Vector Mechanics for Engineers : Statics Book

Preface     xii
List of Symbols     xviii
Introduction     1
What Is Mechanics?     2
Fundamental Concepts and Principles     2
Systems of Units     5
Conversion from One System of Units to Another     10
Method of Problem Solution     11
Numerical Accuracy     13
Statics of Particles     15
Introduction     16
Forces in a Plane     16
Force on a Particle: Resultant of Two Forces     16
Vectors     17
Addition of Vectors     18
Resultant of Several Concurrent Forces     20
Resolution of a Force into Components     21
Rectangular Components of a Force. Unit Vectors     27
Addition of Forces by Summing x and y Components     30
Equilibrium of a Particle     35
Newton's First Law of Motion     36
Problems Involving the Equilibrium of a Particle. Free-Body Diagrams     36
Forces in Space     45
Rectangular Components of a Force in Space     45
Force Defined by Its Magnitude and Two Points on Its Line of Action     48
Addition of Concurrent Forces in Space     49
Equilibrium ofa Particle in Space     57
Review and Summary for Chapter 2     64
Review Problems     67
Computer Problems     69
Rigid Bodies: Equivalent Systems of Forces     73
Introduction     74
External and Internal Forces     74
Principle of Transmissibility. Equivalent Forces     75
Vector Product of Two Vectors     77
Vector Products Expressed in Terms of Rectangular Components     79
Moment of a Force about a Point     81
Varignon's Theorem     83
Rectangular Components of the Moment of a Force     83
Scalar Product of Two Vectors     93
Mixed Triple Product of Three Vectors     95
Moment of a Force about a Given Axis     97
Moment of a Couple     107
Equivalent Couples     108
Addition of Couples     110
Couples Can Be Represented by Vectors     110
Resolution of a Given Force Into a Force at O and a Couple     111
Reduction of a System of Forces to One Force and One Couple     122
Equivalent Systems of Forces     123
Equipollent Systems of Vectors     124
Further Reduction of a System of Forces     124
Reduction of a System of Forces to a Wrench     127
Review and Summary for Chapter 3     146
Review Problems     151
Computer Problems     153
Equilibrium of Rigid Bodies     157
Introduction     158
Free-Body Diagram     159
Equilibrium in Two Dimensions     160
Reactions at Supports and Connections for a Two-Dimensional Structure     160
Equilibrium of a Rigid Body in Two Dimensions     162
Statically Indeterminate Reactions: Partial Constraints     164
Equilibrium of a Two-Force Body     183
Equilibrium of a Three-Force Body     184
Equilibrium in Three Dimensions     191
Equilibrium of a Rigid Body in Three Dimensions     191
Reactions at Supports and Connections for a Three-Dimensional Structure     191
Review and Summary for Chapter 4     211
Review Problems     213
Computer Problems     215
Distributed Forces: Centroids and Centers of Gravity     219
Introduction     220
Areas and Lines     220
Center of Gravity of a Two-Dimensional Body     220
Centroids of Areas and Lines     222
First Moments of Areas and Lines      223
Composite Plates and Wires     226
Determination of Centroids by Integration     236
Theorems of Pappus-Guldinus     238
Distributed Loads on Beams     248
Forces on Submerged Surfaces     249
Volumes     259
Center of Gravity of a Three-Dimensional Body: Centroid of a Volume     259
Composite Bodies     262
Determination of Centroids of Volumes by Integration     262
Review and Summary for Chapter 5     274
Review of Problems     278
Computer Problems     281
Analysis of Structures     284
Introduction     285
Trusses     286
Definition of a Truss     286
Simple Trusses     288
Analysis of Trusses by the Method of Joints     289
Joints under Special Loading Conditions     291
Space Trusses     293
Analysis of Trusses by the Method of Sections     303
Trusses Made of Several Simple Trusses     304
Frames and Machines     315
Structures Containing Multiforce Members     315
Analysis of a Frame     315
Frames Which Cease to Be Rigid When Detached from Their Supports      316
Machines     331
Review and Summary for Chapter 6     343
Review Problems     346
Computer Problems     349
Forces in Beams and Cables     353
Introduction     354
Internal Forces in Members     354
Beams     361
Various Types of Loading and Support     361
Shear and Bending Moment in a Beam     362
Shear and Bending-Moment Diagrams     364
Relations among Load, Shear, and Bending Moment     372
Cables     383
Cables with Concentrated Loads     383
Cables with Distributed Loads     384
Parabolic Cable     385
Catenary     394
Review and Summary for Chapter 7     402
Review Problems     405
Computer Problems     408
Friction     411
Introduction     412
The Laws of Dry Friction. Coefficients of Friction     412
Angles of Friction     415
Problems Involving Dry Friction     416
Wedges     431
Square-Threaded Screws     431
Journal Bearings: Axle Friction     440
Thrust Bearings: Disk Friction      442
Wheel Friction: Rolling Resistance     443
Belt Friction     450
Review and Summary for Chapter 8     461
Review Problems     464
Computer Problems     467
Distributed Forces: Moments of Inertia     471
Introduction     472
Moments of Inertia of Areas     473
Second Moment, or Moment of Inertia, of an Area     473
Determination of the Moment of Inertia of an Area by Integration     474
Polar Moment of Inertia     475
Radius of Gyration of an Area     476
Parallel-Axis Theorem     483
Moments of Inertia of Composite Areas     484
Product of Inertia     497
Principal Axes and Principal Moments of Inertia     498
Mohr's Circle for Moments and Products of Inertia     506
Moments of Inertia of Masses     512
Moment of Inertia of a Mass     512
Parallel-Axis Theorem     514
Moments of Inertia of Thin Plates     515
Determination of the Moment of Inertia of a Three-Dimensional Body by Integration     516
Moments of Inertia of Composite Bodies     516
Moment of Inertia of a Body with Respect to an Arbitrary Axis through O: Mass Products of Inertia      531
Ellipsoid of Inertia: Principal Axes of Inertia     532
Determination of the Principal Axes and Principal Moments of Inertia of a Body of Arbitrary Shape     534
Review and Summary for Chapter 9     545
Review Problems     551
Computer Problems     554
Method of Virtual Work     557
Introduction     558
Work of a Force     558
Principle of Virtual Work     561
Applications of the Principle of Virtual Work     562
Real Machines: Mechanical Efficiency     564
Work of a Force during a Finite Displacement     578
Potential Energy     580
Potential Energy and Equilibrium     581
Stability of Equilibrium     582
Review and Summary for Chapter 10     592
Review Problems     595
Computer Problems     597
Fundamentals of Engineering Examination     601
Photo Credits     603
Index     605
Answers to Problems     611