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Continuing in the spirit of its successful previous editions, the ninth edition of Beer, Johnston, Mazurek, and Cornwell'sVector Mechanics for Engineersprovides conceptually accurate and thorough coverage together with a significant refreshment of the exercise sets and online delivery of homework problems to your students. Nearly forty percent of the problems in the text are changed from the previous edition.The Beer/Johnston textbooks introduced significant pedagogical innovations into engineering mechanics teaching. The consistent, accurate problem-solving methodology gives your students the best opportunity to learn statics and dynamics. At the same time, the careful presentation of content, unmatched levels of accuracy, and attention to detail have made these texts the standard for excellence.

Born in France and educated in France and Switzerland, Ferd held an M.S. degree from the Sorbonne and an Sc.D. degree in theoretical mechanics from the University of Geneva. He came to the United States after serving in the French army during the early part of World War II and had taught for four years at Williams College in the Williams-MIT joint arts and engineering program. Following his service at Williams College, Ferd joined the faculty of Lehigh University where he taught for thirty-seven years. He held several positions, including the University Distinguished Professors Chair and Chairman of the Mechanical Engineering and Mechanics Department, and in 1995 Ferd was awarded an honorary Doctor of Engineering degree by Lehigh University.

Born in Philadelphia, Russ holds a B.S. degree in civil engineering from the University of Delaware and an Sc.D. degree in the field of structural engineering from The Massachusetts Institute of Technology (MIT). He taught at Lehigh University and Worchester Polytechnic Institute (WPI) before joining the faculty of the University of Connecticut where he held the position of Chairman of the Civil Engineering Department and taught for twenty-six years. In 1991 Russ received the Outstanding Civil Engineer Award from the Connecticut Section of the American Society of Civil Engineers.

David holds a B.S. degree in ocean engineering and a M.S. degree in civil engineering from the Florida Institute of Technology, and a Ph.D. degree in civil engineering from the University of Connecticut. He was employed by General Dynamics Corporation Electric Boat Division for five years, where he provided submarine construction support and conducted engineering design and analysis associated with pressure hull and other structures. In addition, he conducted research in the area of noise and vibration transmission reduction in submarines. He then taught at Lafayette College for one year prior to joining the civil engineering faculty at the U.S. Coast Guard Academy, where he has been since 1990. David is currently a member of the American Railway Engineering & Maintenance-of-way Association Committee 15 (Steel Structures), and the American Society of Civil Engineers Committee on Blast, Shock, and Vibratory Effects. He has also worked with the Federal Railroad Administration on their bridge inspection training program. Professional interests include bridge engineering, railroad engineering, tall towers, structural forensics, and blast-resistant design. He is a licensed professional engineer in Connecticut and Pennsylvania.

Table of Contents

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

shop us with confidence

Summary

Continuing in the spirit of its successful previous editions, the ninth edition of Beer, Johnston, Mazurek, and Cornwell'sVector Mechanics for Engineersprovides conceptually accurate and thorough coverage together with a significant refreshment of the exercise sets and online delivery of homework problems to your students. Nearly forty percent of the problems in the text are changed from the previous edition.The Beer/Johnston textbooks introduced significant pedagogical innovations into engineering mechanics teaching. The consistent, accurate problem-solving methodology gives your students the best opportunity to learn statics and dynamics. At the same time, the careful presentation of content, unmatched levels of accuracy, and attention to detail have made these texts the standard for excellence.

Author Bio

Born in France and educated in France and Switzerland, Ferd held an M.S. degree from the Sorbonne and an Sc.D. degree in theoretical mechanics from the University of Geneva. He came to the United States after serving in the French army during the early part of World War II and had taught for four years at Williams College in the Williams-MIT joint arts and engineering program. Following his service at Williams College, Ferd joined the faculty of Lehigh University where he taught for thirty-seven years. He held several positions, including the University Distinguished Professors Chair and Chairman of the Mechanical Engineering and Mechanics Department, and in 1995 Ferd was awarded an honorary Doctor of Engineering degree by Lehigh University.

Born in Philadelphia, Russ holds a B.S. degree in civil engineering from the University of Delaware and an Sc.D. degree in the field of structural engineering from The Massachusetts Institute of Technology (MIT). He taught at Lehigh University and Worchester Polytechnic Institute (WPI) before joining the faculty of the University of Connecticut where he held the position of Chairman of the Civil Engineering Department and taught for twenty-six years. In 1991 Russ received the Outstanding Civil Engineer Award from the Connecticut Section of the American Society of Civil Engineers.

David holds a B.S. degree in ocean engineering and a M.S. degree in civil engineering from the Florida Institute of Technology, and a Ph.D. degree in civil engineering from the University of Connecticut. He was employed by General Dynamics Corporation Electric Boat Division for five years, where he provided submarine construction support and conducted engineering design and analysis associated with pressure hull and other structures. In addition, he conducted research in the area of noise and vibration transmission reduction in submarines. He then taught at Lafayette College for one year prior to joining the civil engineering faculty at the U.S. Coast Guard Academy, where he has been since 1990. David is currently a member of the American Railway Engineering & Maintenance-of-way Association Committee 15 (Steel Structures), and the American Society of Civil Engineers Committee on Blast, Shock, and Vibratory Effects. He has also worked with the Federal Railroad Administration on their bridge inspection training program. Professional interests include bridge engineering, railroad engineering, tall towers, structural forensics, and blast-resistant design. He is a licensed professional engineer in Connecticut and Pennsylvania.

Table of Contents

Table of Contents

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

Publisher Info

Publisher: McGraw-Hill Publishing Company

Published: 2010

International: No

Published: 2010

International: No

Born in Philadelphia, Russ holds a B.S. degree in civil engineering from the University of Delaware and an Sc.D. degree in the field of structural engineering from The Massachusetts Institute of Technology (MIT). He taught at Lehigh University and Worchester Polytechnic Institute (WPI) before joining the faculty of the University of Connecticut where he held the position of Chairman of the Civil Engineering Department and taught for twenty-six years. In 1991 Russ received the Outstanding Civil Engineer Award from the Connecticut Section of the American Society of Civil Engineers.

David holds a B.S. degree in ocean engineering and a M.S. degree in civil engineering from the Florida Institute of Technology, and a Ph.D. degree in civil engineering from the University of Connecticut. He was employed by General Dynamics Corporation Electric Boat Division for five years, where he provided submarine construction support and conducted engineering design and analysis associated with pressure hull and other structures. In addition, he conducted research in the area of noise and vibration transmission reduction in submarines. He then taught at Lafayette College for one year prior to joining the civil engineering faculty at the U.S. Coast Guard Academy, where he has been since 1990. David is currently a member of the American Railway Engineering & Maintenance-of-way Association Committee 15 (Steel Structures), and the American Society of Civil Engineers Committee on Blast, Shock, and Vibratory Effects. He has also worked with the Federal Railroad Administration on their bridge inspection training program. Professional interests include bridge engineering, railroad engineering, tall towers, structural forensics, and blast-resistant design. He is a licensed professional engineer in Connecticut and Pennsylvania.

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