Table of Contents Statics 1 General Principles 3 Chapter Objectives 3 1.1 Mechanics 3 1.2 Fundamental Concepts 4 1.3 Units of Measurement 7 1.4 The International System of Units 9 1.5 Numerical Calculations 10 1.6 General Procedure for Analysis 12 2 Force Vectors 17 Chapter Objectives 17 2.1 Scalars and Vectors 17 2.2 Vector Operations 18 2.3 Vector Addition of Forces 20 2.4 Addition of a System of Coplanar Forces 30 2.5 Cartesian Vectors 38 2.6 Addition of Cartesian Vectors 41 2.7 Position Vectors 50 2.8 Force Vector Directed Along a Line 53 2.9 Dot Product 60 3 Force System Resultants 75 Chapter Objectives 75 3.1 Moment of a Force–Scalar Formulation 75 3.2 Cross Product 79 3.3 Moment of a Force–Vector Formulation 82 3.4 Principle of Moments 86 3.5 Moment of a Force about a Specified Axis 96 3.6 Moment of a Couple 103 3.7 Simplification of a Force and Couple System 112 3.8 Further Simplification of a Force and Couple System 122 4 Equilibrium of a Rigid Body 139 Chapter Objectives 139 4.1 Conditions for Rigid-Body Equilibrium 139 4.2 Free-Body Diagrams 141 4.3 Equations of Equilibrium 151 4.4 Two- and Three-Force Members 157 4.5 Free-Body Diagrams 167 4.6 Equations of Equilibrium 172 4.7 Characteristics of Dry Friction 180 4.8 Problems Involving Dry Friction 184 4.9 Frictional Forces on Flat Belts 197 4.10 Frictional Forces on Screws 200 5 Structural Analysis 215 Chapter Objectives 215 5.1 Simple Trusses 215 5.2 The Method of Joints 218 5.3 Zero-Force Members 224 5.4 The Method of Sections 231 5.5 Frames and Machines 240 6 Center of Gravity, Centroid, and Moment of Inertia 261 Chapter Objectives 261 6.1 Center of Gravity, Center of Mass, and the Centroid of a Body 261 6.2 Composite Bodies 273 6.3 Resultant of a Distributed Loading 281 6.4 Moments of Inertia for Areas 290 6.5 Parallel-Axis Theorem for an Area 291 6.6 Moments of Inertia for Composite Areas 298 7 Stress and Strain 309 Chapter Objectives 309 7.1 Introduction 309 7.2 Internal Resultant Loadings 310 7.3 Stress 322 7.4 Average Normal Stress in an Axially Loaded Bar 324 7.5 Average Shear Stress 331 7.6 Allowable Stress 342 7.7 Design of Simple Connections 343 7.8 Deformation 355 7.9 Strain 356 Mechanics of Materials 8 Mechanical Properties of Materials 373 Chapter Objectives 373 8.1 The Tension and Compression Test 373 8.2 The Stress—Strain Diagram 375 8.3 Stress—Strain Behavior of Ductile and Brittle Materials 379 8.4 Hooke’s Law 382 8.5 Strain Energy 384 8.6 Poisson’s Ratio 392 8.7 The Shear Stress—Strain Diagram 394 9 Axial Load 405 Chapter Objectives 405 9.1 Saint-Venant’s Principle 405 9.2 Elastic Deformation of an Axially Loaded Member 408 9.3 Principle of Superposition 421 9.4 Statically Indeterminate Axially Loaded Member 422 9.5 The Force Method of Analysis for Axially Loaded Members 428 9.6 Thermal Stress 434 9.7 Stress Concentrations 440 10 Torsion 451 Chapter Objectives 451 10.1 Torsional Deformation of a Circular Shaft 451 10.2 The Torsion Formula 454 10.3 Power Transmission 461 10.4 Angle of Twist 468 10.5 Statically Indeterminate Torque-Loaded Members 481 10.6 Solid Noncircular Shafts 488 10.7 Stress Concentration 492 11 Bending 501 Chapter Objectives 501 11.1 Shear and Moment Diagrams 501 11.2 Graphical Method for Constructing Shear and Moment Diagrams 508 11.3 Bending Deformation of a Straight Member 525 11.4 The Flexure Formula 529 11.5 Unsymmetric Bending 542 11.6 Stress Concentrations 550 12 Transverse Shear 559 Chapter Objectives 559 12.1 Shear in Straight Members 559 12.2 The Shear Formula 561 12.3 Shear Flow in Built-Up Members 578 13 Combined Loadings 591 Chapter Objectives 591 13.1 Thin-Walled Pressure Vessels 591 13.2 State of Stress Caused by Combined Loadings 598 14 Stress and Strain Transformation 619 Chapter Objectives 619 14.1 Plane-Stress Transformation 619 14.2 General Equations of Plane-Stress Transformation 624 14.3 Principal Stresses and Maximum In-Plane Shear Stress 627 14.4 Mohr’s Circle–Plane Stress 639 14.5 Absolute Maximum Shear Stress 650 14.6 Plane Strain 657 14.7 General Equations of Plane-Strain Transformation 658 14.8 Mohr’s Circle–Plane Strain 666 14.9 Strain Rosettes 674 14.10 Material-Property Relationships 676 15 Design of Beams and Shafts 693 Chapter Objectives 693 15.1 Basis for Beam Design 693 15.2 Prismatic Beam Design 696 15.3 Fully Stressed Beams 710 16 Deflection of Beams and Shafts 717 Chapter Objectives 717 16.1 The Elastic Curve 717 16.2 Slope and Displacement by Integration 721 16.3 Discontinuity Functions 735 16.4 Method of Superposition 745 16.5 Statically Indeterminate Beams and Shafts—Method of Superposition 752 17 Buckling of Columns 769 Chapter Objectives 769 17.1 Critical Load 769 17.2 Ideal Column with Pin Supports 772 17.3 Columns Having Various Types of Supports 778 17.4 The Secant Formula 788 17.5 Inelastic Buckling 794 Appendices A. Mathematical Review and Expressions 804 B. Geometric Properties of An Area and Volume 808 C. Geometric Properties of Wide-Flange Sections 810 D. Slopes and Deflections of Beams 814 Fundamental Problems Partial Solutions and Answers 816 Answers to Selected Problems 844 Index 871