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Vector Mechanics for Engineers: Statics

by: Beer, Ferdinand P.; Johnston, Russell E., Jr.

Vector Mechanics for Engineers: Statics

by: Beer, Ferdinand P.; Johnston, Russell E., Jr.

ISBN 13:
9780071140577
ISBN 10:
0071140573
Edition: 6th
Format: Paperback
Copyright: 04/01/2000
Publisher: MCGRAW HILL BOOK CO LTD

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Preface

xvii

List of Symbols

xxiii

Introduction

(14)

What Is Mechanics?

(1)

Fundamental Concepts and Principles

(3)

Systems of Units

(5)

Conversion from One System of Units to Another

(2)

Method of Problem Solution

(1)

Numerical Accuracy

(2)

Statics of Particles

(56)

Introduction

(1)

Forces In a Plane

(1)

Force on a Particle. Resultant of Two Forces

(1)

Vectors

(1)

Addition of Vectors

(2)

Resultant of Several Concurrent Forces

(1)

Resolution of a Force into Components

(6)

Rectangular Components of a Force. Unit Vectors

(3)

Addition of Forces by Summing x and y Components

(5)

Equilibrium of a Particle

(1)

Newton's First Law of Motion

(1)

Problems Involving the Equilibrium of a Particle. Free-Body Diagrams

(9)

Forces in Space

(1)

Rectangular Components of a Force in Space

(3)

Force Defined by Its Magnitude and Two Points on Its Line of Action

(1)

Addition of Concurrent Forces in Space

(8)

Equilibrium of a Particle in Space

(14)

Review and Summary for Chapter 2

(3)

Review Problems

(4)

Rigid Bodies: Equivalent Systems of Forces

(82)

Introduction

(1)

External and Internal Forces

(1)

Principle of Transmissibility. Equivalent Forces

(2)

Vector Product of Two Vectors

(2)

Vector Products Expressed in Terms of Rectangular Components

(2)

Moment of a Force about a Point

(2)

Varignon's Theorem

(1)

Rectangular Components of the Moment of a Force

(10)

Scalar Product of Two Vectors

(2)

Mixed Triple Product of Three Vectors

(2)

Moment of a Force about a Given Axis

(10)

Moment of a Couple

105

(1)

Equivalent Couples

106

(2)

Addition of Couples

108

(1)

Couples Can Be Represented by Vectors

108

(1)

Resolution of a Given Force Into a Force at O and a Couple

109

(11)

Reduction of a System of Forces to One Force and One Couple

120

(2)

Equivalent Systems of Forces

122

(1)

Equipollent Systems of Vectors

122

(1)

Further Reduction of a System of Forces

123

(2)

Reduction of a System of Forces to a Wrench

125

(28)

Review and Summary for Chapter 3

144

(5)

Review Problems

149

(4)

Equilibrium of Rigid Bodies

153

(56)

Introduction

154

(1)

Free-Body Diagram

155

(1)

Equilibrium in Two Dimensions

156

(1)

Reactions at Supports and Connections for a Two-Dimensional Structure

156

(2)

Equilibrium of a Rigid Body in Two Dimensions

158

(2)

Statically Indeterminate Reactions. Partial Constraints

160

(17)

Equilibrium of a Two-Force Body

177

(1)

Equilibrium of a Three-Force Body

178

(7)

Equilibrium in Three Dimensions

185

(1)

Equilibrium of a Rigid Body in Three Dimensions

185

(1)

Reactions at Supports and Connections for a Three-Dimensional Structure

185

(24)

Review and Summary for Chapter 4

202

(2)

Review Problems

204

(5)

Distributed Forces: Centroids and Centers of Gravity

209

(65)

Introduction

210

(1)

Areas and Lines

210

(1)

Center of Gravity of a Two-Dimensional Body

210

(2)

Centroids of Areas and Lines

212

(1)

First Moments of Areas and Lines

213

(3)

Composite Plates and Wires

216

(11)

Determination of Centroids by Integration

227

(2)

Theorems of Pappus-Guldinus

229

(11)

Distributed Loads on Beams

240

(1)

Forces on Submerged Surfaces

241

(10)

