05229c55f5f3fb Engineering Mechanics contents

Contents Preface to Adapted Edition .............................................................................. (v) P...

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Contents Preface to Adapted Edition .............................................................................. (v) Preface to Third Edition ................................................................................. (vii) List of Symbols and Abbreviations.................................................................. (xi)

PART - I

STATICS Chapter 1 Introductory Concepts 1-1 1-2 1.3 1-4 1-5 1-6 1-7 1-8 1-9 1-10

Scope of Mechanics ....................................................................... 1 Preview if Statics ........................................................................... 1 Fundamental Concepts and Axioms .............................................. 2 Scalar and Vector Quantities ......................................................... 5 Introduction to Free-body Diagrams .............................................. 6 Guide to Solving Problems ............................................................ 7 Dimensional Checks .................................................................... 8 Conversion of Units ...................................................................... 9 Numerical Computations Slide Rules and Calculators ................ 10 Useful Techniques and Information ............................................. 12

Chapter 2 Resultants of Force System 2-1 2-2 2-3 2-4 2-5 2-6 2-7 2-8 2-9

Introduction .................................................................................. 16 Parallelogram Law ...................................................................... 16 Forces and Components .............................................................. 18 Resultant of Coplanar Concurrent Forces ................................... 25 Components of Forces in Space .................................................. 30 Vector Notation ........................................................................... 37 Vector Algebra, Dot Product ...................................................... 40 Vector Algebra, Cross Product ................................................... 46 Moment of Force Principle of Moments ...................................... 54 (xv)

Contents ...................................................................................................................... (xvi)

2-10 2-11 2-12 2-13

Coplanar Applications ................................................................ 57 Spatial Applications .................................................................... 63 Couples ....................................................................................... 73 Resultant of any Force System .................................................... 74

Chapter 3 Equilibrium of Force Systems 3-1 3-2 3-3 3-4 3-5 3-6

Introduction ................................................................................. 91 Free-body Diagrams .................................................................... 92 Equations of Equilibrium ............................................................ 93 Equilibrium of Planar Systems .................................................... 94 Further Discussion of Planar Equilibrium ................................ 104 Equilibrium of Spatial Systems ................................................. 118

Chapter 4 Analysis of Structures 4-1 4-2 4-3 4-4 4-5 4-6 4-7

Introduction ............................................................................... 137 Construction of Trusses ............................................................ 138 Method of Joints ....................................................................... 143 Methods of Sections .................................................................. 154 Redundant Members; Counter Diagonals .................................. 167 Method of Members Frames ..................................................... 169 Space Trusses ............................................................................ 184

Chapter 5 Friction 5-1 5-2 5-3 5-4 5-5 5-6 5-7 5-8 5-9

Introduction ................................................................................ 195 Theory of Friction ...................................................................... 195 Angle of Friction ........................................................................ 198 Laws of Friction ......................................................................... 200 Further Applications of Friction ................................................ 210 Square-threaded Screws ............................................................ 223 Belt Friction ............................................................................... 226 Disk Friction ............................................................................ 233 Rolling Resistance .................................................................... 238

Contents .....................................................................................................................(xvii)

Chapter 6 Centroids and Centers of Gravity 6-1 Introduction ............................................................................... 241 6-2 Centre of Gravity of Flat Plate ................................................... 242 6-3 Centroids of Areas and Lines .................................................... 243 6-4 Importance of Centroids and Moments of Area ........................ 244 6-5 Centroids Determined by Integration ........................................ 245 6-6 Centroids of Composite Figures ............................................... 252 6-7 Theorem of Pappus .................................................................... 264 6-8 Center of Gravity of Bodies Centroids of Volumes ................... 270 Summary .................................................................................... 276

Chapter 7 Moments of Inertia 7-1 Definition of Moment of Inertia ................................................ 278 7-2 Polar Moment of Inertia ............................................................ 280 7-3 Radius of Gyration .................................................................... 281 7-4 Transfer Formula for Moment of Inertia ................................... 281 7-5 Moments of Inertia by Integration ............................................ 283 7-6 Moments of Inertia for Composite Areas .................................. 289 7-7 Product of Inertia ...................................................................... 297 7-8 Product of Inertia is Zero with Respect to Axes of Symmetry . 298 7-9 Transfer Formula for Product of Inertia ..................................... 299 7-10 Moment of Inertia with Respect to Inclined Axes .................... 306 7-11 Mohr’s Circle for Moments of Inertia ....................................... 309 7-12 Maximum and Minimum Moments of Inertia Principal Axes .. 312 7-13 Moments of Inertia of Masses ................................................... 316 7-14 Radius of Gyration .................................................................... 317 7-15 Transfer Formula for Mass Moments of Inertia ........................ 317 7-16 Mass Moments of Inertia by Integration ................................... 319 7-17 Moments of Inertia of Composite Bodies ................................. 327 Summary .................................................................................... 337

Contents ................................................................................................................... (xviii)

