Engineering Mechanics: Combined Statics & Dynamics Book

STATICS

1 General Principles 3

Chapter Objectives 3

1.1 Mechanics 3

1.2 Fundamental Concepts 4

1.3 Units of Measurement 7

1.4 The International System of Units 9

1.5 Numerical Calculations 10

1.6 General Procedure for Analysis 12

2 Force Vectors 17

Chapter Objectives 17

2.1 Scalars and Vectors 17

2.2 Vector Operations 18

2.3 Vector Addition of Forces 20

2.4 Addition of a System of Coplanar Forces 32

2.5 Cartesian Vectors 43

2.6 Addition of Cartesian Vectors 46

2.7 Position Vectors 56

2.8 Force Vector Directed Along a Line 59

2.9 Dot Product 69

3 Equilibrium of a Particle 85

Chapter Objectives 85

3.1 Condition for the Equilibrium of a

Particle 85

3.2 The Free-Body Diagram 86

3.3 Coplanar Force Systems 89

3.4 Three-Dimensional Force Systems 103

4 Force System

Resultants 117

Chapter Objectives 117

4.1 Moment of a Force—Scalar

Formulation 117

4.2 Cross Product 121

4.3 Moment of a Force—Vector

Formulation 124

4.4 Principle of Moments 128

4.5 Moment of a Force about a

Specified Axis 139

4.6 Moment of a Couple 148

4.7 Simplification of a Force and Couple

System 160

4.8 Further Simplification of a Force and

Couple System 170

4.9 Reduction of a Simple Distributed

Loading 183

5 Equilibrium of a Rigid Body 199

Chapter Objectives 199

5.1 Conditions for Rigid-Body Equilibrium 199

5.2 Free-Body Diagrams 201

5.3 Equations of Equilibrium 214

5.4 Two- and Three-Force Members 224

5.5 Free-Body Diagrams 237

5.6 Equations of Equilibrium 242

5.7 Constraints and Statical Determinacy 243

6 Structural Analysis 263

Chapter Objectives 263

6.1 Simple Trusses 263

6.2 The Method of Joints 266

6.3 Zero-Force Members 272

6.4 The Method of Sections 280

6.5 Space Trusses 290

6.6 Frames and Machines 294

7Internal Forces 329

Chapter Objectives 329

7.1 Internal Forces Developed in Structural

Members 329

7.2 Shear and Moment Equations and

Diagrams 345

7.3 Relations between Distributed Load, Shear,

and Moment 354

7.4 Cables 365

8 Friction 387

Chapter Objectives 387

8.1 Characteristics of Dry Friction 387

8.2 Problems Involving Dry Friction 392

8.3 Wedges 412

8.4 Frictional Forces on Screws 414

8.5 Frictional Forces on Flat Belts 421

8.6 Frictional Forces on Collar Bearings, Pivot

Bearings, and Disks 429

8.7 Frictional Forces on Journal Bearings 432

8.8 Rolling Resistance 434

9 Center of Gravity andCentroid 447

Chapter Objectives 447

9.1 Center of Gravity, Center of Mass, and the

Centroid of a Body 447

9.2 Composite Bodies 470

9.3 Theorems of Pappus and Guldinus 484

9.4 Resultant of a General Distributed

Loading 493

9.5 Fluid Pressure 494

10 Moments of Inertia 511

Chapter Objectives 511

10.1 Definition of Moments of Inertia

for Areas 511

10.2 Parallel-Axis Theorem for an Area 512

10.3 Radius of Gyration of an Area 513

10.4 Moments of Inertia for

Composite Areas 522

10.5 Product of Inertia for an Area 530

10.6 Moments of Inertia for an Area about

Inclined Axes 534

10.7 Mohr’s Circle for Moments of Inertia 537

10.8 Mass Moment of Inertia 545

11 Virtual Work 563

Chapter Objectives 563

11.1 Definition of Work 563

11.2 Principle of Virtual Work 565

11.3 Principle of Virtual Work for a System of

Connected Rigid Bodies 567

11.4 Conservative Forces 579

11.5 Potential Energy 580

11.6 Potential-Energy Criterion for

Equilibrium 582

11.7 Stability of Equilibrium Configuration 583

Appendix

A. Mathematical Review and

Expressions 598

Fundamental Problems

Partial Solutions and

Answers 603

Answers to Selected

Problems 620

Index 650

DYNAMICS

12 Kinematics of a Particle 3

Chapter Objectives 3

12.1 Introduction 3

12.2 Rectilinear Kinematics: Continuous

Motion 5

12.3 Rectilinear Kinematics: Erratic Motion 19

12.4 General Curvilinear Motion 32

12.5 Curvilinear Motion: Rectangular

Components 34

