MECHANICS OF MATERIALS

Transcription

1 STATICS AND MECHANICS OF MATERIALS Ferdinand P. Beer E. Russell Johnston, Jr, John T. DeWolf David E Mazurek \Cawect Mc / iur/» Craw SugomcT Hilt

2 Introduction What is Mechanics? Fundamental Concepts and Principles- Mechanics of Rigid Bodies Fundamental Concepts Mechanics of Deformable Bodies Systems of Units Conversion from One System of Units to Another Method of Problem Solution Numerical Accuracy 13 Statics of Particles Introduction 16 Forces in a Plane Force on a Particle. Resultant of Two Forces Vectors Addition of Vectors Resultant of Several Concurrent Forces Resolution of a Force into Components Rectangular Components of a Force. Unit Vectors Addition of Forces by Summing x and y Components Equilibrium of a Particle Newton's First Law of Motion Problems Involving the Equilibrium of a Particle. Free-Body Diagrams 34 Forces in Space Rectangular Components of a Force in Space Force Defined by its Magnitude and Two Points on Its Line of Action Addition of Concurrent Forces in Space Equilibrium of a Particle in Space 52 Review and Summary 58 Review Problems 61

3 IV Rigid Bodies: Equivalent Systems of Forces Introduction External and Internal Forces Principle of Transmissibility. Equivalent Forces Vector Product of Two Vectors Vector Products Expressed in Terms of Rectangular Components Moment of a Force about a Point Varignon's Theorem Rectangular Components 3.9 Scalar Product of Two Vectors Mixed Triple of the Moment of a Force 75 Product of Three Vectors Moment of a Force about a Given Axis Moment of a Couple Equivalent Couples Addition of Couples Couples Can be Represented by Vectors Resolution of a Given Force into a Force at O and a Couple Reduction of a System of Forces to One Force and One Couple 108 of Forces Equivalent Systems 3.19 Equipollent Systems of Vectors Further Reduction of a System of Forces 110 Review and Summary 122 Review Problems 127 Equilibrium of Rigid Bodies Introduction Free-Body Diagram 133 Equilibrium in Two Dimensions Reactions at Supports and Connections for a Two-Dimensional Structure Equilibrium of Rigid Body a in Two Dimensions Statically Indeterminate Reactions. Partial Constraints Equilibrium of a Two-Force Body Equilibrium of Three-Force Body a 150 Equilibrium in Three Dimensions Equilibrium of a Rigid Body in Three Dimensions Reactions at Supports and Connections for a Three-Dimensional Structure 155

4 Friction Friction Forces The Laws of Dry Friction. Coefficients of Fricfion Angles of Friction Problems Involving Dry Review and Summary 179 Review Problems 183 Friction Distributed Forces: Centroids and Centers of Gravity Introduction 188 Areas and Lines Center of Gravity of Two-Dimensional Body a Centroids of Areas and Lines First Moments of Areas and Lines Composite Plates and Wires Determination of Centroids by Integration 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 Analysis of Structures Introduction 228 Trusses Definition of a Truss Simple Trusses Analysis of Trusses by the Method ofjoints Joints under Special Loading Conditions Analysis of Trusses by the Method of Sections 240 *6.7 Trusses Made of Several Simple Trusses 241 Frames and Machines Structures Containing Multiforce Members Analysis of a Frame Frames Which Cease to Be Rigid when Detached from Their Supports Machines 260 Review and Summary 271 Review Problems 274

5 vi Distributed Forces: Moments f Inertia of Areas Introduction Second Moment, or Moment of Inertia, of an Area Determination of the Moment of Inertia of an Area by Integration Polar Moment of Inertia Radius of Gyration of an Area Parallel-Axis Theorem Moments of Inertia of Composite Areas 288 Review and Summary 295 Review Problems 297 Concepts of Stress Introduction Stresses in the Members of a Structure Axial Loading. Normal Stress Shearing Stress Bearing Stress in Connections Application to the Analysis of a Simple Structure Design Stress on an Oblique Plane under Axial Loading Stress under General Loading Conditions. Components of Stress Design Considerations 324 Review and Summary 335 Review Problems 338 Stress and Strain-Axial Loading Introduction Normal Strain under Axial Loading Stress-Strain Diagram Hooke's Law. Modulus of Elasticity 351 *9.5 Elastic versus Plastic Behavior of a Material 352 *9.6 Repeated Loadings. Fatigue Deformations of Members under Axial Loading Statically Indeterminate Problems Problems Involving Temperature Changes 368

6 9.10 Poisson's Ratio Mulriaxial Loading: Generalized Hooke's Law Shearing Strain 382 *9.13 Further Discussion of Deformations under Axial Loading. Relation Among E, v, and G 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 Introduction Preliminary Discussion of the Stresses in a Shaft Deformations in a Circular Shaft Stresses Angle of Twist Statically Indeterminate Shafts 427 Review and Summary 437 Review Problems 439 Pure Bending Introduction Symmetric Member in Pure Bending Deformations in a Symmetric Member in Pure Bending Stresses and Deformations Bending of Materials Made of Several Materials 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 Introduction Shear and Bending-Momenl Diagrams Relations among Load, Shear, and Bending Moment Design of Prismatic Beams for Bending 524 Review and Summary 531 Review Problems 533

7 Shearing Stresses in Beams and Thin-Walled Members Introduction Shear on the Horizontal Face of a Beam Element Determination of the Shearing Stresses in a Beam 542 of Beams Shearing Stresses rxy in Common Types 13.5 Longitudinal Shear on a Beam Element of Arbitrary Shape Shearing Stresses in Thin-Walled Members 554 Review and Summary 564 Review Problems 566 Transformations of Stress Introduction Transformation of Plane Stress Principal Stresses. Maximum Shearing Stresses Mohr's Circle for Plane Stress Stresses in Thin-Walled Pressure Vessels 592 Review and Summary 599 Review Problems 602 Deflection of Beams Introduction Deformation of a Beam under Transverse Loading Equation of the Elastic Curve Direct Determination of the Elastic Curve from the Load Distribution Statically Indeterminate Beams Method of Superposition Application of Superposition to Statically Indeterminate Beams 626 Review and Summary 634 Review Problems 637

8 Columns 640 tx 16.1 Introduction Stability of Structures Euler's Formula for Pin-Ended Columns 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