Statics For Dummies

Statics For Dummies

by PE James H. Allen III, PhD
Released September 2010
Publisher(s): For Dummies
ISBN: 9780470598948

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Book description

The fast and easy way to ace your statics course

Does the study of statics stress you out? Does just the thought of mechanics make you rigid? Thanks to this book, you can find balance in the study of this often-intimidating subject and ace even the most challenging university-level courses.

Statics For Dummies gives you easy-to-follow, plain-English explanations for everything you need to grasp the study of statics. You'll get a thorough introduction to this foundational branch of engineering and easy-to-follow coverage of solving problems involving forces on bodies at rest; vector algebra; force systems; equivalent force systems; distributed forces; internal forces; principles of equilibrium; applications to trusses, frames, and beams; and friction.

  • Offers a comprehensible introduction to statics

  • Covers all the major topics you'll encounter in university-level courses

  • Plain-English guidance help you grasp even the most confusing concepts

If you're currently enrolled in a statics course and looking for a friendlier way to get a handle on the subject, Statics For Dummies has you covered.

Table of contents

  1. Copyright
  2. About the Author
  3. Author's Acknowledgments
  4. Publisher's Acknowledgments
  5. Introduction
    1. About This Book
    2. Conventions Used in This Book
    3. What You're Not to Read
    4. Foolish Assumptions
    5. How This Book Is Organized
      1. Part I: Setting the Stage for Statics
      2. Part II: Your Statics Foundation: Vector Basics
      3. Part III: Forces and Moments as Vectors
      4. Part IV: A Picture Is Worth a Thousand Words (Or At Least a Few Equations): Free-Body Diagrams
      5. Part V: A Question of Balance: Equilibrium
      6. Part VI: Statics in Action
      7. Part VII: The Part of Tens
    6. Icons Used in This Book
    7. Where to Go from Here
  6. I. Setting the Stage for Statics
    1. 1. Using Statics to Describe the World around You
      1. 1.1. What Mechanics Is All About
      2. 1.2. Putting Vectors to Work
        1. 1.2.1. Peeking at a few vector types
        2. 1.2.2. Understanding some purposes of vectors
      3. 1.3. Defining Actions in Statics
      4. 1.4. Sketching the World around You: Free-Body Diagrams
      5. 1.5. Unveiling the Concept of Equilibrium
      6. 1.6. Applying Statics to the Real World
    2. 2. A Quick Mathematics Refresher
      1. 2.1. Keeping Things Accurate and Determining What's Significant
      2. 2.2. Nomenclature with Little Superscripts: Using Scientific and Exponential Notation
      3. 2.3. Recalling Some Basic Algebra
        1. 2.3.1. Hitting the slopes of functions and lines
        2. 2.3.2. Rearranging equations to solve for unknown variables
        3. 2.3.3. Sigma notation
      4. 2.4. Getting into Shapes with Basic Geometry and Trigonometry
        1. 2.4.1. Getting a handle on important geometry concepts
          1. 2.4.1.1. Computing angles inside polygons
          2. 2.4.1.2. Constructing angles created from line segments
          3. 2.4.1.3. Double-checking angles with degrees and radians
          4. 2.4.1.4. Recalling the Pythagorean theorem
        2. 2.4.2. Tackling the three basic identities of trigonometry
      5. 2.5. Brushing Up on Basic Calculus
        1. 2.5.1. The power rule: Differentiation and integration of polynomials
          1. 2.5.1.1. Basic differentiation and tangents to functions
          2. 2.5.1.2. Basic integration
        2. 2.5.2. Using calculus to define local maximum and minimum values
    3. 3. Working with Unit Systems and Constants
      1. 3.1. Measuring Up in Statics
        1. 3.1.1. The metric system
          1. 3.1.1.1. Converting to larger and smaller metric units
          2. 3.1.1.2. Making multiple conversions in one equation
        2. 3.1.2. U.S. customary units
        3. 3.1.3. The kip: One crazy exception
        4. 3.1.4. Never the twain shall meet: Avoiding mixing unit systems
      2. 3.2. Looking at Units of Measure and Constants Used in Statics
        1. 3.2.1. Constants worth noting
        2. 3.2.2. Three common statics units for everyday life
