STATICS AND MECHANICS OF MATERIALS Ferdinand P. Beer E. Russell Johnston, Jr, John T. DeWolf David E Mazurek \Cawect Mc / iur/» Craw SugomcT Hilt
Introduction 1 1.1 What is Mechanics? 2 1.2 Fundamental Concepts and Principles- Mechanics of Rigid Bodies 2 1.3 Fundamental Concepts Mechanics of Deformable Bodies 5 1.4 Systems of Units 5 1.5 Conversion from One System of Units to Another 10 1.6 Method of Problem Solution 11 1.7 Numerical Accuracy 13 Statics of Particles 14 2.1 Introduction 16 Forces in a Plane 16 2.2 Force on a Particle. Resultant of Two Forces 16 2.3 Vectors 17 2.4 Addition of Vectors 18 2.5 Resultant of Several Concurrent Forces 20 2.6 Resolution of a Force into Components 21 2.7 Rectangular Components of a Force. Unit Vectors 26 2.8 Addition of Forces by Summing x and y Components 29 2.9 Equilibrium of a Particle 33 2.10 Newton's First Law of Motion 34 2.11 Problems Involving the Equilibrium of a Particle. Free-Body Diagrams 34 Forces in Space 42 2.12 Rectangular Components of a Force in Space 42 2.13 Force Defined by its Magnitude and Two Points on Its Line of Action 45 2.14 Addition of Concurrent Forces in Space 46 2.15 Equilibrium of a Particle in Space 52 Review and Summary 58 Review Problems 61
IV Rigid Bodies: Equivalent Systems of Forces 64 3.1 Introduction 66 3.2 External and Internal Forces 66 3.3 Principle of Transmissibility. Equivalent Forces 67 3.4 Vector Product of Two Vectors 69 3.5 Vector Products Expressed in Terms of Rectangular Components 71 3.6 Moment of a Force about a Point 73 3.7 Varignon's Theorem 75 3.8 Rectangular Components 3.9 Scalar Product of Two Vectors 84 3.10 Mixed Triple of the Moment of a Force 75 Product of Three Vectors 86 3.11 Moment of a Force about a Given Axis 87 3.12 Moment of a Couple 94 3.13 Equivalent Couples 95 3.14 Addition of Couples 97 3.15 Couples Can be Represented by Vectors 97 3.16 Resolution of a Given Force into a Force at O and a Couple 98 3.17 Reduction of a System of Forces to One Force and One Couple 108 of Forces 109 3.18 Equivalent Systems 3.19 Equipollent Systems of Vectors 110 3.20 Further Reduction of a System of Forces 110 Review and Summary 122 Review Problems 127 Equilibrium of Rigid Bodies 130 4.1 Introduction 132 4.2 Free-Body Diagram 133 Equilibrium in Two Dimensions 134 4.3 Reactions at Supports and Connections for a Two-Dimensional Structure 134 4.4 Equilibrium of Rigid Body a in Two Dimensions 136 4.5 Statically Indeterminate Reactions. Partial Constraints 138 4.6 Equilibrium of a Two-Force Body 149 4.7 Equilibrium of Three-Force Body a 150 Equilibrium in Three Dimensions 155 4.8 Equilibrium of a Rigid Body in Three Dimensions 155 4.9 Reactions at Supports and Connections for a Three-Dimensional Structure 155
Friction 167 4.10 Friction Forces 167 4.11 The Laws of Dry Friction. Coefficients of Fricfion 167 4.12 Angles of Friction 170 4.13 Problems Involving Dry Review and Summary 179 Review Problems 183 Friction 171 5 Distributed Forces: Centroids and Centers of Gravity 186 5.1 Introduction 188 Areas and Lines 188 5.2 Center of Gravity of Two-Dimensional Body a 188 5.3 Centroids of Areas and Lines 190 5.4 First Moments of Areas and Lines 191 5.5 Composite Plates and Wires 194 5.6 Determination of Centroids by Integration 201 5.7 Theorems of Pappus-Guldinus 203 *5.8 Distributed Loads on Beams 210 Volumes 213 *5.9 Center of Gravity of Three-Dimensional Body. a Centroid of a Volume 213 *5.10 Composite Bodies 214 Review and Summary 221 Review Problems 224 6 Analysis of Structures 226 6.1 Introduction 228 Trusses 229 6.2 Definition of a Truss 229 6.3 Simple Trusses 231 6.4 Analysis of Trusses by the Method ofjoints 232 6.5 Joints under Special Loading Conditions 234 6.6 Analysis of Trusses by the Method of Sections 240 *6.7 Trusses Made of Several Simple Trusses 241 Frames and Machines 248 6.8 Structures Containing Multiforce Members 248 6.9 Analysis of a Frame 248 6.10 Frames Which Cease to Be Rigid when Detached from Their Supports 249 6.11 Machines 260 Review and Summary 271 Review Problems 274
