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Book SynopsisTable of ContentsChapter 1 Principles and Tools For Static Analysis 1
1.1 How Does Engineering Analysis Fit Into Engineering Practice? 2
1.2 Physics Principles: Newton’s Laws Reviewed 4
1.3 Properties and Units in Engineering Analysis 5
Exercises 1.3 8
1.4 Coordinate Systems and Vectors 9
Exercises 1.4 12
1.5 Drawing 12
Exercises 1.5 15
1.6 Problem Solving 16
Exercises 1.6 20
1.7 A Map of This Text 21
1.8 Just the Facts 23
Chapter 2 Forces 25
2.1 What are Forces? An Overview 26
2.2 Gravitational Forces 27
Example 2.2.1 Gravity, Weight, and Mass 30
Example 2.2.2 Is Assuming Gravity is a Constant Reasonable? 32
Example 2.2.3 Gravitational Force from Two Planets 33
Exercises 2.2 34
2.3 Contact Forces 34
Example 2.3.1 Identifying Types of Forces 38
Exercises 2.3 39
2.4 Identifying Forces for Analysis 40
Example 2.4.1 Defining a System for Analysis 43
Exercises 2.4 45
2.5 Representing Force Vectors 46
Example 2.5.1 Rectangular Components of a Nonplanar Force Given its Line of Action 51
Example 2.5.2 Representing Nonplanar Forces with Rectangular Coordinates 52
Example 2.5.3 Representing a Planar Force in Skewed Coordinate System 54
Example 2.5.4 Representing Direction of a Planar Force 59
Example 2.5.5 Scalar Components of a Planar Force 60
Example 2.5.6 Representing a Planar Force with Spherical Coordinates 63
Example 2.5.7 Representing Nonplanar Forces with Spherical Angles 64
Exercises 2.5 66
2.6 Resultant Force—Vector Addition 76
Example 2.6.1 Component Addition: Planar 79
Example 2.6.2 Component Addition: Nonplanar 80
Example 2.6.3 Graphical Addition Using Force Triangle 83
Example 2.6.4 Graphical Addition Using Parallelogram Law 85
Example 2.6.5 Resultant of Two Forces Using a Trigonometric Approach 87
Example 2.6.6 Analyzing a System: Trigonometric Addition 89
Example 2.6.7 Analyzing a System: Trigonometric Approach 90
Exercises 2.6 92
2.7 Angle Between Two Forces—the Dot Product 99
Example 2.7.1 Projection of a Vector in Two Dimensions 102
Example 2.7.2 Projection of a Vector in Three Dimensions 103
Example 2.7.3 Angle Between Two Vectors 104
Exercises 2.7 105
2.8 Just the Facts 108
System Analysis (SA) Exercises 112
Chapter 3 Moments 117
3.1 What are Moments? 118
Example 3.1.1 Specifying the Position Vector - Planar 125
Example 3.1.2 Specifying the Position Vector - Nonplanar 126
Example 3.1.3 The Magnitude of a Moment - Planar 127
Example 3.1.4 The Magnitude of a Moment - Nonplanar 128
Example 3.1.5 Moment Center on the Line of Action of Force 130
Exercises 3.1 131
3.2 Mathematical Representation of a Moment 135
Example 3.2.1 Calculating the Moment About the z Axis with a Vector-Based Approach 140
Example 3.2.2 Calculating the Moment About the z Axis with the Component of the Force Perpendicular to the Position Vector 141
Example 3.2.3 Calculating the Moment - Nonplanar 142
Example 3.2.4 Calculating the Magnitude and Direction of a Moment - Nonplanar 144
Example 3.2.5 Finding the Force to Create a Moment - Nonplanar 145
Exercises 3.2 146
3.3 Finding Moment Components in a Particular Direction 155
Example 3.3.1 Finding the Moment About the z Axis 157
Example 3.3.2 Finding the Moment in a Particular Direction 158
Exercises 3.3 159
3.4 When are Two Forces Equal to a Moment? (When They are a Couple) 162
Example 3.4.1 A Couple in the xy Plane 164
Example 3.4.2 Working with Couples 165
Exercises 3.4 167
3.5 Equivalent Loads 171
Example 3.5.1 Equivalent Moment and Equivalent Force - Planar 173
Example 3.5.2 Equivalent Moment and Equivalent Force - Nonplanar 175
Example 3.5.3 Equivalent Load for an Applied Couple 177
Exercises 3.5 178
3.6 Just the Facts 184
System Analysis (SA) Exercises 188
Chapter 4 Modeling Systems with Free-Body Diagrams 195
4.1 Types of External Loads Acting on Systems 196
Exercises 4.1 198
4.2 Planar System Supports 200
Example 4.2.1 Free-Body Diagram of a Planar System 206
