Engineering Mechanics: Statics Modeling and Analyzing Systems in Equilibrium

by Sheppard, Sheri D.; Anagnos, Thalia; Billington, Sarah L.

• ISBN13: 9781119725138
• ISBN10: 1119725135
• eBook ISBN(s): 9781119321996
• Edition: 1st
• Format: Loose-leaf
• Copyright: 2020-09-23
• Publisher: Wiley
• More Book Details

Summary

Mechanics courses tend to provide engineering students with a precise, mathematical, but less than engaging experience. Students often view the traditional approach as a mysterious body of facts and “tricks” that allow idealized cases to be solved. When confronted with more realistic systems, they are often at a loss as to how to proceed. To address this issue, this course empowers students to tackle meaningful problems at an early stage in their studies.

Engineering Mechanics: Statics, First Edition begins with a readable overview of the concepts of mechanics. Important equations are introduced, but the emphasis is on developing a “feel” for forces and moments, and for how loads are transferred through structures and machines. From that foundation, the course helps lay a motivational framework for students to build their skills in solving engineering problems.

Author Biography

Sheri D. Sheppard, Ph.D., is the Carnegie Foundation for the Advancement of Teaching Senior Scholar principally responsible for the Preparations for the Professions Program (PPP) engineering study. She is an Associate Professor of Mechanical Engineering at Stanford University. She received her Ph.D. from the University of Michigan in 1985. Besides teaching both undergraduate and graduate design-related classes at Stanford University, she conducts research on weld fatigue and impact failures, fracture mechanics, and applied finite element analysis.
Dr. Sheppard was recently named co-principal investigator on a NSF grant to form the Center for the Advancement of Engineering Education (CAEE), along with faculty at the University of Washington, Colorado School of Mines, and Howard University. She was co-principal investigator with Professor Larry Leifer on a multi-university NSF grant that was critically looking at engineering undergraduate curriculum (Synthesis). In 1999, Sheri was named a fellow of the American Society of Mechanical Engineering (ASME) and the American Association for the Advancement of Science (AAAS). Recently Sheri was awarded the 20 04 ASEE Chester F. Carlson Award in recognition of distinguished accomplishments in engineering education. Before coming to Stanford University, she held several positions in the automotive industry, including senior research engineering at Ford Motor Company's Scientific Research Lab. She also worked as a design consultant, providing companies with structural analysis expertise.

Thalia Anagnos, Ph.D., is the Associate Vice President for Graduate and Undergraduate Programs at San Jose State University. She has taught graduate and undergraduate courses in mechanics, structural analysis nd design, probability and reliability, and technical writing. She earned her Ph.D. from Stanford University and has focused much of her research on seismic hazard mitigation. Most recently she was involved in a multi-university study of older nonductile concrete buildings that are vulnerable to collapse in earthquakes. She is the Past-President of the Earthquake Engineering Research Institute (EERI) and served as the co-Leader of Education, Outreach, and Training for the Network for Earthquake Engineering Simulation from 2009 to 2014. She was named as San Jose State's Outstanding Professor in 2011 and received the College of Engineering Applied Materials Award for Excellence in Teaching in 2013.

Sarah L. Billington, Ph.D., is professor of Civil & Environmental Engineering at Stanford University where she is a Senior Fellow at the Woods Institute for the Environment and the Milligan Family University Fellow in Undergraduate Education. She teaches undergraduate and graduate design, as well as analysis and materials related classes, and her research focuses on durable and sustainable materials for the built environment. Sarah served as Associate Chair of her Department from 2009-2015. She is a Fellow of the American Concrete Institute and has served on the Board of Directors for the Network for Earthquake Engineering Simulation (NEES Inc., 2006-2009) and the Structural Engineers Association of Northern California (SEAONC, 2012-2014). Prior to joining Stanford's faculty she was Assistant Professor of Civil & Environmental Engineering at Cornell University from 1997 to 2002. She completed her M.S. and Ph.D. at The University of Texas at Austin and her undergraduate degree was from Princeton University.

Table of Contents

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

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 _, 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