vi Distributed Forces: Moments f Inertia of Areas 276 7.1 Introduction 278 7.2 Second Moment, or Moment of Inertia, of an Area 278 7.3 Determination of the Moment of Inertia of an Area by Integration 279 7.4 Polar Moment of Inertia 281 7.5 Radius of Gyration of an Area 282 7.6 Parallel-Axis Theorem 287 7.7 Moments of Inertia of Composite Areas 288 Review and Summary 295 Review Problems 297 Concepts of Stress 300 8.1 Introduction 302 8.2 Stresses in the Members of a Structure 302 8.3 Axial Loading. Normal Stress 303 8.4 Shearing Stress 305 8.5 Bearing Stress in Connections 306 8.6 Application to the Analysis of a Simple Structure 307 8.7 Design 312 8.8 Stress on an Oblique Plane under Axial Loading 320 8.9 Stress under General Loading Conditions. Components of Stress 321 8.10 Design Considerations 324 Review and Summary 335 Review Problems 338 Stress and Strain-Axial Loading 342 9.1 Introduction 344 9.2 Normal Strain under Axial Loading 345 9.3 Stress-Strain Diagram 346 9.4 Hooke's Law. Modulus of Elasticity 351 *9.5 Elastic versus Plastic Behavior of a Material 352 *9.6 Repeated Loadings. Fatigue 354 9.7 Deformations of Members under Axial Loading 355 9.8 Statically Indeterminate Problems 364 9.9 Problems Involving Temperature Changes 368
9.10 Poisson's Ratio 379 9.11 Mulriaxial Loading: Generalized Hooke's Law 380 9.12 Shearing Strain 382 *9.13 Further Discussion of Deformations under Axial Loading. Relation Among E, v, and G 385 9.14 Stress and Strain Distribution under Axial Loading. Saint-Venant's Principle 39] 9.15 Stress Concentrations 393 Review and Summary 397 Review Problems 402 Torsion 406 10.1 Introduction 408 10.2 Preliminary Discussion of the Stresses in a Shaft 409 10.3 Deformations in a Circular Shaft 411 10.4 Stresses 413 10.5 Angle of Twist 423 10.6 Statically Indeterminate Shafts 427 Review and Summary 437 Review Problems 439 Pure Bending 442 11.1 Introduction 444 11.2 Symmetric Member in Pure Bending 446 11.3 Deformations in a Symmetric Member in Pure Bending 448 11.4 Stresses and Deformations 451 11.5 Bending of Materials Made of Several Materials 461 11.6 Eccentric Axial Loading in a Plane of Symmetry 471 *11.7 Unsymmelric Bending 479 *U.8 General Case of Eccentric Axial Loading 485 Review and Summary 493 Review Problems 496 Analysis and Design of Beams for Bending 500 12.1 Introduction 502 12.2 Shear and Bending-Momenl Diagrams 505 12.3 Relations among Load, Shear, and Bending Moment 514 12.4 Design of Prismatic Beams for Bending 524 Review and Summary 531 Review Problems 533
Shearing Stresses in Beams and Thin-Walled Members 536 13.1 Introduction 538 13.2 Shear on the Horizontal Face of a Beam Element 540 13.3 Determination of the Shearing Stresses in a Beam 542 of Beams 543 13.4 Shearing Stresses rxy in Common Types 13.5 Longitudinal Shear on a Beam Element of Arbitrary Shape 552 13.6 Shearing Stresses in Thin-Walled Members 554 Review and Summary 564 Review Problems 566 Transformations of Stress 570 14.1 Introduction 572 14.2 Transformation of Plane Stress 574 14.3 Principal Stresses. Maximum Shearing Stresses 575 14.4 Mohr's Circle for Plane Stress 582 14.5 Stresses in Thin-Walled Pressure Vessels 592 Review and Summary 599 Review Problems 602 Deflection of Beams 604 15.1 Introduction 606 15.2 Deformation of a Beam under Transverse Loading 607 15.3 Equation of the Elastic Curve 608 15.4 Direct Determination of the Elastic Curve from the Load Distribution 614 15.5 Statically Indeterminate Beams 616 15.6 Method of Superposition 624 15.7 Application of Superposition to Statically Indeterminate Beams 626 Review and Summary 634 Review Problems 637
Columns 640 tx 16.1 Introduction 642 16.2 Stability of Structures 642 16.3 Euler's Formula for Pin-Ended Columns 644 16.4 Extension of Euler's Formula to Columns with Other End Conditions 648 *16.5 Design of Columns under a Concentric load 658 Review and Summary 670 Review Problems 672 Appendices 675 A B c Typical Properties of Selected Materials Used in Engineering 676 Properties of Rolled-Steel Shapes 680 Beam Deflections and Slopes 692 Photo Credits 693 Index 695 Answers to Problems 705