Contents Preface to the Second Editionv Preface to the First Edition vii Chapter 1 Introduction1 1.1 Interdisciplinary 1 1.2 Brief Historical Review 1 1.3 Organisation of the Book 1 Chapter 2 Simple Stresses and Strains 2.1 General Meaning of Stress 3 2.2 Unit of stress 4 2.3' Simple Stresses 5 2.3.1 Normal Stress 5 2.3.2 Shear Stress 6 2.4 Strain7 2.5 Stress Strain Relation 8 2.5.1 Behaviour in Tension 8 2.5.2 Behaviour of Materials under Compression10 2.6 Nominal Stress and True Stress 11 2.7 Behaviour of Materials under Repeated Loadings11 2.8 Factor of Safety 13 2.9 Hooke's Law 13 2.10 Extension/Shortening of a Bar 14 2.11 Bars with Cross-sections Varying in Steps 18 2.12 Bars with Continuously Varying Cross-sections 21 2.13 Bars Subjected to Varying Loads 25 2.14 Indeterminate Structural Problems 29 2.15 Compound Bars 33 2.16 Temperature Stresses 43 2.17 Simple Shear 54 2.18Poisson'sRatio 56 2.19 Volumetric Strain56 2.20 Elastic Constants 58 2.21 Relationship between Modulus of Elasticity and Modulus of Rigidity 59 2.22 Relationship between Modulus of Elasticity and Bulk Modulus 59 2.23 Strain Energy due to Direct Stresses and Impact Loads 68 2.24 Strain Energy due to shear stresses 71 Important Definitions 78 Important Concepts and Formulae 79 Problems for Exercises 81 Chapter 3 Shear Force and Bending Moment Diagrams in Statically Determinate Beams87 3.1 Shear Force and Bending Moment 87 3.2 Sign Convention 89 3.3 Relationship between Load Intensity, Shear Force and Bending Moment 90 3.4 Shear Force and Bending Moment Diagrams 90 3.5 SFD and BMD For Standard Cases 91 3.5.1 Cantilever Subjected to a Central Concentrated Load91 3.5.2 Cantilever Subjected to Uniformly Distributed Load 92 3.5.3 Cantilever Subjected to Uniformly Varying Load 92 3.5.4 Simply Supported Beam Subjected to a Concentrated Load93 3.5.5 Simply Supported Beam Subjected to UDL 95 3.5.6 Simply Supported Beam Subjected to Uniformly Varying Load 96 3.5.7 Simply Supported Beam Subjected to External Moment MO at x = a from Left Support 98 3.5.8 Overhanging Beam Subjected to Concentrated Load at Free End 99 3.6 SFD and BMD for Beams Subjected to Various Loads 100 3.7 Short Cut Procedure113 Important Definitions 119 Important Concepts and Formulae 119 Problems for Exercise 120 Chapter 4 Stresses in Beams 4.1 Theory of Simple Bending123 4.1.1 Assumptions in Simple Theory of Bending124 4.1.2 Relationship between Bending Stresses and Radius of Curvature124 4.1.3 Relationship between Moment and Radius of Curvature126 4.2 Moment Carrying Capacity of a Section127 4.3 Composite Beams/Flitched beams 145 4.4 Beams of Uniform strength 151 4.5 Leaf Springs153 4.6 Shearing Stresses in Beams 154 4.7 Shear Stresses across a Few Standard Sections156 4.7.1 Rectangular Section156 4.8 Shear Stresses in Built Up Sections 161 4.9 Limitation of Theory Developed171 Important Definitions172 Important Concepts and Formulae 173 Problems for Exercises 174 Chapter 5 Deflections of Beams by Double Integration Method ' 179 5.1. Differential Equation for Deflection179 5.2 Other Useful Equations181 5.3 Double Integration Method182 5.4 A few General Cases 182 5.4.1 Cantilever Subject to Moment at Free End182 5.4.2 Cantilever Subject to Concentrated Load at Free End 183 5.4.3 A Cantilever Subject to Uniformly Distributed Load185 5.4.4 A Cantilever Subject to Load Varying Linearly from Zero at Free End to w/unit Length at Fixed End186 5.4.5 Simply Supported Beam Subjected to a Central Concentrated Load187 5.4.6 Simply Supported Beam Subject to Uniformly Distributed Load188 5.4.7 A Simply Supported Beam Subjected to a Load Varying Linearly from Zero at One End to w/unit Length at Other End190 5.5 Mecaulay's Method198 Important Definition 216 Important Concepts and Formulae 216 Problems for Exercises 218 Chapter 6 Torsion Introduction 221 6.1 Pure Torsion 221 6.2 Assumptions in the Theory of Pure Torsion222 6.3 Derivation of Torsional Equations 222 6.4 Polar Modulus 224 6.5 Power Transmitted 225 6.6 Torsional Rigidity/Stiffness of Shafts 225 6.7 Stepped Shafts and Composite Shafts 237 6.8 Shear Keys 246 6.9 Coupling 246 6.10 Torsion of a Tapering Shaft248 6.11 Strain Energy in Torsion 250 6.12 Closed Coiled Helical Springs 253 6.13 Torsion of Shafts of Non-circular Sections 256 Important Definitions 258 Important Concepts and Formulae 258 Problems for Exercise 260 Chapter 7 Compound Stresses 263 7.1 Stresses on an Inclined Plane 264 7.1.1 Element Subjected to Uniaxial Direct Stress 264 7.1.2 Elements Subjected to Biaxial Direct Stresses 266 7.1.3 Element Subjected to General Two Dimensional Stress System 269 7.2 Mohr's Circle of Stress 281 7.3 Compound Stresses in Beams 287 7.4 Shafts Subjected to Combined Bending and Torsion 292 7.5 Shafts Subjected to Combined Action of Bending, Torsion and Axial Thrust 299 Important Definitions 301 Important Concepts and Equations 301 Problems for Exercise 302 Chapter 8 Thin and Thick Cylinders and Spheres 8.1 Stresses in Thin Cylinders 305 8.1.1 Circumferential Stress f1305 8.1.2 Longitudinal Stressf2 306 8.2 Changes in Dimensions of Cylinder 307 8.3 Riveted Cylinders311 8.4 Wire Wound Cylinders 313 8.5 Thin Spherical Shells 316 8.6 Thick Cylinders 320 8.7 Compound Cylinders329 8.8 Shrinkage Allowance 333 8.9 Thick Spherical Shells 338 Important Concepts and Equations 342 Problems for Exercise 343 Chapter 9 Columns and Struts 347 9.1 Short Columns Subjected to Axial Loads 347 9.2 Eccentrically Loaded Masonry Columns348 9.2.1 Eccentricity with Respect to Only One Axis 348 9.2.2 Eccentricity with Respect to Both X and Y Axes 349 9.3 Euler's Theory for Axially Loaded Elastic Long Columns 353 9.3.1 Both Ends Hinged 353 9.3.2 One End Fixed and the Other End Free 355 9.3.3 Both Ends are Fixed 356 9.3.4 One End Fixed the Other End Hinged 358 9.4 Effective Length 359 9.5 Limitations of Euler's Theory 360 9.6 Rankine's Formula 361 9.7 Formula Used by Indian Standard Code 375 Important Definitions 377 Important Concepts and Formulae 377 Problems for Exercise 3 77 Chapter 10 Theories of Failures 381 10.1 Maximum Principal Stress Theory 381 10.2 Maximum Shear Stress Theory381 10.3 Maximum Strain Theory382 10.4 Maximum Strain Energy Theory382 10.5 Maximum Distortion Energy Theory384 Important Concepts and Formulae 391 Problems for Exercise 392