        3. 3.2.3. All the derived units you'll ever need
  7. II. Your Statics Foundation: Vector Basics
    1. 4. Viewing the World through Vectors
      1. 4.1. Defining a Vector
        1. 4.1.1. Understanding the difference between scalars and vectors
        2. 4.1.2. Taking a closer look at vectors
        3. 4.1.3. Applying vector basics
      2. 4.2. Drawing a Vector's Portrait
        1. 4.2.1. The single-headed arrow approach
        2. 4.2.2. A two-headed monster: The double-headed arrow approach
      3. 4.3. Exploring Different Types of Vectors
        1. 4.3.1. Fixed vector
        2. 4.3.2. Free vector
        3. 4.3.3. Sliding vector
    2. 5. Using Vectors to Better Define Direction
      1. 5.1. Taking Direction from the Cartesian Coordinate System
      2. 5.2. As a Crow Flies: Using Position Vectors to Determine Direction
        1. 5.2.1. Describing direction in detail
        2. 5.2.2. Moving from Point A to Point B and back again
      3. 5.3. A First Glance at Determining a Vector's Magnitude
        1. 5.3.1. Recognizing the notation for magnitude
        2. 5.3.2. Computing the magnitude of a position vector: Pythagoras to the rescue!
          1. 5.3.2.1. The two-dimensional Pythagorean theorem
          2. 5.3.2.2. Going vertical: The Pythagorean theorem in three dimensions
          3. 5.3.2.3. Putting Pythagoras to work
      4. 5.4. Unit Vectors Tell Direction, Too!
        1. 5.4.1. Cartesian-vector notation
        2. 5.4.2. Using unit vectors to create position vectors
          1. 5.4.2.1. Position vectors can be Cartesian too!
          2. 5.4.2.2. Relationship between a vector, its magnitude, and its direction
      5. 5.5. Creating Unit Vectors from Scratch
        1. 5.5.1. Shrinking down position vectors
        2. 5.5.2. Using angular data and direction cosines
        3. 5.5.3. Utilizing proportions and similar triangles
        4. 5.5.4. Knowing which technique to use
    3. 6. Vector Mathematics and Identities
      1. 6.1. Performing Basic Vector Operations
        1. 6.1.1. Adding vectors
        2. 6.1.2. Subtracting vectors
        3. 6.1.3. Moving vectors head to tail
      2. 6.2. What Do You Mean I Can't Multiply Vectors? Creating Products
        1. 6.2.1. Dot products
        2. 6.2.2. Cross products
      3. 6.3. Useful Vector Operation Identities
    4. 7. Turning Multiple Vectors into a Single Vector Resultant
      1. 7.1. Getting a Handle on Resultant Vectors
        1. 7.1.1. Depicting a resultant vector
        2. 7.1.2. Principles of resultants
        3. 7.1.3. Calculating resultant magnitude and direction
      2. 7.2. Using Graphical Techniques to Construct Resultants
      3. 7.3. Using Geometric Methods to Construct Resultants: The Parallelogram Method
        1. 7.3.1. Useful geometric relationships
          1. 7.3.1.1. Law of cosines
          2. 7.3.1.2. Law of sines
        2. 7.3.2. The parallelogram method
      4. 7.4. Using Vector Methods to Compute Resultants
        1. 7.4.1. Using vector addition
        2. 7.4.2. Calculating the direction of the vector resultant
    5. 8. Breaking Down a Vector into Components
      1. 8.1. Defining a Vector Component
      2. 8.2. Resolving a Vector into Cartesian and Non-Cartesian Components
        1. 8.2.1. Using Cartesian concepts to calculate Cartesian components
          1. 8.2.1.1. Figuring component magnitudes
          2. 8.2.1.2. Using scalar magnitudes and directions to create vector components
          3. 8.2.1.3. Computing vector components in three dimensions
        2. 8.2.2. Determining components on a non-Cartesian orientation
        3. 8.2.3. Calculating non-Cartesian components of two-dimensional vectors
          1. 8.2.3.1. Using the parallelogram method
          2. 8.2.3.2. Using Cartesian techniques to find non-Cartesian components
  8. III. Forces and Moments as Vectors
    1. 9. Applying Concentrated Forces and External Point Loads
      1. 9.1. Comparing Internal and External Forces and Rigid and Deformable Bodies
      2. 9.2. Exploring External Concentrated Forces
        1. 9.2.1. Normal forces from contact
        2. 9.2.2. Friction
        3. 9.2.3. Concentrated loads
      3. 9.3. Revealing the Unseen with Concentrated Internal Loads
        1. 9.3.1. Forces in ropes and cables
        2. 9.3.2. Forces in springs
