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 30
2.5 Cartesian Vectors 38
2.6 Addition of Cartesian Vectors 41
2.7 Position Vectors 50
2.8 Force Vector Directed Along a Line 53
2.9 Dot Product 60

3 Force System Resultants 75
Chapter Objectives 75
3.1 Moment of a Force–Scalar Formulation 75
3.2 Cross Product 79
3.3 Moment of a Force–Vector Formulation 82
3.4 Principle of Moments 86
3.5 Moment of a Force about a Specified Axis 96
3.6 Moment of a Couple 103
3.7 Simplification of a Force and Couple System 112
3.8 Further Simplification of a Force and Couple System 122

4 Equilibrium of a Rigid Body 139
Chapter Objectives 139
4.1 Conditions for Rigid-Body Equilibrium 139
4.2 Free-Body Diagrams 141
4.3 Equations of Equilibrium 151
4.4 Two- and Three-Force Members 157
4.5 Free-Body Diagrams 167
4.6 Equations of Equilibrium 172
4.7 Characteristics of Dry Friction 180
4.8 Problems Involving Dry Friction 184
4.9 Frictional Forces on Flat Belts 197
4.10 Frictional Forces on Screws 200

5 Structural Analysis 215
Chapter Objectives 215
5.1 Simple Trusses 215
5.2 The Method of Joints 218
5.3 Zero-Force Members 224
5.4 The Method of Sections 231
5.5 Frames and Machines 240

6 Center of Gravity, Centroid, and Moment of Inertia 261
Chapter Objectives 261
6.1 Center of Gravity, Center of Mass, and the Centroid of a Body 261
6.2 Composite Bodies 273
6.3 Resultant of a Distributed Loading 281
6.4 Moments of Inertia for Areas 290
6.5 Parallel-Axis Theorem for an Area 291
6.6 Moments of Inertia for Composite Areas 298

7 Stress and Strain 309
Chapter Objectives 309
7.1 Introduction 309
7.2 Internal Resultant Loadings 310
7.3 Stress 322
7.4 Average Normal Stress in an Axially Loaded Bar 324
7.5 Average Shear Stress 331
7.6 Allowable Stress 342
7.7 Design of Simple Connections 343
7.8 Deformation 355
7.9 Strain 356

Mechanics of Materials

8 Mechanical Properties of Materials 373
Chapter Objectives 373
8.1 The Tension and Compression Test 373
8.2 The Stress—Strain Diagram 375
8.3 Stress—Strain Behavior of Ductile and Brittle Materials 379
8.4 Hooke’s Law 382
8.5 Strain Energy 384
8.6 Poisson’s Ratio 392
8.7 The Shear Stress—Strain Diagram 394

9 Axial Load 405
Chapter Objectives 405
9.1 Saint-Venant’s Principle 405
9.2 Elastic Deformation of an Axially Loaded Member 408
9.3 Principle of Superposition 421
9.4 Statically Indeterminate Axially Loaded Member 422
9.5 The Force Method of Analysis for Axially Loaded Members 428
9.6 Thermal Stress 434
9.7 Stress Concentrations 440

10 Torsion 451
Chapter Objectives 451
10.1 Torsional Deformation of a Circular Shaft 451
10.2 The Torsion Formula 454
10.3 Power Transmission 461
10.4 Angle of Twist 468
10.5 Statically Indeterminate Torque-Loaded Members 481
*10.6 Solid Noncircular Shafts 488
10.7 Stress Concentration 492

11 Bending 501
Chapter Objectives 501
11.1 Shear and Moment Diagrams 501
11.2 Graphical Method for Constructing Shear and Moment Diagrams 508
11.3 Bending Deformation of a Straight Member 525
11.4 The Flexure Formula 529
11.5 Unsymmetric Bending 542
11.6 Stress Concentrations 550

12 Transverse Shear 559
Chapter Objectives 559
12.1 Shear in Straight Members 559
12.2 The Shear Formula 561
12.3 Shear Flow in Built-Up Members 578

13 Combined Loadings 591
Chapter Objectives 591
13.1 Thin-Walled Pressure Vessels 591
13.2 State of Stress Caused by Combined
Loadings 598

14 Stress and Strain Transformation 619
Chapter Objectives 619
14.1 Plane-Stress Transformation 619
14.2 General Equations of Plane-Stress
Transformation 624
14.3 Principal Stresses and Maximum In-Plane
Shear Stress 627
14.4 Mohr’s Circle–Plane Stress 639
14.5 Absolute Maximum Shear Stress 650
14.6 Plane Strain 657
14.7 General Equations of Plane-Strain Transformation 658
*14.8 Mohr’s Circle–Plane Strain 666
14.9 Strain Rosettes 674
14.10 Material-Property Relationships 676

15 Design of Beams and Shafts 693
Chapter Objectives 693
15.1 Basis for Beam Design 693
15.2 Prismatic Beam Design 696
*15.3 Fully Stressed Beams 710

16 Deflection of Beams and Shafts 717
Chapter Objectives 717
16.1 The Elastic Curve 717
16.2 Slope and Displacement by Integration 721
*16.3 Discontinuity Functions 735
16.4 Method of Superposition 745
16.5 Statically Indeterminate Beams and Shafts—Method of Superposition 752

17 Buckling of Columns 769
Chapter Objectives 769
17.1 Critical Load 769
17.2 Ideal Column with Pin Supports 772
17.3 Columns Having Various Types of Supports 778
*17.4 The Secant Formula 788
*17.5 Inelastic Buckling 794

Appendices
A. Mathematical Review and Expressions 804
B. Geometric Properties of An Area and Volume 808
C. Geometric Properties of Wide-Flange Sections 810
D. Slopes and Deflections of Beams 814
Fundamental Problems Partial Solutions and Answers 816
Answers to Selected Problems 844
Index 871

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