viii Contents 7 Shear Stress Distribution 154 Summary 154 Introduction 155 7.1 Distribution of shear stress due to bending 156 7.2 Application to rectangular sections 157 7.3 Application to I-section beams 158 7.3.1 Vertical shear in the web 159 7.3.2 Vertical shear in the flanges 159 7.3.3 Horizontal shear in the flanges 160 7.4 Application to circular sections 162 7.5 Limitation of shear stress distribution theory 164 7.6 Shear centre 165 Examples 166 Problems 173 8 Torsion 176 Summary 176 8.1 Simple torsion theory 177 8.2 Polar second moment of area 179 8.3 Shear stress and shear strain in shafts 180 8.4 Section modulus 181 8.5 Torsional rigidity 182 8.6 Torsion of hollow shafts 182 8.7 Torsion of thin-walled tubes 182 8.8 Composite shafts-series connection 182 8.9 Composite shafts-parallel connection 183 8.10 Principal stresses 184 8.11 Strain energy in torsion 184 8.12 Variation of data along shaft length-torsion of tapered shafts 186 8.13 Power transmitted by shafts 186 8.14 Combined stress systems-combined bending and torsion 187 8.15 Combined bending and torsion-equivalent bending moment 187 8.16 Combined bending and torsion-equivalent torque 188 8.17 Combined bending,torsion and direct thrust 189 8.18 Combined bending,torque and internal pressure 189 Examples 190 Problems 195Contents ... Vlll 7 Shear Stress Distribution Summary Introduction 7.1 7.2 7.3 7.4 7.5 7.6 Distribution of shear stress due to bending Application to rectangular sections Application to I-section beams 7.3.1 Vertical shear in the web 7.3.2 Vertical shear in the flanges 7.3.3 Horizontal she& in the flanges Application to circular sections Limitation of shear stress distribution theory Shear centre Examples Problems 8 Torsion Summary 8.1 Simple torsion theory 8.2 Polar second moment of area 8.3 Shear stress and shear strain in shafts 8.4 Section modulus 8.5 Torsional rigidity 8.6 Torsion of hollow shafts 8.7 Torsion of thin-walled tubes 8.8 Composite shafts -series connection 8.9 Composite shafts -parallel connection 8.10 Principal stresses 8.1 1 Strain energy in torsion 8.12 Variation of data along shaft length -torsion of tapered shafts 8.13 Power transmitted by shafts 8,14 Combined stress systems -combined bending and torsion 8.15 Combined bending and torsion - equivalent bending moment 8.16 Combined bending and torsion -equivalent torque 8.17 Combined bending, torsion and direct thrust 8.18 Combined bending, torque and internal pressure Examples Problems 154 154 155 156 157 158 159 159 160 162 164 165 166 173 176 176 177 179 180 181 182 182 182 182 183 184 184 186 186 187 187 188 189 189 190 195