IV. A Picture Is Worth a Thousand Words (Or At Least a Few Equations): Free-Body Diagrams
by James H. Allen, III, PE, PhD
Statics For Dummies
- Copyright
- About the Author
- Author's Acknowledgments
- Publisher's Acknowledgments
- Introduction
- About This Book
- Conventions Used in This Book
- What You're Not to Read
- Foolish Assumptions
- How This Book Is Organized
- Part I: Setting the Stage for Statics
- Part II: Your Statics Foundation: Vector Basics
- Part III: Forces and Moments as Vectors
- Part IV: A Picture Is Worth a Thousand Words (Or At Least a Few Equations): Free-Body Diagrams
- Part V: A Question of Balance: Equilibrium
- Part VI: Statics in Action
- Part VII: The Part of Tens
- Icons Used in This Book
- Where to Go from Here
- I. Setting the Stage for Statics
- 1. Using Statics to Describe the World around You
- 2. A Quick Mathematics Refresher
- 2.1. Keeping Things Accurate and Determining What's Significant
- 2.2. Nomenclature with Little Superscripts: Using Scientific and Exponential Notation
- 2.3. Recalling Some Basic Algebra
- 2.4. Getting into Shapes with Basic Geometry and Trigonometry
- 2.5. Brushing Up on Basic Calculus
- 3. Working with Unit Systems and Constants
- II. Your Statics Foundation: Vector Basics
- 4. Viewing the World through Vectors
- 5. Using Vectors to Better Define Direction
- 6. Vector Mathematics and Identities
- 7. Turning Multiple Vectors into a Single Vector Resultant
- 8. Breaking Down a Vector into Components
- 8.1. Defining a Vector Component
- 8.2. Resolving a Vector into Cartesian and Non-Cartesian Components
- 8.2.1. Using Cartesian concepts to calculate Cartesian components
- 8.2.2. Determining components on a non-Cartesian orientation
- 8.2.3. Calculating non-Cartesian components of two-dimensional vectors
- 8.2.3.1. Using the parallelogram method
- 8.2.3.2. Using Cartesian techniques to find non-Cartesian components
- III. Forces and Moments as Vectors
- 9. Applying Concentrated Forces and External Point Loads
- 10. Spreading It Out: Understanding Distributed Loads
- 11. Finding the Centers of Objects and Regions
- 11.1. Defining Location for Distributed Loads
- 11.2. Getting to the Center of Centroids
- 11.3. Understanding Centers of Mass and Gravity
- 12. Special Occasions in the Life of a Force Vector: Moments and Couples
- 12.1. I Need a Moment: Exploring Rotation and Moments of Force
- 12.2. Calculating a Moment with Scalar Data
- 12.3. Calculating a Moment by Using Vector Information
- 12.4. Using Double-Headed Arrows to Find Moment Resultants and Components
- 12.5. Relocating a Force by Using a Moment: Equivalent Force Couples
- IV. A Picture Is Worth a Thousand Words (Or At Least a Few Equations): Free-Body Diagrams
- 13. Anatomy of a Free-Body Diagram
- 13.1. Free-Body Diagrams in a Nutshell
- 13.2. Displaying External Forces
- 13.3. Axial Loads and Beyond: Depicting Internal Forces
- 13.4. Restricting Movements with Support Reactions
- 13.5. Weighing In with Self Weight
- 14. The F.B.D.: Knowing What to Draw and How to Draw It
- 15. Simplifying a Free-Body Diagram
- 13. Anatomy of a Free-Body Diagram
- V. A Question of Balance: Equilibrium
- 16. Mr. Newton Has Entered the Building: The Basics of Equilibrium
- 17. Taking a Closer Look at Two-Dimensional Equilibrium: Scalar Methods
- 18. Getting Better Acquainted with Three-Dimensional Equilibrium: Vector Methods
- 18.1. Finding a Starting Point
- 18.2. Seeing Equilibrium within Vector Notation
- 18.3. Figuring Support Reactions with Three-Dimensional Equilibrium Equations
- 18.3.1. Establishing the F.B.D.
- 18.3.2. Writing the equilibrium equations
- 18.3.2.1. Summing forces
- 18.3.2.2. Summing moments
- 18.3.2.3. Setting up to complete the cross product
- VI. Statics in Action
- 19. Working with Trusses
- 20. Analyzing Beams and Bending Members
- 20.1. Defining the Internal Bending Forces
- 20.2. Calculating Internal Loads at a Point
- 20.3. Writing Generalized Equations for Internal Forces
- 20.4. Creating Shear and Moment Diagrams by Area Calculations
- 21. Working with Frames and Machines
- 22. A Different Kind of Axial System: Cable Systems
- 23. Those Darn Dam Problems: Submerged Surfaces
- 23.1. Feeling the Pressure: Understanding Fluid Pressure
- 23.2. Making Calculations under (Fluid) Pressure
- 23.3. Figuring Partial Pressures on Openings and Gates
- 24. Incorporating Friction into Your Applications
- VII. The Part of Tens
- 25. Ten Steps to Solving Any Statics Problem
- 25.1. Sketches Come First
- 25.2. Determine the Supports
- 25.3. Don't Forget the Applied Loads and Self Weight
- 25.4. Calculate As Many Unknown Support Reactions As You Can
- 25.5. Guess It's a Frame or Machine
- 25.6. Get Out the Dynamite: Separating Pieces from the Problem for Internal Analysis
- 25.7. Assume Directions of Internal Forces
- 25.8. Be Consistent with Your Assumptions
- 25.9. Guess That Three (or Six) Equilibrium Equations Are Necessary
- 25.10. If Friction Is Involved, Guess That the Object Slides
- 26. Ten Tips for Surviving a Statics Exam
- 26.1. Find Problems You Know How to Solve
- 26.2. State Your Assumptions
- 26.3. Relax and Remember Your Basic Steps
- 26.4. Identify Your Origin and Coordinate System
- 26.5. Remember Your Vectors
- 26.6. Write Your Equilibrium Equations
- 26.7. Stuck? Draw More Free-Body Diagrams
- 26.8. Draw Your Shear and Moment Diagrams Correctly
- 26.9. Assess Your Answers
- 26.10. Acknowledge Mistakes and Don't Erase
- 25. Ten Steps to Solving Any Statics Problem
In this part . . .
Free-body diagrams (F.B.Ds) are a vital part of solving a statics problem, so these chapters give you a basic checklist for constructing the pictures that describe an object and the loads acting on it. You also discover how to include external applied loads, internal forces, and self weight. I introduce the different types of physical restraints (known as support reactions) and show you how to include them on your F.B.D. I then illustrate how to simplify complex free-body diagrams by moving loads from one point on an object to another while maintaining the same object's behavior.
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