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
CONTENTS ★*5.11 Built-Up Beams and Shear Flow 408 ★★5.12 Beams with Axial Loads 412 ★*5.13 Stress Concentrations in Bending 418 Chapter Summary Review 421 Problems 424 6 Stresses in Beams (Advanced Topics) 454 6.1 Introduction 457 6.2 Composite Beams 457 6.3 Transformed-Section Method 466 6.4 Doubly Symmetric Beams with Inclined Loads 472 6.5 Bending of Unsymmetric Beams 479 6.6 The Shear-Center Concept 487 6.7 Shear Stresses in Beams of Thin-Walled Open Cross Sections 489 6.8 Shear Stresses in Wide-Flange Beams 492 6.9 Shear Centers of Thin-Walled Open Sections 496 ★*6.10 Elastoplastic Bending 504 Chapter Summary Review 514 Problems 516 7 Analysis of Stress and Strain 536 7.1 Introduction 539 7.2 Plane Stress 540 73 Principal Stresses and Maximum Shear Stresses 548 7.4 Mohr's Circle for Plane Stress 558 7.5 Hooke's Law for Plane Stress 575 7.6 Triaxial Stress 580 7.7 Plane Strain 584 Chapter Summary Review 600 Problems 602 8 Applications of Plane Stress(Pressure Vessels,Beams,and Combined Loadings) 618 8.1 Introduction 621 8.2 Spherical Pressure Vessels 621 8.3 Cylindrical Pressure Vessels 627 B.4 Maximum Stresses in Beams 635 8.5 Combined Loadings 645 Chapter Summary Review 661 Problems 663 *Advanced topics
★★5.11 Built-Up Beams and Shear Flow 408 ★★5.12 Beams with Axial Loads 412 ★★5.13 Stress Concentrations in Bending 418 Chapter Summary & Review 421 Problems 424 6 Stresses in Beams (Advanced Topics) 454 6.1 Introduction 457 6.2 Composite Beams 457 6.3 Transformed-Section Method 466 6.4 Doubly Symmetric Beams with Inclined Loads 472 6.5 Bending of Unsymmetric Beams 479 6.6 The Shear-Center Concept 487 6.7 Shear Stresses in Beams of Thin-Walled Open Cross Sections 489 6.8 Shear Stresses in Wide-Flange Beams 492 6.9 Shear Centers of Thin-Walled Open Sections 496 ★★6.10 Elastoplastic Bending 504 Chapter Summary & Review 514 Problems 516 7 Analysis of Stress and Strain 536 7.1 Introduction 539 7.2 Plane Stress 540 7.3 Principal Stresses and Maximum Shear Stresses 548 7.4 Mohr’s Circle for Plane Stress 558 7.5 Hooke’s Law for Plane Stress 575 7.6 Triaxial Stress 580 7.7 Plane Strain 584 Chapter Summary & Review 600 Problems 602 8 Applications of Plane Stress (Pressure Vessels, Beams, and Combined Loadings) 618 8.1 Introduction 621 8.2 Spherical Pressure Vessels 621 8.3 Cylindrical Pressure Vessels 627 8.4 Maximum Stresses in Beams 635 8.5 Combined Loadings 645 Chapter Summary & Review 661 Problems 663 CONTENTS v ★★ Advanced topics
i CONTENTS 9 Deflections of Beams 676 9.1 Introduction 679 9.2 Differential Equations of the Deflection Curve 679 93 Deflections by Integration of the Bending-Moment Equation 685 9.4 Deflections by Integration of the Shear-Force and Load Equations 696 9.5 Method of Superposition 702 9.6 Moment-Area Method 711 9.7 Nonprismatic Beams 720 9.8 Strain Energy of Bending 725 ★*9.9 Castigliano's Theorem 731 ★★9.10 Deflections Produced by Impact 744 *9.11 Temperature Effects 746 Chapter Summary Review 749 Problems 751 10 Statically Indeterminate Beams 770 10.1 Introduction 773 10.2 Types of Statically Indeterminate Beams 773 10.3 Analysis by the Differential Equations of the Deflection Curve 777 10.4 Method of Superposition 784 **10.5 Temperature Effects 797 ★*10.6 Longitudinal Displacements at the Ends of a Beam 801 Chapter Summary Review 805 Problems 806 11 Columns 816 11.1 Introduction 819 11.2 Buckling and Stability 819 113 Columns with Pinned Ends 823 11.4 Columns with Other Support Conditions 834 11.5 Columns with Eccentric Axial Loads 845 11.6 The Secant Formula for Columns 850 11.7 Elastic and Inelastic Column Behavior 856 ★★Advanced topics
