Engineering Mechanics, livre ebook

Engineering mechanics provides the theories and methods of describing and predicting the state of equilibrium or accelerated motion of particles or rigid bodies under the action of forces. It consists of three parts: statics (chapters 1–5), kinematics (chapters 6 and 7) and kinetics (chapters 8–10) and it is basically corresponding to the course of “theoretical mechanics” in China. It is hoped that this book will help to develop in engineering students the correct understanding of the principles of mechanics and the ability to analyze and solve engineering problems using the principles. This book can be used as a teaching material for civil engineering, hydraulic engineering, mechanical engineering, aerospace, transportation and other engineering majors in colleges and universities, and as a self-study book for relevant technical personnel.

Foreword................................................... III

CHAPTER 1

Introduction................................................. 1

1.1Mechanics .............................................. 1

1.2Fundamental Concepts and Principles ......................... 2

1.2.1Fundamental Concepts ............................... 2

1.2.2Newton’s Laws of Motion ............................. 3

1.2.3Newton’s Law of Gravitational Attraction ................ 3

1.3 Units of Measurement ..................................... 4

1.4Procedure of Problem Solving ............................... 6

CHAPTER 2

Vectors and Vector Operations ................................... 11

2.1 Vectors and the Parallelogram Law ........................... 11

2.2Cartesian Vectors ........................................ 14

2.2.1Cartesian Vector Representation ....................... 16

2.2.2Addition and Subtraction of Cartesian Vectors............. 19

2.3 Vector Directed Along a Line ............................... 21

2.4 Dot Product and Cross Product ............................. 24

2.4.1Cartesian Vector Formulation of the Dot Product .......... 25

2.4.2Applications of the Dot Product........................ 26

2.4.3Cartesian Vector Formulation of the Cross Product ......... 29

CHAPTER 3

Simplificationof Force Systems................................... 37

3.1 Momentof a Force about a Point ............................ 37

3.1.1Vector Formulation ................................. 38

3.1.2Principle of Moments ................................ 43

3.1.3Scalar Formulation .................................. 43

3.2 Momentof a Force about a Specified Axis ..................... 47

3.3 Momentof a Couple ...................................... 52

3.3.1Vector Formulation ................................. 52

3.3.2Scalar Formulation .................................. 54

3.4Simplification of a System of Forces and Couples ................ 58

3.4.1Equivalent System .................................. 58

3.4.2Reduction to One Force and One Couple ................. 59

3.4.3Further Simplification ............................... 63

3.5Application of Simplification of Parallel Forces .................. 70

3.5.1Center of Gravity, Center of Mass, and Centroid of a Body ... 70

3.5.2Center of Gravity, Center of Mass, and Centroid of Composite Bodies........................................... 78

3.5.3Reduction in Distributed Loading ...................... 82

CHAPTER 4

Equilibriumof Rigid Bodies ..................................... 105

4.1Conditions for Rigid-Body Equilibrium ........................ 105

4.2Free-Body Diagrams ...................................... 109

4.2.1Support Reactions .................................. 109

4.2.2Procedure of Drawing a Free-Body Diagram ............... 114

4.3Equilibrium Problems of a Rigid Body ........................ 120

4.4 Two-and Three-Force Members ............................. 127

4.5 Constrains and Statical Determinacy ......................... 129

4.6Equilibrium Problems of Structures........................... 132

4.7 SimpleTrusses .......................................... 142

4.7.1 The Method of Joints................................ 143

4.7.2Zero-Force Members ................................. 148

4.7.3 The Method of Sections .............................. 149

CHAPTER 5

Friction.................................................... 171

5.1Characteristics of Friction .................................. 171

5.1.1 Laws of Sliding Friction .............................. 172

5.1.2Angles of Friction and Self-Locking ..................... 174

5.2Problems Involving Sliding Friction ........................... 175

5.3 Rolling Resistance ........................................ 182

CHAPTER 6

Kinematics of Particles ......................................... 193

6.1 General Curvilinear Motion................................. 194

6.2Curvilinear Motion: Rectangular Components ................... 196

6.3Curvilinear Motion: Tangential and Normal Components .......... 203

6.3.1 Thet-n-b Coordinate System .......................... 204

6.3.2Velocity .......................................... 205

6.3.3Acceleration ....................................... 205

6.4Absolute Dependent Motion Analysis of Particles ................ 212

6.5Relative-Motion Analysis Using Translating Axes ................ 218

CHAPTER 7

Planar Kinematics of Rigid Bodies ................................ 233

7.1Translation ............................................. 235

7.2Rotation about a Fixed Axis................................ 237

7.2.1Angular Motion .................................... 237

7.2.2Motion of a Particle on a Rotating Body ................. 239

7.3Absolute Dependent Motion Analysis of Bodies.................. 249

7.4 General Plane Motion ..................................... 251

7.4.1Relative-Motion Analysis: Velocity and Acceleration......... 253

7.4.2Instantaneous Center of Rotation ....................... 265

CHAPTER 8

Kinetics:Equations of Motion.................................... 289

8.1Newton’s Second Law of Motion ............................. 289

8.2Equation of Motion for a Particle ............................ 290

8.3Equation of Motion for a System of Particles ................... 303

8.4 Mass Moment of Inertia ................................... 305

8.4.1Parallel-Axis Theorem and Radius of Gyration ............. 309

8.4.2 Mass Moment of Inertia of Composite Bodies .............. 311

8.5 Planar Kinetic Equations of Motion .......................... 314

8.5.1Equations of Motion for Translation ..................... 319

8.5.2Equations of Motion for Rotation about a Fixed Axis ....... 324

8.5.3Equations of Motion for General Plane Motion ............. 329

CHAPTER 9

Kinetics:Work and Energy ...................................... 351

9.1 Workand Power ......................................... 351

9.1.1 Work............................................ 351

9.1.2 Power........................................... 362

9.2 KineticEnergy .......................................... 364

9.2.1Kinetic Energy of a Particle ........................... 364

9.2.2Kinetic Energy of a System of Particles .................. 365

9.2.3Kinetic Energy of a Rigid Body in Planar Motion .......... 366

9.3Principle of Work and Energy ............................... 370

9.3.1Principle of Work and Energy for a Particle ............... 370

9.3.2Principle of Work and Energy for a System of Particles ...... 375

9.4Conservative Forces and Conservation of Energy ................. 385

9.4.1Conservative Forces ................................. 385

9.4.2Potential Energy ................................... 387

9.4.3Principle of Conservation of Energy ..................... 388

CHAPTER 10

Kinetics:Impulse and Momentum ................................. 409

10.1Principle of Linear Impulse and Momentum for a Particle ......... 409

10.1.1Linear Momentum and Linear Impulse ................. 409

10.1.2Principle of Linear Impulse and Momentum ............. 411

10.2Principle of Angular Impulse and Momentum for a Particle ........ 417

10.2.1Angular Momentum ............................... 417

10.2.2Principle of Angular Impulse and Momentum ............ 418

10.3Principle of Impulse and Momentum for a System of Particles...... 421

10.3.1Linear Momentum of a System of Particles .............. 423

10.3.2Angular Momentum of a System of Particles ............. 423

10.3.3Angular Momentum of Rigid Bodies in Planar Motion ..... 426

10.3.4Principle of Impulse and Momentum for Rigid Bodies in Planar Motion ..........430

10.4Principle of Conservation of Momentum ...................... 441

Answers.................................................... 455

References.................................................. 465