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Chapter 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
1.4 Coordinate Systems and Vectors 8
1.5 Drawing 11
1.6 Problem Solving 14
1.7 A Map of This Text 18
1.8 Just the Facts 20
Chapter 2 Forces 23
2.1 What are Forces? An Overview 24
2.2 Gravitational Forces 25
Example 2.2.1 Gravity, Weight, and Mass 28
Example 2.2.2 Is Assuming Gravity is a Constant Reasonable? 30
Example 2.2.3 Gravitational Force from Two Planets 31
2.3 Contact Forces 32
Example 2.3.1 Identifying Types of Forces 36
2.4 Identifying Forces for Analysis 37
Example 2.4.1 Defining a System for Analysis 40
2.5 Representing Force Vectors 42
Example 2.5.1 Rectangular Components of a Nonplanar Force Given its Line of Action 46
Example 2.5.2 Representing Nonplanar Forces with Rectangular Coordinates 47
Example 2.5.3 Representing a Planar Force in Skewed Coordinate System 49
Example 2.5.4 Representing Direction of a Planar Force 54
Example 2.5.5 Scalar Components of a Planar Force 55
Example 2.5.6 Representing a Planar Force with Spherical Coordinates 58
Example 2.5.7 Representing Nonplanar Forces with Spherical Angles 59
2.6 Resultant Force—Vector Addition 60
Example 2.6.1 Component Addition: Planar 63
Example 2.6.2 Component Addition: Nonplanar 64
Example 2.6.3 Graphical Addition Using Force Triangle 67
Example 2.6.4 Graphical Addition Using Parallelogram Law 69
Example 2.6.5 Resultant of Two Forces Using a Trigonometric Approach 71
Example 2.6.6 Analyzing a System: Trigonometric Addition 73
Example 2.6.7 Analyzing a System: Trigonometric Approach 74
2.7 Angle Between Two Forces— the Dot Product 75
Example 2.7.1 Projection of a Vector in Two Dimensions 78
Example 2.7.2 Projection of a Vector in Three Dimensions 79
Example 2.7.3 Angle Between Two Vectors 80
2.8 Just the Facts 82
Chapter 3 Moments 87
3.1 What are Moments? 88
Example 3.1.1 Specifying the Position Vector - Planar 95
Example 3.1.2 Specifying the Position Vector - Nonplanar 96
Example 3.1.3 The Magnitude of a Moment - Planar 97
Example 3.1.4 The Magnitude of a Moment - Nonplanar 98
Example 3.1.5 Moment Center on the Line of Action of Force 100
3.2 Mathematical Representation of a Moment 101
Example 3.2.1 Calculating the Moment About the z Axis with a Vector-Based Approach 105
Example 3.2.2 Calculating the Moment About the z Axis with the Component of the Force Perpendicular to the Position Vector 106
Example 3.2.3 Calculating the Moment - Nonplanar 107
Example 3.2.4 Calculating the Magnitude and Direction of a Moment - Nonplanar 109
Example 3.2.5 Finding the Force to Create a Moment - Nonplanar 110
3.3 Finding Moment Components in a Particular Direction 111
Example 3.3.1 Finding the Moment About the z Axis 113
Example 3.3.2 Finding the Moment in a Particular Direction 114
3.4 When are Two Forces Equal to a Moment? (When They are a Couple) 115
Example 3.4.1 A Couple in the xy Plane 117
Example 3.4.2 Working with Couples 118
3.5 Equivalent Loads 120
Example 3.5.1 Equivalent Moment and Equivalent Force - Planar 122
Example 3.5.2 Equivalent Moment and Equivalent Force - Nonplanar 124
Example 3.5.3 Equivalent Load for an Applied Couple 126
3.6 Just the Facts 127
Chapter 4 Modeling Systems with Free-Body Diagrams 131
4.1 Types of External Loads Acting on Systems 132
4.2 Planar System Supports 134
Example 4.2.1 Free-Body Diagram of a Planar System 140
Example 4.2.2 Free-Body Diagram of a Planar System with Moment 141