Volumes

251

(1)

Center of Gravity of a Three-Dimensional Body. Centroid of a Volume

251

(3)

Composite Bodies

254

(1)

Determination of Centroids of Volumes by Integration

254

(20)

Review and Summary for Chapter 5

266

(4)

Review Problems

270

(4)

Analysis of Structures

274

(67)

Introduction

275

(1)

Trusses

276

(1)

Definition of a Truss

276

(2)

Simple Trusses

278

(1)

Analysis of Trusses by the Method of Joints

279

(2)

Joints under Special Loading Conditions

281

(2)

Space Trusses

283

(10)

Analysis of Trusses by the Method of Sections

293

(1)

Trusses Made of Several Simple Trusses

294

(11)

Frames and Machines

305

(1)

Structures Containing Multiforce Members

305

(1)

Analysis of a Frame

305

(1)

Frames Which Cease to Be Rigid When Detached from Their Supports

306

(15)

Machines

321

(20)

Review and Summary for Chapter 6

333

(3)

Review Problems

336

(5)

Forces in Beams and Cables

341

(55)

Introduction

342

(1)

Internal Forces in Members

342

(7)

Beams

349

(1)

Various Types of Loading and Support

349

(1)

Shear and Bending Moment in a Beam

350

(2)

Shear and Bending-Moment Diagrams

352

(8)

Relations among Load, Shear, and Bending Moment

360

(11)

Cables

371

(1)

Cables with Concentrated Loads

371

(1)

Cables with Distributed Loads

372

(1)

Parabolic Cable

373

(9)

Catenary

382

(14)

Review and Summary for Chapter 7

390

(3)

Review Problems

393

(3)

Friction

396

(59)

Introduction

397

(1)

The Laws of Dry Friction. Coefficients of Friction

397

(3)

Angles of Friction

400

(1)

Problems Involving Dry Friction

401

(16)

Wedges

417

(1)

Square-Threaded Screws

417

(9)

Journal Bearings. Axle Friction

426

(2)

Thrust Bearings. Disk Friction

428

(1)

Wheel Friction. Rolling Resistance

429

(7)

Belt Friction

436

(19)

Review and Summary for Chapter 8

447

(3)

Review Problems

450

(5)

Distributed Forces: Moments of Inertia

455

(84)

Introduction

456

(1)

Moments of Inertia of Areas

457

(1)

Second Moment, or Moment of Inertia, of an Area

457

(1)

Determination of the Moment of Inertia of an Area by Integration

458

(1)

Polar Moment of Inertia

459

(1)

Radius of Gyration of an Area

460

(7)

Parallel-Axis Theorem

467

(1)

Moments of Inertia of Composite Areas

468

(13)

Product of Inertia

481

(1)

Principal Axes and Principal Moments of Inertia

482

(8)

Mohr's Circle for Moments and Products of Inertia

490

(6)

Moments of Inertia of Masses

496

(1)

Moment of Inertia of a Mass

496

(2)

Parallel-Axis Theorem

498

(1)

Moments of Inertia of Thin Plates

499

(1)

Determination of the Moment of Inertia of a Three-Dimensional Body by Integration

500

(1)

Moments of Inertia of Composite Bodies

500

(15)

Moment of Inertia of a Body with Respect to an Arbitrary Axis through O. Mass Products of Inertia

515

(1)

Ellipsoid of Inertia. Principal Axes of Inertia

516

(2)

Determination of the Principal Axes and Principal Moments of Inertia of s Body of Arbitrary Shape

518

(21)

Review and Summary for Chapter 9

529

(6)

Review Problems

535

(4)

Method of Virtual Work

539

(42)

Introduction

540

(1)

Work of a Force

540

(3)

Principle of Virtual Work

543

(1)

Applications of the Principle of Virtual Work

544

(2)

Real Machines. Mechanical Efficiency

546

(14)

Work of a Force during a Finite Displacement

560

(2)

Potential Energy

562

(1)

Potential Energy and Equilibrium

563

(1)

Stability of Equilibrium

564

(17)

Review and Summary for Chapter 10

574

(3)

