticity (9r Young's Modulus) Factor of Safety Constitutive Relationship between Stress and Strain Analysis of Bars of Varying Sections 1.11. Analysis of Uf;llformly Tapering Circular Rod 1.12. Analysis of Uniformly Tapering Rectangular Bar 1.13. Analysis of Bars of Composite Sections 1.14. Thermal Stresses 1.15. Thermal Stresses in Composite Bars 1.16. Elongation of a Bar Due to its Own Weight 1.17. Analysis of Bar of Uniform Strength Highlights Exercise 1 Chapter 2. Elastic Constants I ), 2.1. 2.2. 2.3. 2.4. 2.5. 2.6. 2. 7. 2.8. 2.9. 2.10. Introduction Longitudinal Strain Lateral Strain Poisson's Ratio Volumetric Strain Volumetric Strain of a Cylindrical Rod Bulk Modulus Expression for Young's Modulus in Terms of Bulk Modulus Principle of Compliitnentary Shear Stresses Stresses on Inclined Sections when the Element is Subjected to Simple Shear Stresses 2.11. Dia_gonal Stresses Produced by Simple Shear on a Square Block 2.12. Direct (Tensile and Compressive) Strains of the Diagonals 2.13. Relationship between Modulus of Elasticity and Modulus of Rigidity Highlights Exercise 2 r 1-58 1 1 2 2 5 6 6 6 6 14 24 27 30 42 44 50 51 53 54 59-84 59 59 59 60 62 68 70 70 73 74 76 77 78 81 82

Pages Chapter Chapter 3. Principal Stresses and Strains 3.1. 3.2. 3.3. 3.4. 3.5. 3.6. Introduction Principal Planes and Principal Stresses Methods of Determining Stresses on Oblique Section Analytical Method for Determining Stresses·on Oblique Section Graphical Method for Determining Stresses on Oblique Section Mohr's Circle Highlights Exercise 3 85,----142 85 85 85 85 123 128 138 139 Pages Chapter Chapter 6. Shear Force and Bending Moment 6.1. 6.2. 6.3. 6.4. 6.5. 6.6. 6.7. 1 Chapter 4. Strain Energy and Impact Loading 4.1. 4.2. 4.3. Introduction Some Definitions Expression for Strain Energy Stored in a Body when the Load is Applied Gradually 4.4. . Expression for Stain Energy Stored in a Body when the Load is Applied Suddenly 4.5. Expression for Strain Energy Stored in a Body when the Load is Applied with Impact 4.6. Expression for Strain Energy Stored in a Body due to Shear Stress .. Highlights Exercise 4 143-169 6 '.8. 143 143 6.9. 6.10. 143 6.11. 145 6.12. 152 165 166 167 6.13. 6.14. Chapter 5. Centre of Gravity and Moment of Inertia 5.1. 5.2. 5.3. 5.4. 5.5. 5.6. 5.7. 5.8. 5.9. 5.10. 5.11. 5.12. 5.13. 5.14. 5. 15. Centre of Gravity Centroid Centroid or Centre of Gravity of Simple Plane Figures Centroid (or centre of gravity) of Areas of Plane Figures by the Method of Moments Important Points Area Moment of Inertia Radius of Gyration Theorem of the Perpendicular Axis Theorem of Parallel Axis Determination of area Moment of Inertia Mass Moment of Inertia Determination of 1\1.ass Moment of Inertia Product oflnertia Principal Axes Principal Moments of Inertia Highlights Exercise 5 170-234 170 170 170 6.15. 6.16. 6.17. 170 172 194 195 195 196 197 211 212 218 219 220 228 229 6.18. Introduction Shear Force and Bending Moment Diagrams Types of Beams Types of Load Sign Conventions for Shear Force and Bending Moment Important Points for Drawing Shear Force and Bending Moment Diagrams Shear Force and Bending Moment Di;;;grams for a Cantilever with a Point Load at the Free End Shear Force and Bending Moment Diagrams for a C3:ntilever with a Uniformly Distributed Load Shear Force and Bending Moment Diagrams for a Cantilever Carrying a Gradually Varying Load Shear Force and Bending Moment Diagrams for a Simply Supported Beam with a Point Load at Mid-point Shear Force and Bending Moment Diagrams for a Simply Supported Beam with an Eccentric Point Load Shear Force and Bending Moment Diagrams for a Simply Supported Beam Carrying a Uniformly Distributed Load Shear Force and Bending Moment Diagrams for a Simply Supported Beam Carrying a Uniformly · Varying Load from Zero at Each End to w Per Unit Length at the Centre Shear Force and Bending Moment Diagrams for a Simply Supported Beam Carrying a Uniformly Varying Load from Zero·at one End tow Per Unit Length at the Other End Shear Force and Bending Moment Diagrams for Overhanging Beams Shear Force and Bending Moment Diagrams for Beams Carrying Inclined Load Shear Force and Bending Moment Diagrams for Beams Subjected to Couples Relations between Load, Shear Eorce and Bending Moment Highlights Exercise 6 Chapter 7. Bending Stresses in Beams 7 .1. 7 .2. 7.3. 7.4. 7.5. 7.6. 7. 7. 7 .8. 7.9. Introduction Pure Bending or Simple Bending Theory of Simple Bending with Assumptions Made Expression for Bending Stress Neutral Axis aq_d Moment of Resistance Bending Stresses in Symmetrical/Sections Section Modulus Section Modulus for Various Shapes of Beam Sections Bending Stress in Unsymmetrical Sections 235-291. 235 235 235 236 237 238 239 242 250 252 254 256 264 266 270 279 284 287 288 289 292-341 292 292 293 294 295 297 300 300 312

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