Example 4.2.2 Free-Body Diagram of a Planar System with Moment 207
Example 4.2.3 Using Questions to Determine Loads at Supports 208
Exercises 4.2 210
4.3 Nonplanar System Supports 213
Example 4.3.1 Exploring Single and Double Bearings and Hinges 219
Exercises 4.3 221
4.4 Modeling Systems as Planar or Nonplanar 223
Example 4.4.1 Identifying Planar and Nonplanar Systems 225
Example 4.4.2 Identifying Planar and Nonplanar Systems with a Plane of Symmetry 226
Exercises 4.4 227
4.5 A Step-By-Step Approach to Free-Body Diagrams 230
Example 4.5.1 Creating a Free-Body Diagram of an Airplane Wing 232
Example 4.5.2 Creating a Free-Body Diagram of a Ladder 234
Example 4.5.3 Creating a Free-Body Diagram of a Nonplanar System 234
Example 4.5.4 Creating a Free-Body Diagram of a Leaning Person 235
Exercises 4.5 236
4.6 Just the Facts 243
System Analysis (SA) Exercises 244
Chapter 5 Mechanical Equilibrium 249
5.1 Conditions of Mechanical Equilibrium 250
Exercises 5.1 251
5.2 The Equilibrium Equations 252
Example 5.2.1 Using a Free-Body Diagram to Write Equilibrium Equations 254
Exercises 5.2 256
5.3 Applying the Planar Equilibrium Equations 257
Example 5.3.1 Applying the Analysis Procedure to a Planar Equilibrium Problem 260
Example 5.3.2 Analysis of a Simple Structure 262
Example 5.3.3 Analysis of a Planar Truss 263
Exercises 5.3 264
5.4 Equilibrium Applied to Four Special Cases 273
Example 5.4.1 Analyzing a Planar Truss Connection as a Particle 274
Exercises 5.4.1 276
Example 5.4.2 Two-Force Member Analysis 279
Exercises 5.4.2 281
Example 5.4.3 Climbing Cam Analysis 283
Example 5.4.4 Three-Force Member Analysis 285
Exercises 5.4.3 287
Example 5.4.5 Ideal Pulley Analysis 289
Exercises 5.4.4 291
5.5 Applying the Nonplanar Equilibrium Equations 293
Example 5.5.1 Analysis of a Nonplanar System with Simple Loading 295
Example 5.5.2 Analysis of a Nonplanar System with Complex Loading 298
Example 5.5.3 High-Wire Circus Act 300
Example 5.5.4 Analysis of a Nonplanar System with Unknowns Other than Loads 302
Exercises 5.5 304
5.6 Zooming in on Subsystems 312
Example 5.6.1 Analysis of a Toggle Clamp 313
Example 5.6.2 Analysis of a Pulley System 316
Exercises 5.6 318
5.7 Determinate, Indeterminate, and Underconstrained Systems 324
Example 5.7.1 Identify Status of a Structure 326
Exercises 5.7 327
5.8 Just the Facts 330
System Analysis (SA) Exercises 333
Chapter 6 Distributed Force 339
6.1 Center of Mass, Center of Gravity, and the Centroid 340
Example 6.1.1 Centroid of a Volume 347
Example 6.1.2 Center of Mass with Variable Density 348
Example 6.1.3 Locating the Centroid of a Composite Volume 349
Example 6.1.4 Finding the Centroid of An Area 351
Example 6.1.5 Center of Mass of a Composite Assembly 353
Example 6.1.6 Centroid of a Built-Up Section 355
Exercises 6.1 356
6.2 Distributed Force Acting on a Boundary 366
Example 6.2.1 Using Integration to Find Total Force 373
Example 6.2.2 Inclined Beam with Nonuniform Distribution 375
Example 6.2.3 Beam Subjected to Polynomial Load Distribution 377
Example 6.2.4 Using Properties of Standard Shapes to Find Total Force 379
Example 6.2.5 Centroid of Distribution Composed of Standard Line Loads 381
Example 6.2.6 Calculating Center of Pressure of a Pressure Distribution 382
Example 6.2.7 Pressure on a Rectangular Water Gate 383
Exercises 6.2 385
6.3 Hydrostatic Pressure 392
Example 6.3.1 Proof of Nondirectionality of Fluid Pressure 395
Example 6.3.2 Proof that Hydrostatic Pressure Increases Linearly with Depth 396
Example 6.3.3 Hydrostatic Pressure on Vertical Reservoir Gate 397
Example 6.3.4 Hydrostatic Pressure on Sloped Gate 398
Example 6.3.5 Pressure Distribution Over a Curved Surface 400
Example 6.3.6 Center of Buoyancy and Stability 402
Exercises 6.3 403
6.4 Area Moment of Inertia 409
Example 6.4.1 Moment of Inertia Using Integration 413
Example 6.4.2 Moment of Inertia Using Parallel Axis Theorem 414
Example 6.4.3 Moment of Inertia of a Composite Area 415
