Table Of Content

Strength of Materia -* q % — + 4 eT re * € + or i ra - S-S-RATTANSU™ a . oss in fre — ae t= Tata McGraw-Hill Published by the Tata McGraw-Hill Publishing Company Limited, 7 West Puel Nagar, New Delhi 110 008, ‘Copyright © 2008 by Tata McGraw-Hill Publishing Company Lintve First reprint RZLQCDDXRCYLO [No par ofthis publicaslon may be repradueed or disribuied in any form or by any means, electronic, mechanical, potocopying, recording r otherwise or storedin a database of etieval system without the priar wrizen permission of the publishers. 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Delhi-1! 032 (Cover: Rashtriya = WH cp CONTENTS Preface xii Visual Walkthrough ai List of Symbols xi 1._ Simple Stress and Strain 1 ‘LL_Introduction L2_Stress_2 13° Shear Suess 3 LA Stain ¢ 1.5 Modulus of Elasticity and Modulus of Rigidity 4 1.6 Elongation of A Bar 5 17_Prineipte of sition _S 1.9 Blongation Due to Self Weight_9 1.10 Column of Uniform Strength 9 1.11 Statically Indetetminate Systems _/0 1.12 ‘Temperature Stresses 2/ 1.13, Shrinking on_29 1.14 Swain Analysis 30 115. Teasile Test Diawram 35 1.16 Factor of Safety 36 117 Elastic Consiomss 26 1.18_Relation Between Elastic Constants_37 Summary 39 Review Questions 40 2._Compound Stress and Strain 44 21_Intuuduction 4 22 Suess Analysis 44 23 Principal Stresses 53 24 Mobr’s Stress Cixcle 35 25 Three Coplanar Stresses 68 2.6 Ellipse of Suess 70 2.7 Principal Suesses From Prineiple Sains 77 28 Swain Analysis 72 Summary 75 Review Questions 76 3. Strain Pnergy and Thearles of Failures » 3.1 Introduction 79 . 3.2 Stesin Energy 80 3.3. Strain Energy (Three-dimensional Stress System) 82 (34 Shear Strain Energy 82 - ‘25 Shear Strain Energy (Three-dimensional Stress System) 82 36 Stresses Due o Various Types of Loading 88 2 si Due ‘38 Graphical Representation of Theories of Failures 95 Summary 97 Review Questions 97 |4._Shear Force and Bending Moment 9 41__Intreduction 99 7 42 Types of Suppors and Beams 99 4.3 Shear Force 101 44 Bending Moment 101 45° Relation Between W, FandM J02 46 ling Moment Diagrams for Cantilevers 103 4.1 Shear Force and Bending Moment Diagrams for ‘Simply Supported Beams 168 4.8__Loading and Bending Moment Diagrams From Shear ‘Force Diagram 125 Suumary 126 Review Questions 127 ‘5,_Bending Stress in Beams 129 ‘S.1_Introduction 129° 52 Theory of Simple Bending 130 /.3._Moment of Inertia 132 ‘54 Beams With Uniform Bending Swengih 142 5.5. Flitched Or Composite Beams [47 ‘$6 Reinforced Concrete Beams 156 ‘$.7_Unsymmetrical Bending 157 5.8 Determination of Principal Axes 162 59 _ Ellipse of Inertia Or Momental Ellipse 170 510” Combined Direet and Bending Suess 177 Sunnwiro 179 Review Questions 181 6 Builup Beams 197 65 Shear Centre 20? jew Quewions 2 7._Slope and Deflection 208 ZL_Inteeduction 208 Copyrghied mate at conics — & 7.2 Beam Differential Equation 208 7.3. Slope and Deflection At A Point 209 14 Double Integration Method 210 15 Macaulay's Method 226 L6Moment=Area Method 234 ‘7:1 Strain Energy Due to Bending 244 7.8 _Castigliano’s First Theorem (Detection From Strain nergy) 24 9 Conjugate Beam Method 251 7.10 Manwell’s Reciprocal Deflection Theorem _257 7.1. Betti's Theorem of Reviprocal Deflections 259 ‘Summary 289 Review Questions 260 8.3 Moment-Ares Metiod 263 Bel Macaulay's Meth! 270 aS on's Three-raoment Equation 275, 8.6 Moment Disrriburion Meshal 287 Summary 297 w Questions 208 9. Bending of Curved Bars 301 91 _Inteosuction 307 9.2 Bars of Small Initial Curvanuee 30d 9.3 Bars of Large Initial Curvature (Winkler-Bach Theory) 304 9.4 Values of P2 for Various Seetions 307 9.5 Stresses In A Circular Ring 315 9.6 Sinesses In. Chain Link 318 9.8 Defeetion By Strnin Energy (Castigliano’s Theorem) 324 Summary 330 Review Questions 331 10._Torsion 38 10.1 _Ineduction 343 10.2 Circular Shafis 232 — 10.4 Torsion of Tapered Shaft 338 10.5 Shafis In Series and Parallel 240 10.5 Strain Energy tn Torsion 345 10.1 Combined Bending and Torsion _35/ 10.8 Thin Tubular Sections (Bredt-Batho Theory) 33 10,10 Thin