Example 4.2.3 Using Questions to Determine Loads at Supports 142
4.3 Nonplanar System Supports 143
Example 4.3.1 Exploring Single and Double Bearings and Hinges 149
4.4 Modeling Systems as Planar or Nonplanar 150
Example 4.4.1 Identifying Planar and Nonplanar Systems 152
Example 4.4.2 Identifying Planar and Nonplanar Systems with a Plane of Symmetry 153
4.5 A Step-By-Step Approach to Free-Body Diagrams 154
Example 4.5.1 Creating a Free-Body Diagram of an Airplane Wing 156
Example 4.5.2 Creating a Free-Body Diagram of a Ladder 157
Example 4.5.3 Creating a Free-Body Diagram of a Nonplanar System 157
Example 4.5.4 Creating a Free-Body Diagram of a Leaning Person 158
4.6 Just the Facts 159
Chapter 5 Mechanical Equilibrium 161
5.1 Conditions of Mechanical Equilibrium 162
5.2 The Equilibrium Equations 163
Example 5.2.1 Using a Free-Body Diagram to Write Equilibrium Equations 165
5.3 Applying the Planar Equilibrium Equations 166
Example 5.3.1 Applying the Analysis Procedure to a Planar Equilibrium Problem 169
Example 5.3.2 Analysis of a Simple Structure 171
Example 5.3.3 Analysis of a Planar Truss 172
5.4 Equilibrium Applied to Four Special Cases 173
Example 5.4.1 Analyzing a Planar Truss Connection as a Particle 174
Example 5.4.2 Two-Force Member Analysis 177
Example 5.4.3 Climbing Cam Analysis 180
Example 5.4.4 Three-Force Member Analysis 182
Example 5.4.5 Ideal Pulley Analysis 185
5.5 Applying the Nonplanar Equilibrium Equations 187
Example 5.5.1 Analysis of a Nonplanar System with Simple Loading 189
Example 5.5.2 Analysis of a Nonplanar System with Complex Loading 192
Example 5.5.3 High-Wire Circus Act 194
Example 5.5.4 Analysis of a Nonplanar System with Unknowns Other than Loads 196
5.6 Zooming in on Subsystems 198
Example 5.6.1 Analysis of a Toggle Clamp 199
Example 5.6.2 Analysis of a Pulley System 202
5.7 Determinate, Indeterminate, and Underconstrained Systems 204
Example 5.7.1 Identify Status of a Structure 206
5.8 Just the Facts 207
Chapter 6 Distributed Force 211
6.1 Center of Mass, Center of Gravity, and the Centroid 212
Example 6.1.1 Centroid of a Volume 219
Example 6.1.2 Center of Mass with Variable Density 220
Example 6.1.3 Locating the Centroid of a Composite Volume 221
Example 6.1.4 Finding the Centroid of An Area 223
Example 6.1.5 Center of Mass of a Composite Assembly 225
Example 6.1.6 Centroid of a Built-Up Section 227
6.2 Distributed Force Acting on a Boundary 228
Example 6.2.1 Using Integration to Find Total Force 235
Example 6.2.2 Inclined Beam with Nonuniform Distribution 237
Example 6.2.3 Beam Subjected to Polynomial Load Distribution 239
Example 6.2.4 Using Properties of Standard Shapes to Find Total Force 241
Example 6.2.5 Centroid of Distribution Composed of Standard Line Loads 243
Example 6.2.6 Calculating Center of Pressure of a Pressure Distribution 244
Example 6.2.7 Pressure on a Rectangular Water Gate 245
6.3 Hydrostatic Pressure 247
Example 6.3.1 Proof of Nondirectionality of Fluid Pressure 250
Example 6.3.2 Proof that Hydrostatic Pressure Increases Linearly with Depth 251
Example 6.3.3 Hydrostatic Pressure on Vertical Reservoir Gate 252
Example 6.3.4 Hydrostatic Pressure on Sloped Gate 253
Example 6.3.5 Pressure Distribution Over a Curved Surface 255
Example 6.3.6 Center of Buoyancy and Stability 257
6.4 Area Moment of Inertia 258
Example 6.4.1 Moment of Inertia Using Integration 262
Example 6.4.2 Moment of Inertia Using Parallel Axis Theorem 263