Review Problems

577

(4)

Kinematics of Particles

581

(86)

Introduction to Dynamics

582

(1)

Rectilinear Motion of Particles

583

(1)

Position, Velocity, and Acceleration

583

(4)

Determination of the Motion of a Particle

587

(9)

Uniform Rectilinear Motion

596

(1)

Uniformly Accelerated Rectilinear Motion

597

(1)

Motion of Several Particles

598

(12)

Graphical Solution of Rectilinear-Motion Problems

610

(1)

Other Graphical Methods

611

(10)

Curvilinear Motion of Particles

621

(1)

Position Vector, Velocity, and Acceleration

621

(2)

Derivatives of Vector Functions

623

(2)

Rectangular Components of Velocity and Acceleration

625

(1)

Motion Relative to a Frame in Translation

626

(17)

Tangential and Normal Components

643

(3)

Radial and Transverse Components

646

(21)

Review and Summary for Chapter 11

659

(4)

Review Problems

663

(4)

Kinetics of Particles: Newton's Second Law

667

(62)

Introduction

668

(1)

Newton's Second Law of Motion

669

(1)

Linear Momentum of a Particle. Rate of Change of Linear Momentum

670

(1)

Systems of Units

671

(2)

Equations of Motion

673

(2)

Dynamic Equilibrium

675

(20)

Angular Momentum of a Particle. Rate of Change of Angular Momentum

695

(1)

Equations of Motion in Terms of Radial and Transverse Components

696

(1)

Motion under a Central Force. Conservation of Angular Momentum

697

(1)

Newton's Law of Gravitation

698

(9)

Trajectory of a Particle under a Central Force

707

(1)

Application to Space Mechanics

708

(3)

Kepler's Laws of Planetary Motion

711

(18)

Review and Summary for Chapter 12

720

(4)

Review Problems

724

(5)

Kinetics of Particles: Energy and Momentum Methods

729

(98)

Introduction

730

(1)

Work of a Force

730

(4)

Kinetic Energy of a Particle. Principle of Work and Energy

734

(2)

Applications of the Principle of Work and Energy

736

(1)

Power and Efficiency

737

(18)

Potential Energy

755

(2)

Conservative Forces

757

(1)

Conservation of Energy

758

(2)

Motion under a Conservative Central Force, Application to Space Mechanics

760

(19)

Principle of Impulse and Momentum

779

(3)

Impulsive Motion

782

(12)

Impact

794

(1)

Direct Central Impact

794

(3)

Oblique Central Impact

797

(3)

Problems Involving Energy and Momentum

800

(27)

Review and Summary for Chapter 13

816

(6)

Review Problems

822

(5)

Systems of Particles

827

(58)

Introduction

828

(1)

Application of Newton's Laws to the Motion of a System of Particles. Effective Forces

828

(3)

Linear and Angular Momentum of a System of Particles

831

(1)

Motion of the Mass Center of a System of Particles

832

(2)

Angular Momentum of a System of Particles about Its Mass Center

834

(2)

Conservation of Momentum for a System of Particles

836

(9)

Kinetic Energy of a System of Particles

845

(2)

Work-Energy Principle. Conservation of Energy for a System of Particles

847

(1)

Principle of Impulse and Momentum for a System of Particles

847

(11)

Variable Systems of Particles

858

(1)

Steady Stream of Particles

858

(3)

Systems Gaining or Losing Mass

861

(24)

Review and Summary for Chapter 14

876

(4)

Review Problems

880

(5)

Kinematics of Rigid Bodies

885

(105)

Introduction

886

(2)

Translation

888

(1)

Rotation about a Fixed Axis

889

(3)

Equations Defining the Rotation of a Rigid Body about a Fixed Axis

892

(10)

General Plane Motion

902

(2)

Absolute and Relative Velocity in Plane Motion

904

(11)

Instantaneous Center of Rotation in Plane Motion

915

(11)

Absolute and Relative Acceleration in Plane Motion

926

(2)

Analysis of Plane Motion in Terms of a Parameter

928

(12)

Rate of Change of a Vector with Respect to a Rotating Frame

940

(2)

