Part I Section-by-Section, Chapter-by-Chapter Summaries

with Review Questions and Answers 1

1 General Principles 3

Main Goals of this Chapter 3

1.1 Mechanics 3

1.2 Fundamental Concepts 3

1.3 Units of Measurement 4

1.4 The International System of Units 6

1.5 Numerical Calculations 6

1.6 General Procedure for Analysis 6

Helpful Tips and Suggestions 7

Review Questions 7

2 Force Vectors 8

Main Goals of this Chapter 8

2.1 Scalars and Vectors 8

2.2 Vector Operations 8

2.3 Vector Addition of Forces 10

2.4 Addition of a System of Coplanar Forces 10

2.5 Cartesian Vectors 11

2.6 Addition and Subtraction of Cartesian Vectors 12

2.7 Position Vectors 12

2.8 Force Vector Directed Along a Line 13

2.9 Dot Product 13

Helpful Tips and Suggestions 13

Review Questions 14

3 Equilibrium of a Particle 15

Main Goals of this Chapter 15

3.1 Condition for the Equilibrium of a Particle 15

3.2 The Free-Body Diagram 15

3.3 Coplanar Force Systems 16

3.4 Three-Dimensional Force Systems 16

Helpful Tips and Suggestions 17

Review Questions 17

4 Force System Resultants 18

Main Goals of this Chapter 18

4.1 Moment of a Force–Scalar Formulation 18

4.2 Cross Product 19

4.3 Moment of a Force–Vector Formulation 20

4.4 Principle of Moments 21

4.5 Moment of a Force About a Specified Axis 21

4.6 Moment of a Couple 22

4.7 Simplification of a Force and Couple System 22

4.8 Further Simplification of a Force and Couple System 24

4.9 Reduction of a Simple Distributed Loading 24

Helpful Tips and Suggestions 24

Review Questions 24

5 Equilibrium of a Rigid Body 26

Main Goals of this Chapter 26

5.1 Conditions for Rigid-Body Equilibrium 26

5.2 Free-Body Diagrams 26

5.3 Equations of Equilibrium 27

5.4 Two- and Three- Force Members 28

5.5 Free-Body Diagrams 28

5.6 Equations of Equilibrium 29

5.7 Constraints and Statical Determinacy 29

Helpful Tips and Suggestions 29

Review Questions 30

6 Structural Analysis 31

Main Goals of this Chapter 31

6.1 Simple Trusses 31

6.2 The Method of Joints 32

6.3 Zero Force Members 32

6.4 The Method of Sections 32

6.5 Space Trusses 33

6.6 Frames and Machines 34

Helpful Tips and Suggestions 34

Review Questions 35

7 Internal Forces 36

Main Goals of this Chapter 36

7.1 Internal Forces Developed in Structural Members 36

7.2 Shear and Moment Equations and Diagrams 37

7.3 Relations Between Distributed Load, Shear and Moment 39

7.4 Cables 39

Helpful Tips and Suggestions 40

Review Questions 41

8 Friction 42

Main Goals of this Chapter 42

8.1 Characteristics of Dry Friction 42

8.2 Problems Involving Dry Friction 43

8.3 Wedges 43

8.4 Frictional Forces on Screws 44

8.5 Frictional Forces on Flat Belts 45

8.6 Frictional Forces on Collar Bearings, Pivot Bearings, and Disks 46

8.7 Frictional Forces on Journal Bearings 47

8.8 Rolling Resistance 47

Helpful Tips and Suggestions 48

Review Questions 48

9 Center of Gravity and Centroid 49

Main Goals of this Chapter 49

9.1 Center of Gravity, Center of Mass and the Centroid of a Body 49

9.2 Composite Bodies 50

9.3 Theorems of Papus and Guldinus 51

9.4 Resultant of a General Distributed Loading 51

9.5 Fluid Pressure 52

Helpful Tips and Suggestions 53

Review Questions 53

10 Moments of Inertia 54

Main Goals of this Chapter 54

10.1 Definition of Moments of Inertia for Areas 54

10.2 Parallel Axis Theorem for an Area 55

10.3 Radius of Gyration of an Area 55

10.4 Moments of Inertia for Composite Areas 56

10.5 Product of Inertia for an Area 56

10.6 Moments of Inertia for an Area About Inclined Axes 57

10.7 Mohr’s Circle for Moments of Inertia 58

10.8 Mass Moment of Inertia 59

Helpful Tips and Suggestions 60

Review Questions 60

11 Virtual Work 61

Main Goals of this Chapter 61

11.1 Definition of Work and Virtual Work 61

11.2 Principle of VirtualWork for a Particle and a Rigid Body 62

11.3 Principle of VirtualWork for a System of Connected Rigid Bodies 62

11.4 Conservative Forces 64

11.5 Potential Energy 64

11.6 Potential Energy Criterion for Equilibrium 64

11.7 Stability of Equilibrium 65

Procedure for Solving Problems 66

Review Questions 66

ANSWERS TO REVIEW QUESTIONS 67

Part II Free-Body Diagram Workbook 71

1 Basic Concepts in Statics 73

1.1 Equilibrium 73

2 Free-Body Diagrams: the Basics 75

2.1 Free-Body Diagram: Particle 75

2.2 Free-Body Diagram: Rigid Body 78

3 Problems 83

3.1 Free-Body Diagrams in Particle Equilibrium 85

3.2 Free-Body Diagrams in the Equilibrium of a Rigid Body 115

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