Chapter 8 Special Topics 8-1 Introduction ............................................................................... 339 8-2 Shear and Moment Equations and Diagrams ............................ 341 8-3 Relations between Load, Shear and Bending Moment ............. 354 8-4 Definition and Meaning of Work .............................................. 373 8-5 Introductory Concepts of Virtual Work Method ....................... 375 8-6 Principle and Application of Virtual Work ............................... 376 8-7 Introduction ............................................................................... 394 8-8 Application of Parallelogram Law ............................................ 394 8-9 Resultant of Coplanar Force Systems ....................................... 395 8-10 String Polygon .......................................................................... 396 8-11 Equilibrium of Force Systems by Graphic Methods .................. 401 8-12 Graphic Analysis of Trusses Maxwell Diagrams....................... 405

PART - II

DYNAMICS Chapter 9 Kinematics of a Particle 9-1 Introduction ................................................................................ 415 9-2 Motion of a Particle ................................................................... 417 9-3 Rectilinear Motion ..................................................................... 422 9-4 Motion Curves ........................................................................... 431 9-5 Introduction to Vector Calculus ................................................ 443 9-6 Rectangular Components of Curvilinear Motion ....................... 444 9-7 Normal and Tangential Components of Acceleration ................ 454 9-8 Radial and Transverse Components Cylindrical Coordinates ... 463 Summary .................................................................................... 474

Contents ......................................................................................................................(xix)

Chapter 10 General Principles of Dynamics 10-1 10-2 10-3 10-4 10-5 10-6

Introduction ................................................................................ 477 Newton’s Laws of Motion for a Particle .................................... 478 Fundamental Equation of Kinetics for a Particle ....................... 480 Gravitational and Absolute System of Units.............................. 481 D’Alembert’s Principle – Motion of the Mass Center ............... 482 Moment Effect of External Forces ............................................. 486 Summary .................................................................................... 489

Chapter 11 Kinetics of Particles 11-1 11-2 11-3 11-4

Introduction ................................................................................ 490 Translation – Analysis as a Particle ........................................... 491 Further Discussion of Particle Kinetics ..................................... 504 Translation – Analysis as a Rigid Body .................................... 518 Summary .................................................................................... 530

Chapter 12 Kinematics of Rigid Bodies 12-1 12-2 12-3 12-4 12-5 12-6

Introduction. Types of Rigid-Body Motion .............................. 531 Angular Motion – Fixed-Axis Rotation .................................... 532 Definition and Analysis of Plane Motion ................................. 542 Application of Kinematic Equations ......................................... 547 Instant Center and Instantaneous Axis of Rotation ................... 565 The Omega Theorem ................................................................ 581

Chapter 13 Kinetics of Rigid Bodies 13-1 13-2 13-3 13-4 13-5

Introduction ................................................................................ 585 Equations of Plane Motion......................................................... 585 Fixed-Axis Rotation ................................................................... 590 Rolling Bodies ........................................................................... 607 General Plane Motion ............................................................... 621 Summary .................................................................................... 637

Contents....................................................................................................................... (xx)

Chapter 14 Work-Energy Method 14-1 Introduction ................................................................................ 639 14-2 Work-Energy Equation for Translation .................................... 640 14-3 Interpretation and Computation of Work .................................. 641 14-4 Work-Energy Applied To Particle Motion ............................... 646 14-5 Power Efficiency ....................................................................... 656 14-6 Work-Energy Applied to Connected Systems .......................... 659 14-7 Work-Energy Method Applied to Fixed-Axis Rotation............. 668 14-8 Work-Energy Applied to Plane Motion .................................... 685 Summary .................................................................................... 701

Chapter 15 Impulse and Momentum 15-1 Introduction ................................................................................ 704 15-2 Linear Impulse-Momentum ...................................................... 704 15-3 Dynamic Action of Jet Streams ................................................ 711 15-4 Conservation of Linear Momentum .......................................... 719 15-5 Elastic Impact ............................................................................ 726 15-6 Impulse Momentum in Plane Motion ........................................ 734 15-7 Satellite Motion ......................................................................... 750 15-8 Introduction to Gyroscopic Action ............................................ 759 Summary .................................................................................... 764

Chapter 16 Mechanical Vibrations 16-1 Introduction, Definitions and Concepts .................................... 768 16-2 Simple Harmonic Motion. Free Vibrations................................ 769 16-3 Simple Pendulum ...................................................................... 774 16-4 Compound Pendulum ................................................................ 776 16-5 Torsion Pendulum ..................................................................... 779

Contents .........................................................................................................................(xxi)

16-6 Graphical Representation of Simple Harmonic Motion............. 782 16-7 Free Vibrations Without Damping : General Case ................... 784 16-8 Free Vibrations Analyzed by Work-Energy Method ................ 793 16-9 Forced Vibrations ...................................................................... 798 Summary .................................................................................... 806 Index .......................................................................................................... 809