Contents 11 Strain Energy 254 Summary 254 Introduction 256 11.1 Strain energy-tension or compression 257 11.2 Strain energy-shear 259 11.3 Strain energy-bending 260 11.4 Strain energy-torsion 261 11.5 Strain energy of a three-dimensional principal stress system 262 11.6 Volumetric or dilatational strain energy 262 11.7 Shear or distortional strain energy 263 11.8 Suddenly applied loads 263 11.9 Impact loads-axial load application 264 11.10 Impact loads-bending applications 265 11.11 Castigliano's first theorem for deflection 266 11.12 "Unit-load"method 268 11.13 Application of Castigliano's theorem to angular movements 269 11.14 Shear deflection 269 Examples 274 Problems 292 12 Springs 297 Summary 297 Introduction 299 12.1 Close-coiled helical spring subjected to axial load W 299 12.2 Close-coiled helical spring subjected to axial torque T 300 12.3 Open-coiled helical spring subjected to axial load W 301 12.4 Open-coiled helical spring subjected to axial torque T 304 12.5 Springs in series 305 12.6 Springs in parallel 306 12.7 Limitations of the simple theory 306 12.8 Extension springs-initial tension 307 12.9 Allowable stresses 308 12.10 Leaf or carriage spring:semi-elliptic 309 12.11 Leaf or carriage spring:quarter-elliptic 312 12.12 Spiral spring 314 Examples 316 Problems 324X Contents 11 Strain Energy 254 Summary Introduction 1 1.1 1 1.2 Strain energy -shear 1 1.3 Strain energy -bending 1 1.4 Strain energy - torsion 1 1.5 Strain energy of a three-dimensional principal stress system 1 1.6 Volumetric or dilatational strain energy 1 1.7 Shear or distortional strain energy 1 1.8 Suddenly applied loads 1 1.9 Impact loads -axial load application 1 1.10 Impact loads -bending applications 1 1.1 1 Castigliano’s first theorem for deflection 1 1.12 “Unit-load ” method 1 1.13 Application of Castigliano ’s theorem to angular movements 1 1.14 Shear deflection Examples Problems Strain energy - tension or compression 12 Springs Summary Introduction 12.1 Close-coiled helical spring subjected to axial load W 12.2 Close-coiled helical spring subjected to axial torque T 12.3 Open-coiled helical spring subjected to axial load W 12.4 Open-coiled helical spring subjected to axial torque T 12.5 Springs in series 12.6 Springs in parallel 12.7 12.8 12.9 Allowable stresses 12.10 Leaf or carriage spring: semi-elliptic 12.1 1 Leaf or carriage spring: quarter-elliptic 12.12 Spiral spring Limitations of the simple theory Extension springs - initial tension Examples Problems 254 256 257 259 260 26 1 262 262 263 263 264 265 266 268 269 269 274 292 297 297 299 299 300 30 1 304 305 306 306 307 308 309 312 314 316 324