Exercises 6.4 416
6.5 Just the Facts 419
System Analysis (SA) Exercises 425
Chapter 7 Dry Friction and Rolling Resistance 431
7.1 Coulomb Friction Model 432
Example 7.1.1 Dry Friction - Sliding or Tipping 435
Exercises 7.1 436
7.2 Friction in Static Analysis: Wedges, Belts, and Journal Bearings 439
Example 7.2.1 Analysis of a Pulley System with Bearing Friction 444
Exercises 7.2 446
7.3 Rolling Resistance 452
Example 7.3.1 Rolling Resistance 453
Exercises 7.3 454
7.4 Just the Facts 456
Chapter 8 Member Loads In Trusses 459
8.1 Defining a Truss 460
8.2 Truss Analysis by Method of Joints 463
Example 8.2.1 Truss Analysis Using Method of Joints 466
Exercises 8.2 468
8.3 Truss Analysis by Method of Sections 473
Example 8.3.1 Method of Sections and Wise Selection of Moment Center Location 475
Example 8.3.2 Method of Sections and Where to Cut 476
Example 8.3.3 Combining Method of Joints and Method of Sections 478
Exercises 8.3 480
8.4 Identifying Zero-Force Members 484
Example 8.4.1 Identifying Zero-Force Members 486
Exercises 8.4 488
8.5 Determinate, Indeterminate, and Unstable Trusses 490
Example 8.5.1 Checking the Status of Planar Trusses 492
Example 8.5.2 Checking the Status of Space Trusses 493
Exercises 8.5 495
8.6 Just the Facts 496
System Analysis (SA) Exercises 498
Chapter 9 Member Loads In Frames And Machines 503
9.1 Defining and Analyzing Frames 504
Example 9.1.1 Identify Systems as Trusses or Frames 505
Example 9.1.2 Planar Frame Analysis 507
Example 9.1.3 Finding Loads at Frame Supports 509
Example 9.1.4 Analysis of Frame with Friction 511
Example 9.1.5 Nonplanar Frame Analysis 512
Exercises 9.1 514
9.2 Defining and Analyzing Machines 526
Example 9.2.1 Analysis of a Bicycle Brake 527
Example 9.2.2 Analysis of a Toggle Clamp 529
Example 9.2.3 Analysis of a Frictionless Gear Train 531
Example 9.2.4 Analysis of a Gear Train with Friction 533
Exercises 9.2 535
9.3 Determinacy and Stability in Frames 543
Example 9.3.1 Determining Status of a Frame 546
Exercises 9.3 547
9.4 Just the Facts 549
System Analysis (SA) Exercises 551
Chapter 10 Internal Loads In Beams 557
10.1 Defining Beams and Recognizing Beam Configurations 558
Example 10.1.1 Beam Identification 561
Example 10.1.2 Determine Loads Acting on a Beam 562
Exercises 10.1 564
10.2 Beam Internal Loads 566
Example 10.2.1 Internal Loads in a Planar Simply Supported Beam 569
Example 10.2.2 Internal Loads in a Planar Cantilever Beam 571
Example 10.2.3 Internal Loads in a Nonplanar Beam 572
Exercises 10.2 574
10.3 Axial Force, Shear Force, and Bending Moment Diagrams 578
Example 10.3.1 Shear, Moment, and Axial Force Diagram for a Simply Supported Beam 581
Example 10.3.2 A Simple Beam with an Applied Moment 583
Example 10.3.3 Beam with Distributed Load 584
Example 10.3.4 Simply Supported Beam with an Overhang 586
Exercises 10.3 588
10.4 Bending Moment Related to Shear Force and Normal Stress 594
Example 10.4.1 Using the Relationships Between ω, V, and M 596
Example 10.4.2 Calculating Beam Normal Stress 598
Exercises 10.4 599
10.5 Just the Facts 602
System Analysis (SA) Exercises 604
Chapter 11 Internal Loads in Cables 611
11.1 Cables with Point Loads 612
Example 11.1.1 Flexible Cable with Concentrated Loads 613
Exercises 11.1 615
11.2 Cables with Distributed Loads 616
Example 11.2.1 Catenary Curve with Supports at Same Height 621
Example 11.2.2 Catenary with Supports at Different Elevations 622
Example 11.2.3 Uniformly Loaded Cable with Supports at Same Height 624
Example 11.2.4 Uniformly Loaded Cable with Supports at Unequal Heights 625
Example 11.2.5 Catenary Versus Parabolic 627
Exercises 11.2 628
11.3 Just the Facts 632
System Analysis (SA) Exercises 637
Appendix A Selected Topics In Mathematics 641
Appendix B Physical Quantities 645
Appendix C Properties of Areas and Volumes 649
Appendix D Case Study: The Bicycle 655
Appendix E Case Study: The Golden Gate Bridge 671
Index 687