Plane Motion of a Particle Relative to a Rotating Frame. Coriolis Acceleration

942

(11)

Motion about a Fixed Point

953

(3)

General Motion

956

(11)

Three-Dimensional Motion of a Particle Relative to a Rotating Frame. Coriolis Acceleration

967

(1)

Frame of Reference in General Motion

968

(22)

Review and Summary for Chapter 15

979

(7)

Review Problems

986

(4)

Plane Motion of Rigid Bodies: Forces and Accelerations

990

(55)

Introduction

991

(1)

Equations of Motion for a Rigid Body

992

(1)

Angular Momentum of a Rigid Body in Plane Motion

993

(1)

Plane Motion of a Rigid Body. D'Alembert's Principle

994

(1)

A Remark on the Axioms of the Mechanics of Rigid Bodies

995

(1)

Solution of Problems Involving the Motion of a Rigid Body

996

(1)

Systems of Rigid Bodies

997

(19)

Constrained Plane Motion

1016

(29)

Review and Summary for Chapter 16

1039

(2)

Review Problems

1041

(4)

Plane Motion of Rigid Bodies: Energy and Momentum Methods

1045

(61)

Introduction

1046

(1)

Principle of Work and Energy for a Rigid Body

1046

(1)

Work of Forces Acting on a Rigid Body

1047

(1)

Kinetic Energy of a Rigid Body in Plane Motion

1048

(1)

Systems of Rigid Bodies

1049

(1)

Conservation of Energy

1050

(1)

Power

1051

(17)

Principle of Impulse and Momentum for the Plane Motion of a Rigid Body

1068

(3)

Systems of Rigid Bodies

1071

(1)

Conservation of Angular Momentum

1071

(13)

Impulsive Motion

1084

(1)

Eccentric Impact

1084

(22)

Review and Summary for Chapter 17

1098

(4)

Review Problems

1102

(4)

Kinetics of Rigid Bodies in Three Dimensions

1106

(65)

Introduction

1107

(1)

Angular Momentum of a Rigid Body in Three Dimensions

1108

(4)

Application of the Principle of Impulse and Momentum to the Three-Dimensional Motion of a Rigid Body

1112

(1)

Kinetic Energy of a Rigid Body in Three Dimensions

1113

(13)

Motion of a Rigid Body in Three Dimensions

1126

(1)

Euler's Equations of Motion. Extension of d'Alembert's Principle to the Motion of a Rigid Body in Three Dimensions

1127

(1)

Motion of a Rigid Body about a Fixed Point

1128

(1)

Rotation of a Rigid Body about a Fixed Axis

1129

(15)

Motion of a Gyroscope. Eulerian Angles

1144

(2)

Steady Precession of a Gyroscope

1146

(1)

Motion of an Axisymmetrical Body under No Force

1147

(24)

Review and Summary for Chapter 18

1160

(5)

Review Problems

1165

(6)

Mechanical Vibrations

1171

(72)

Introduction

1172

(1)

Vibrations without Damping

1172

(1)

Free Vibrations of Particles. Simple Harmonic Motion

1172

(4)

Simple Pendulum (Approximate Solution)

1176

(1)

Simple Pendulum (Exact Solution)

1177

(9)

Free Vibrations of Rigid Bodies

1186

(12)

Application of the Principle of Conservation of Energy

1198

(11)

Forced Vibrations

1209

(10)

Damped Vibrations

1219

(1)

Damped Free Vibrations

1219

(3)

Damped Forced Vibrations

1222

(1)

Electrical Analogues

1223

(20)

Review and Summary for Chapter 19

1234

(5)

Review Problems

1239

(4)

Index

1243

(12)

Answers to Problems

1255

Amazon no longer offers textbook rentals. We do!

Vector Mechanics for Engineers: Statics

Vector Mechanics for Engineers: Statics

9780071140577

0071140573

Table of Contents

Supplemental Materials

Write a Review

Amazon no longer offers textbook rentals. We do!

Vector Mechanics for Engineers: Statics

Vector Mechanics for Engineers: Statics

9780071140577

0071140573

Table of Contents

Supplemental Materials

Write a Review

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