Rectangular Members 357 ay Content Summary 360 Review Questions _361 L1._ Springs 364 LL._tnwroduction 26 1.2 Close-coited Helical Springs 36 11.3 _ Springs In Series and Parallel 370 114 Concentric (Clusten Springs 377 15 _Open-coiled Helical Springs 373 (1.6 Flat Spiral Springs 378 117 Leaf Or Laminated Springs 380 Summary 384 Review Questions 385 12._Colwmns and Stuts__ 12.1 Introduction 288 2.2__Euler’s ‘Theory 388 12.3 Equivalent Length 397 124 Limitations of Euler's Formula 397 12.5 Rankine's Formula 396 126 Other Formulue 397 Ecce Load (Seeant Fo 12.9 Serut With Lateral 405 12.10 Tie With Lateral Loading 2/1 12.11 Struts of Varying Cross-section 413 Summary 415 Review Questions 416 13,_ Cylinders and Spheres 419 13.L_Inteoduction 419 13.2 Thin Cylinder _ 419 13.3 Thin Spherical Shell 42/ 134_Ihin Cylinder With Spherical Ends 42 13,5 Volumetric Swain 422 13.6__Wire Winding of Thin Cylinders 430 13.7_Thick Cylinders 433 13.8 Compound Tubes _ 439 139 Hub on Solid Shaft _dtt 13.10_Wire Winding of Thick Cylinders 47 TR.M_Design of a Thick Cylindrical Shell 457 IR.12. Thick Spherical Shells 454 Summary 457 Review Questions 458 14, Rotating Discs and Cylinders 461 14.1 Introduction 467 co 7 142 Rotating Ring _46/ 14.3 _ Disc of Unilorn Thickness 463 144 Long Cylinder 176 145 Disc of Uniform Strength 487 146 Collapse Speed 482 Summary 484 Review Questions 485 15.1_Inuoduction 487 15.2 _ Symmetcically Loaded Circular Plates _487 15.3 Uniformly Disiibuted Load on A Solid Plate 497 154 Cenural Point Loud on Solid Pluwe 497 15.5_Lond Round A Citele on A Soli Plate 303 186 Annolar Ring, Load Round An nner Fage $03 Stanmary SH Review Questions 512 16._Plastic Bending and Torsion 513 16.1 Introduction 513 16.2 _Plastic Theory of Bending 512 163 _ Moment of Resistance At Plastic Hinge 5/4 16.4 Symmetrical Bending 515 16.5 Unsymmetrical Bending 576 16.6 Collapse Load 523 16.7 Torsion of Cireular Shafts 525 168 Combined Direct and Bending Stress 528 Summary 529 Review Questions $30 17_Plane Krame Structures. S32 17.2 Perivc: Frames 532 173 Reactions At the Suppons 533 17.4 Suiicaly Determinace Frames _533 17.5 Assumptions In che Analysis of Frames 534 17.6 Sign Convention 534 17.7 Methods of Analysis _535 17.8 Method of Joints 535 179 Method of Sections 540 Summary_$44 Review Questions S48 18._Properties and Testing of Materials 548 781 Inwroduetion 548 18.2 Mechanical Propeties 548 183 Factor of Safety 549 ¢ 184° Tensile Testing 350 185 Compression Testing 552 186 Torsion Testing 552 187 Hardness Testing 553 188 t Testing So 189 Column Testing 555 18.10 Creep Testing 555, T8.11 Fatigue Testing 556 Summary 558 Review Questions 558 Appendix 1 Appendix U1 Index 581 PREFACE ‘An engineer alvays endeavours to design structural or machine safe, durable and economical. To accomplish this, he has to evaluate the load-carry capacity of the members so that they are able to withstand the various forces on them. The subject Sirengeh of Materials deals with the strength stability and rigidity of various structural ar machine members such as beams. columns, shufs, springs, cylinders, etc. These days, a number of hooks on the subject are avilable in the market. However, it is observed that most of the books are feature wise fine when considered on parameters ike eavernge ofa topic, lucidity of writing, variety af solved tnd unsolved problems, quality of diagrams, ee, hot usually the students have 1 supplement a book with another book for one reason ar the other. The present book sims to cover all good features in a sinate book. ‘The book is mainly aimed to be useful to degree-level students of mechanical and civil engineering as well as those preparing for AMIE and various other competitive examinations, However diploma-level studs will aso find the book to be of immense use. The book will also benefit post-graduate students to some extent as it also contains some advance topics ike bending of curved bars, rotating diss and eylinders, plastic bending and circular plates, ec. The salient features ofthe book are