CONTENTS Prefacev 1 Stresses and Strains 1 1.1 Load 1 1.2 Effect of a load on a member 2 1.3 Stress 2 1.4 Strains 3 1.5 Volumetric Strain 4 1.6 Poisson's Ratio 5 1.7 Elasticity and Elastic limit 6 1.8 Hook's Law 6 1.9 Modulus 7 1.10 Stress and Strain in simple and Compound bar 7 1.11 Principle of super position 9 1.12 Temperature stress and strain 9 1.13 Relations between E, G and K 10 Solved Exercises 12 Exercise 28 2 Thin Pressure Vessels 33 2.1 Introduction 33 2.2 Assumptions for Determining Stresses in thin pressure vessel 33 2.3 Stresses in thin Pressure vessel 34 2.4 Volumetric Strain in Pressure Vessel 35 2.5 Modification for Built up Pressure vessels 36 Solved Exercise 37 Exercises 43 3 Resilience and Instantaneous Stress 45 3.1 Mechanical Properties 45 3.2 Behaviour of a Ductile material 46 3.3 Stress-Strain Diagrams 46 3.4 Ultimate Stress, working Stress and factor of safety 48 3.5 Elastic and plastic zone 48 3.6 Strain hardening or work hardening 48 3.7 Percentage Elongation and Reduction is area 48 3.8 Homogeneous and Isotropic materia 48 3.9 Proof stress 49 3.10 Types of loading 49 Solved Exercises 50 Exercise 67 4 Moment of Inertia 71 4.1 Introduction 71 4.2 Moment of Inertia (M.O.I.) 72 4.3 Parallel axis theorem 72 4.4 Perpendicular axis Theorem 73 4.5 Moment of Inertia of different bodies 74 4.6 Section modulus 79 Solved Exercises 79 Exercises 93 5 Bending Stresses 97 5.1 Definitions 97 5.2 Assumptions for theory of simple bending 98 5.3 Theory of simple bending or bending Equation 98 5.4 Comparison between moment of resistance or flexural Strength of different sections of beam 101 5.5 Section modulus for different shapes of beam sections 102 Solved Exercises 103 Exerases 118 6 Torsion 120 6.1Introduction 120 6.2 Assumptions for Torsion Equation 120 6.3 Torsion equation for solid shaft 121 6.4 Torsion equation for hollow circular Shaft 123 6.5 Comparison between Hollow and Solid Shaft 124 6.6 Power Transmitted 128 6.7 Stiffness of a shaft 128 6.8 Concept of mean and maximum torque 128 6.9 When shaft in series 128 6.10 When Shaft in parallel 129 Solved Exercises 129 Exercise 140 7 Spring 143 7.1 Definitions 143 7.2 Close Coild helical spring subjected to axial load 144 7.3 Spring under impact load 147 7.4 Composite springs 147 7.5 Close coil helical spring subjected to axial twist 148 7.6 Leaf spring 150 Solved Exercises 152 Exercises 170 8 Column and Struts 173 8.1 Definitions 173 8.2 Types of Column 174 8.3 Strength of column. 174 8.4 End conditions 174 8.5 Euler's theory 175 8.6 Assumptions made in euler's theory 175 8.7 Euler's derivations 175 8.8 Limitations of Euler's Formula 182 8.9 Rankine formula. 182 Solved Exercise 184 Exercise 198 9 : Shear Force and Bending Moment Diagrams 202 9.1 Beam 202 9.2 Classificantion of Beams 203 9.3 Types of Support 204 9.4 Types of Loading 204 9.5 Shear Force 205 9.6 Bending Moment 205 9.7 Sign Conventions for SFD and BMD 205 9.8 Relation Between Load Intensity, Shear Force and Bending Moment 206 9.9 Steps followed to draw SFD and BMD For Beams other than Cantilever Beam 207 9.10 Method to Draw SFD and BMD for Cantilever Beam 208 9.11 Cantilever Beam Carrying a Concentrated Load at Free end 208 9.12 Cantilever Carrying a UDL Over its Entire Span 208 9.13 Point of Contra Flexture 209 9.14 Simply Supported Beam Carrying a Point Load 209 9.15 Simply Supported Beam Carrying a UDL 210 9.16 Overhang Beam Carries Point Load on both ends (Both side overhang) 211 9.17 Overhanging Beam Carries a UDL over whole span (Over hanging from both sides) 213 Solved Exercises 215 Exercise 246 10 Direct and Bending Stresses 248 10.1 Introduction 248 10.2 Direct and bending stresses 248 10.3 Eccentric loading about one axis 249 10.4 Eccentric Loading about two axis 250 10.5 Middle thirdrule 252 Solved Exercises 254 Exercise 261 11 Slope and Deflection 263 11.1Introduction 263 11.2 Methods as determining slope and deflection at any section in a loaded beam 264 11.3 Simply supported beam carrying a point at the centre 264 11.4 Simply supported beam with an ecentric point load 266 11.5 Simply supported beam carries a u.d.l. over whole length 272 11.6 Cantilever beam having point load at free end 274 11.7 Cantilever beam with a point load not at free end 276 11.8 Cantilever beam with U.D.L. over entire length 277 11.9 Cantilever beam carrying a u.d.l. from fixed end 277 Solved exercise 278 Exercise. 286 Index289