###### 1 General Principles 3

**Chapter Objectives 3**

1.1 Mechanics 3

1.2 Fundamental Concepts 4

1.3 Units of Measurement 7

1.4 T he 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 C artesian 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 ForceScalar Formulation 117

4.2 Cross Product 121

4.3 Moment of a ForceVector 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

**7 Internal Forces 331**

**Chapter Objectives 331**

7.1 Internal Loadings Developed in Structural Members 331

7.2 Shear and Moment Equations and Diagrams 347

7.3 Relations between Distributed Load, Shear, and Moment 356

7.4 Cables 367

**8 Friction 389**

**Chapter Objectives 389**

8.1 Characteristics of Dry Friction 389

8.2 Problems Involving Dry Friction 394

8.3 Wedges 416

8.4 Frictional Forces on Screws 418

8.5 Frictional Forces on Flat Belts 425

8.6 Frictional Forces on Collar Bearings, Pivot Bearings, and Disks 433

8.7 Frictional Forces on Journal Bearings 436

8.8 Rolling Resistance 438

**9 Center of Gravity and Centroid 451**

**Chapter Objectives 451**

9.1 Center of Gravity, Center of Mass, and the Centroid of a Body 451

9.2 Composite Bodies 474

9.3 Theorems of Pappus and Guldinus 488

9.4 Resultant of a General Distributed Loading 497

9.5 Fluid Pressure 498

**10 Moments of Inertia 515**

**Chapter Objectives 515**

10.1 Definition of Moments of Inertia for Areas 515

10.2 Parallel-Axis Theorem for an Area 516

10.3 Radius of Gyration of an Area 517

10.4 Moments of Inertia for Composite Areas 526

10.5 Product of Inertia for an Area 534

10.6 Moments of Inertia for an Area about Inclined Axes 538

10.7 Mohrs Circle for Moments of Inertia 541

10.8 Mass Moment of Inertia 549

**11 Virtual Work 567**

**Chapter Objectives 567**

11.1 Definition of Work 567

11.2 Principle of Virtual Work 569

11.3 Principle of Virtual Work for a System of Connected Rigid Bodies 571

11.4 Conservative Forces 583

11.5 Potential Energy 584

11.6 Potential-Energy Criterion for Equilibrium 586

11.7 Stability of Equilibrium Configuration 587 Appendix