the following: ‘= A moderately concise and compact book covering all major topics ‘= Simple language to make it useful even te the average and weak students * Logical and evolutionary approach in descriptions for better imagination and visualisation ‘= Physical concepts from simple and readily comprehensible principles = Large number of solved examples Theoretical questions as well as suth end of each chapter + Summary atthe end of each chapter An appendix containing ojective-type questions ‘© Another appendix comaining important relations and results It is expected that students using this book might have eampleted a course in applied mechanics. Chapters 1 und 2 introduce the concept of simple and compound Sueases at a point. I is shown that an axial load may produce shicar stresses along with normal stresses depending upon the section considered. The utility of Mohe’s cirele in transformation of sires at 2 point is also diseuseed, Chapter 3 explains the concept of strain energy that forms the basis of analysis in many cases, Chapters 4 to 88 are related to beams which may be simply supported, fixed at one or both ends or continuous having more than two supports. ‘The analysis includes the computations of bending moment, shear force and bending and shear stresses under transverse loads. The concept of plastic deformations of beams beyond the elastic limit, being ‘anagvanced topic is taken up later and is discussed in Chapter 6. Sometimes, curved members such as rings and hooks are also loaded. Chapter $ discusses the stresses developed in such members, ‘The theory of torsion is developed in Chapter 10 which nt number of unsolved probieras atthe a pat also inclodes its opplicetion to shefts trensmitting power. The springs based on the same theory are discussed inthe subsequent chapter. Columns are important merabers of structures. Chapter 12 discusses the equilibrium of columns and struts. However, the computation of stress in plane frame structures which is mostly included im the civil engineering curriculum is discussed later in Chapter 17. Some other important ‘machine members include cylinders and spheres under internal or extemal pressures, flywheels, discs and cylinders which rotate while performing the required function; circular plates under concentrated or uniform loads. These topics are covered in chapters 131015, Chapter 18 discusses the properties of materials as well asthe methods to determine the same. ‘Though students are expected to exert and solve the numerical problems given at the end of cach chapter. hints to most ofthese are availeble atthe publisher's website ofthe book for the benefit of average and weak students, However, full solutions of the unsolved problems are available to the faculty members atthe same site, ‘The {acility can be availed by logging on to hip//www.nkihe.comirattan In preparing the scrip, [relied heavily on the works of renowned cuthors whose ‘writings ure considered classics inthe Field. Iam indeed indebted to them. sincerely acknovledge the help of my many colleagues, who helped me in one form or the aber in preparing this treatise. I also acknowledge the efforts of the editorial nc production staff st Tata McGraw-Hill for taking pains in bringing out tis book in an excelent format Tain immensely thanktal to the following reviewers who went trough manuscript and enriched it with their feedback Name Aiton ‘Anup Maiti Haldia Insivuce of Tech. Hat West engat PR Kundu Dept of Mechanical Eneincering, Heriage Inve of Technology. Kolbe PS Mukherjee Dept. of Mechanical Freineering, _Iulian Schoo! of Mines, Dhanbad AKDotta Dept. of Applied Mechanics Nationa! Ins of Technolog: Durgapur ‘A Duta Depr. af Chil Engineering, MT. Gea ‘Sukhwinder Singh Jolly [Dept of Mechanica! Engircering. Sri Subloman site of Engineering end Technology, Derabossi. Punjab ‘Chandana Rath ‘Schoo! af Materials Setence and Tecknology, ararns Hind University, Varanasi Sunil Kumar Srivastava | Dept. of Mechanica! Engineering, Madan Moun Mabsiva Ei Gorakhpur neering College,