iv CONTENTS ★2.12 Elastoplastic Analysis 175 Chapter Summary Review 181 Problems 182 3 Torsion 220 3.1 Introduction 222 3.2 Torsional Deformations of a Circular Bar 223 33 Circular Bars of Linearly Elastic Materials 226 3.4 Nonuniform Torsion 238 3.5 Stresses and Strains in Pure Shear 245 3.6 Relationship Between Moduli of Elasticity E and G 252 3.7 Transmission of Power by Circular Shafts 254 3.8 Statically Indeterminate Torsional Members 259 3.9 Strain Energy in Torsion and Pure Shear 263 3.10 Thin-Walled Tubes 270 *3.11 Stress Concentrations in Torsion 279 Chapter Summary Review 282 Problems 283 4 Shear Forces and Bending Moments 304 4.1 Introduction 306 4.2 Types of Beams,Loads,and Reactions 306 43 Shear Forces and Bending Moments 313 4.4 Relationships Between Loads,Shear Forces, and Bending Moments 320 4.5 Shear-Force and Bending-Moment Diagrams 325 Chapter Summary Review 337 Problems 338 5 Stresses in Beams(Basic Topics) 350 5.1 Introduction 353 5.2 Pure Bending and Nonuniform Bending 353 53 Curvature of a Beam 354 5.4 Longitudinal Strains in Beams 356 55 Normal Stresses in Beams(Linearly Elastic Materials)361 5.6 Design of Beams for Bending Stresses 374 5.7 Nonprismatic Beams 383 5.8 Shear Stresses in Beams of Rectangular Cross Section 387 5.9 Shear Stresses in Beams of Circular Cross Section 397 5.10 Shear Stresses in the Webs of Beams with Flanges 400★2.12 Elastoplastic Analysis 175 Chapter Summary & Review 181 Problems 182 3 Torsion 220 3.1 Introduction 222 3.2 Torsional Deformations of a Circular Bar 223 3.3 Circular Bars of Linearly Elastic Materials 226 3.4 Nonuniform Torsion 238 3.5 Stresses and Strains in Pure Shear 245 3.6 Relationship Between Moduli of Elasticity E and G 252 3.7 Transmission of Power by Circular Shafts 254 3.8 Statically Indeterminate Torsional Members 259 3.9 Strain Energy in Torsion and Pure Shear 263 3.10 Thin-Walled Tubes 270 ★3.11 Stress Concentrations in Torsion 279 Chapter Summary & Review 282 Problems 283 4 Shear Forces and Bending Moments 304 4.1 Introduction 306 4.2 Types of Beams, Loads, and Reactions 306 4.3 Shear Forces and Bending Moments 313 4.4 Relationships Between Loads, Shear Forces, and Bending Moments 320 4.5 Shear-Force and Bending-Moment Diagrams 325 Chapter Summary & Review 337 Problems 338 5 Stresses in Beams (Basic Topics) 350 5.1 Introduction 353 5.2 Pure Bending and Nonuniform Bending 353 5.3 Curvature of a Beam 354 5.4 Longitudinal Strains in Beams 356 5.5 Normal Stresses in Beams (Linearly Elastic Materials) 361 5.6 Design of Beams for Bending Stresses 374 5.7 Nonprismatic Beams 383 5.8 Shear Stresses in Beams of Rectangular Cross Section 387 5.9 Shear Stresses in Beams of Circular Cross Section 397 5.10 Shear Stresses in the Webs of Beams with Flanges 400 iv CONTENTS