Example 6.4.3 Moment of Inertia of a Composite Area 264
6.5 Just the Facts 265
Chapter 7 Dry Friction and Rolling Resistance 271
7.1 Coulomb Friction Model 272
Example 7.1.1 Dry Friction - Sliding or Tipping 275
7.2 Friction in Static Analysis: Wedges, Belts, and Journal Bearings 276
Example 7.2.1 Analysis of a Pulley System with Bearing Friction 281
7.3 Rolling Resistance 283
Example 7.3.1 Rolling Resistance 284
7.4 Just the Facts 285
Chapter 8 Member Loads in Trusses 289
8.1 Defining a Truss 290
8.2 Truss Analysis by Method of Joints 293
Example 8.2.1 Truss Analysis Using Method of Joints 296
8.3 Truss Analysis by Method of Sections 298
Example 8.3.1 Method of Sections and Wise Selection of Moment Center Location 300
Example 8.3.2 Method of Sections and Where to Cut 301
Example 8.3.3 Combining Method of Joints and Method of Sections 303
8.4 Identifying Zero-Force Members 305
Example 8.4.1 Identifying Zero-Force Members 306
8.5 Determinate, Indeterminate, and Unstable Trusses 308
Example 8.5.1 Checking the Status of Planar Trusses 310
Example 8.5.2 Checking the Status of Space Trusses 312
8.6 Just the Facts 313
Chapter 9 Member Loads in Frames and Machines 315
9.1 Defining and Analyzing Frames 316
Example 9.1.1 Identify Systems as Trusses or Frames 317
Example 9.1.2 Planar Frame Analysis 319
Example 9.1.3 Finding Loads at Frame Supports 321
Example 9.1.4 Analysis of Frame with Friction 323
Example 9.1.5 Nonplanar Frame Analysis 324
9.2 Defining and Analyzing Machines 326
Example 9.2.1 Analysis of a Bicycle Brake 327
Example 9.2.2 Analysis of a Toggle Clamp 329
Example 9.2.3 Analysis of a Frictionless Gear Train 331
Example 9.2.4 Analysis of a Gear Train with Friction 333
9.3 Determinacy and Stability in Frames 335
Example 9.3.1 Determining Status of a Frame 338
9.4 Just the Facts 339
Chapter 10 Internal Loads in Beams 341
10.1 Defining Beams and Recognizing Beam Configurations 342
Example 10.1.1 Beam Identification 345
Example 10.1.2 Determine Loads Acting on a Beam 346
10.2 Beam Internal Loads 347
Example 10.2.1 Internal Loads in a Planar Simply Supported Beam 351
Example 10.2.2 Internal Loads in a Planar Cantilever Beam 353
Example 10.2.3 Internal Loads in a Nonplanar Beam 354
10.3 Axial Force, Shear Force, and Bending Moment Diagrams 356
Example 10.3.1 Shear, Moment, and Axial Force Diagram for a Simply Supported Beam 359
Example 10.3.2 A Simple Beam with an Applied Moment 361
Example 10.3.3 Beam with Distributed Load 362
Example 10.3.4 Simply Supported Beam with an Overhang 364
10.4 Bending Moment Related to Shear Force and Normal Stress 365
Example 10.4.1 Using the Relationships Between ω, V, and M 368
Example 10.4.2 Calculating Beam Normal Stress 370
10.5 Just the Facts 371
Chapter 11 Internal Loads in Cables 373
11.1 Cables with Point Loads 374
Example 11.1.1 Flexible Cable with Concentrated Loads 375
11.2 Cables with Distributed Loads 377
Example 11.2.1 Catenary Curve with Supports at Same Height 381
Example 11.2.2 Catenary with Supports at Different Elevations 382
Example 11.2.3 Uniformly Loaded Cable with Supports at Same Height 384
Example 11.2.4 Uniformly Loaded Cable with Supports at Unequal Heights 385
Example 11.2.5 Catenary Versus Parabolic 387
11.3 Just the Facts 388
Appendix A Selected Topics in Mathematics 393
Appendix B Physical Quantities 397
Appendix C Properties of Areas and Volumes 401
Appendix D Case Study: The Bicycle 407
Appendix E Case Study: The Golden Gate Bridge 419
Index 433