12.6 Motion of a Projectile 39

12.7 Curvilinear Motion: Normal and Tangential

Components 53

12.8 Curvilinear Motion: Cylindrical

Components 67

12.9 Absolute Dependent Motion Analysis of

Two Particles 81

12.10 Relative-Motion of Two Particles Using

Translating Axes 87

13 Kinetics of a Particle: Force and Acceleration 107

Chapter Objectives 107

13.1 Newton’s Second Law of Motion 107

13.2 The Equation of Motion 110

13.3 Equation of Motion for a System of

Particles 112

13.4 Equations of Motion: Rectangular

Coordinates 114

13.5 Equations of Motion: Normal and

Tangential Coordinates 131

13.6 Equations of Motion: Cylindrical

Coordinates 144

*13.7 Central-Force Motion and Space

Mechanics 155

14 Kinetics of a Particle: Work and Energy 169

Chapter Objectives 169

14.1 The Work of a Force 169

14.2 Principle of Work and Energy 174

14.3 Principle of Work and Energy for a System

of Particles 176

14.4 Power and Efficiency 192

14.5 Conservative Forces and Potential

Energy 201

14.6 Conservation of Energy 205

15 Kinetics of a Particle: Impulse and Momentum 221

Chapter Objectives 221

15.1 Principle of Linear Impulse and

Momentum 221

15.2 Principle of Linear Impulse and Momentum

for a System of Particles 228

15.3 Conservation of Linear Momentum for a

System of Particles 236

15.4 Impact 248

15.5 Angular Momentum 262

15.6 Relation Between Moment of a Force and

Angular Momentum 263

15.7 Principle of Angular Impulse and

Momentum 266

15.8 Steady Flow of a Fluid Stream 277

*15.9 Propulsion with Variable Mass 282

Review

1. Kinematics and Kinetics of a Particle 298

16 Planar Kinematics of a Rigid Body 311

Chapter Objectives 311

16.1 Planar Rigid-Body Motion 311

16.2 Translation 313

16.3 Rotation about a Fixed Axis 314

16.4 Absolute Motion Analysis 329

16.5 Relative-Motion Analysis: Velocity 337

16.6 Instantaneous Center of Zero Velocity 351

16.7 Relative-Motion Analysis: Acceleration 363

16.8 Relative-Motion Analysis using Rotating

Axes 377

17 Planar Kinetics of a Rigid Body: Force and Acceleration 395

Chapter Objectives 395

17.1 Moment of Inertia 395

17.2 Planar Kinetic Equations of Motion 409

17.3 Equations of Motion: Translation 412

17.4 Equations of Motion: Rotation about a

Fixed Axis 425

17.5 Equations of Motion: General Plane

Motion 440

18 Planar Kinetics of aRigid Body: Work and Energy 455

Chapter Objectives 455

18.1 Kinetic Energy 455

18.2 The Work of a Force 458

18.3 The Work of a Couple 460

18.4 Principle of Work and Energy 462

18.5 Conservation of Energy 477

19 Planar Kinetics of a RigidBody: Impulse and Momentum 495

Chapter Objectives 495

19.1 Linear and Angular Momentum 495

19.2 Principle of Impulse and Momentum 501

19.3 Conservation of Momentum 517

*19.4 Eccentric Impact 521

Review

2. Planar Kinematics and Kinetics of a Rigid

Body 534

20 Three-Dimensional Kinematics of a Rigid Body 549

Chapter Objectives 549

20.1 Rotation About a Fixed Point 549

*20.2 The Time Derivative of a Vector Measured

from Either a Fixed or Translating-Rotating

System 552

20.3 General Motion 557

*20.4 Relative-Motion Analysis Using Translating

and Rotating Axes 566

21 Three-Dimensional Kinetics of a Rigid Body 579

Chapter Objectives 579

*21.1 Moments and Products of Inertia 579

21.2 Angular Momentum 589

21.3 Kinetic Energy 592

*21.4 Equations of Motion 600

*21.5 Gyroscopic Motion 614

21.6 Torque-Free Motion 620

CONTENTS X I I I

22 Vibrations 631

Chapter Objectives 631

*22.1 Undamped Free Vibration 631

*22.2 Energy Methods 645

*22.3 Undamped Forced Vibration 651

*22.4 Viscous Damped Free Vibration 655

*22.5 Viscous Damped Forced Vibration 658

*22.6 Electrical Circuit Analogs 661

Appendix

A. Mathematical Expressions 670

B. Vector Analysis 672

C. The Chain Rule 677

Fundamental Problems

Partial Solutions and

Answers 679

Answers to Selected

Problems 000

Index 000