9 Deflections of Beams 676 9.1 Introduction 679 9.2 Differential Equations of the Deflection Curve 679 9.3 Deflections by Integration of the Bending-Moment Equation 685 9.4 Deflections by Integration of the Shear-Force and Load Equations 696 9.5 Method of Superposition 702 9.6 Moment-Area Method 711 9.7 Nonprismatic Beams 720 9.8 Strain Energy of Bending 725 ★★9.9 Castigliano’s Theorem 731 ★★9.10 Deflections Produced by Impact 744 ★★9.11 Temperature Effects 746 Chapter Summary & Review 749 Problems 751 10 Statically Indeterminate Beams 770 10.1 Introduction 773 10.2 Types of Statically Indeterminate Beams 773 10.3 Analysis by the Differential Equations of the Deflection Curve 777 10.4 Method of Superposition 784 ★★10.5 Temperature Effects 797 ★★10.6 Longitudinal Displacements at the Ends of a Beam 801 Chapter Summary & Review 805 Problems 806 11 Columns 816 11.1 Introduction 819 11.2 Buckling and Stability 819 11.3 Columns with Pinned Ends 823 11.4 Columns with Other Support Conditions 834 11.5 Columns with Eccentric Axial Loads 845 11.6 The Secant Formula for Columns 850 11.7 Elastic and Inelastic Column Behavior 856 vi CONTENTS ★★ Advanced topics
CONTENTS vii 11.8 Inelastic Buckling 858 11.9 Design Formulas for Columns 863 Chapter Summary Review 882 Problems 883 12 Review of Centroids and Moments of Inertia 900 12.1 Introduction 902 12.2 Centroids of Plane Areas 902 12.3 Centroids of Composite Areas 905 12.4 Moments of Inertia of Plane Areas 909 12.5 Parallel-Axis Theorem for Moments of Inertia 912 12.6 Polar Moments of Inertia 916 12.7 Products of Inertia 918 12.8 Rotation of Axes 921 12.9 Principal Axes and Principal Moments of Inertia 923 Problems 927 References and Historical Notes 935 Appendix A Systems of Units and Conversion Factors 943 A.1 Systems of Units 943 A.2 SI Units 944 A.3 U.S.Customary Units 951 A.4 Temperature Units 952 A.5 Conversions Between Units 953 Appendix B Problem Solving 956 B.1 Types of Problems 956 B.2 Steps in Solving Problems 957 B.3 Dimensional Homogeneity 958 B.4 Significant Digits 959 B.5 Rounding of Numbers 961 Appendix C Mathematical Formulas 962 Appendix D Properties of Plane Areas 966 Appendix E Properties of Structural-Steel Shapes 972
11.8 Inelastic Buckling 858 11.9 Design Formulas for Columns 863 Chapter Summary & Review 882 Problems 883 12 Review of Centroids and Moments of Inertia 900 12.1 Introduction 902 12.2 Centroids of Plane Areas 902 12.3 Centroids of Composite Areas 905 12.4 Moments of Inertia of Plane Areas 909 12.5 Parallel-Axis Theorem for Moments of Inertia 912 12.6 Polar Moments of Inertia 916 12.7 Products of Inertia 918 12.8 Rotation of Axes 921 12.9 Principal Axes and Principal Moments of Inertia 923 Problems 927 References and Historical Notes 935 Appendix A Systems of Units and Conversion Factors 943 A.1 Systems of Units 943 A.2 SI Units 944 A.3 U.S. Customary Units 951 A.4 Temperature Units 952 A.5 Conversions Between Units 953 Appendix B Problem Solving 956 B.1 Types of Problems 956 B.2 Steps in Solving Problems 957 B.3 Dimensional Homogeneity 958 B.4 Significant Digits 959 B.5 Rounding of Numbers 961 Appendix C Mathematical Formulas 962 Appendix D Properties of Plane Areas 966 Appendix E Properties of Structural-Steel Shapes 972 CONTENTS vii
viii CONTENTS Appendix F Properties of Structural Lumber 983 Appendix G Deflections and Slopes of Beams 984 Appendix H Properties of Materials 990 Answers to Problems 995 Name Index 1016 Subject Index 1017
Appendix F Properties of Structural Lumber 983 Appendix G Deflections and Slopes of Beams 984 Appendix H Properties of Materials 990 Answers to Problems 995 Name Index 1016 Subject Index 1017 viii CONTENTS