          1. 9.3.2.1. Stretch in springs
          2. 9.3.2.2. Spring constants
      4. 9.4. Surveying Self Weight as an External Load Value
        1. 9.4.1. Getting specific on specific gravity and self weight properties
        2. 9.4.2. Working with lumped mass calculations
      5. 9.5. Introducing the Principle of Transmissibility
    2. 10. Spreading It Out: Understanding Distributed Loads
      1. 10.1. Getting a Handle on Some Distributed Load Vocab
      2. 10.2. Take a (Distributed) Load Off: Types of Distributed Loads
        1. 10.2.1. Distributed forces
        2. 10.2.2. Surface loads (pressures)
        3. 10.2.3. Volumetric loads
      3. 10.3. Calculating the Resultant of a Distributed Load
        1. 10.3.1. Uniform and linearly varying forces
          1. 10.3.1.1. Zero order (uniform) distributions
          2. 10.3.1.2. First order (linearly varying) distributions
          3. 10.3.1.3. Other two dimensional distributions
        2. 10.3.2. Surface loads and pressures in multiple dimensions
        3. 10.3.3. Avoiding the double integral
      4. 10.4. Looking at Mass and Self Weight as Distributed Values
    3. 11. Finding the Centers of Objects and Regions
      1. 11.1. Defining Location for Distributed Loads
      2. 11.2. Getting to the Center of Centroids
        1. 11.2.1. Defining a centroid's region type
        2. 11.2.2. Computing the centroid of a discrete region
          1. 11.2.2.1. Noting geometric properties of simple shapes
          2. 11.2.2.2. Building a centroid calculation table
          3. 11.2.2.3. Including holes in discrete regions
          4. 11.2.2.4. Handling trapezoidal regions
        3. 11.2.3. Finding centroids of continuous regions
        4. 11.2.4. Taking advantage of symmetry
      3. 11.3. Understanding Centers of Mass and Gravity
        1. 11.3.1. Center of mass
        2. 11.3.2. Center of gravity
    4. 12. Special Occasions in the Life of a Force Vector: Moments and Couples
      1. 12.1. I Need a Moment: Exploring Rotation and Moments of Force
        1. 12.1.1. Developing rotational behaviors: Meeting couples and concentrated moments
          1. 12.1.1.1. One force and one distance
          2. 12.1.1.2. Two parallel forces and a distance: Couples
          3. 12.1.1.3. No distance? Concentrated moments
        2. 12.1.2. Taking on torque and bending: Types of concentrated moments
        3. 12.1.3. Getting a handle on the right-hand rule for moments of force
      2. 12.2. Calculating a Moment with Scalar Data
        1. 12.2.1. Planar rotation about a point
        2. 12.2.2. Determining the magnitude and sense of a two-dimensional couple
      3. 12.3. Calculating a Moment by Using Vector Information
        1. 12.3.1. Completing the cross product
        2. 12.3.2. Using unit vectors to create moment vectors
      4. 12.4. Using Double-Headed Arrows to Find Moment Resultants and Components
      5. 12.5. Relocating a Force by Using a Moment: Equivalent Force Couples
  9. IV. A Picture Is Worth a Thousand Words (Or At Least a Few Equations): Free-Body Diagrams
    1. 13. Anatomy of a Free-Body Diagram
      1. 13.1. Free-Body Diagrams in a Nutshell
      2. 13.2. Displaying External Forces
        1. 13.2.1. Portraying concentrated forces
        2. 13.2.2. Depicting distributed forces
        3. 13.2.3. Looking at the F.B.D. so far
        4. 13.2.4. Conveying concentrated moments
          1. 13.2.4.1. Moments in two dimensions
          2. 13.2.4.2. Moments in three dimensions
      3. 13.3. Axial Loads and Beyond: Depicting Internal Forces
      4. 13.4. Restricting Movements with Support Reactions
        1. 13.4.1. Three basic planar support reactions
          1. 13.4.1.1. Rolling along with roller supports
          2. 13.4.1.2. Freeing up rotation with pinned supports
          3. 13.4.1.3. Restricting everything with fixed supports
          4. 13.4.1.4. Moving on up (or down) with inclined supports
        2. 13.4.2. Three-dimensional support conditions
          1. 13.4.2.1. Ye olde ball and socket: Pinned supports in three dimensions
          2. 13.4.2.2. Collar assembly supports
      5. 13.5. Weighing In with Self Weight
    2. 14. The F.B.D.: Knowing What to Draw and How to Draw It
      1. 14.1. Getting Your F.B.D. Started
        1. 14.1.1. Assuming a direction for support reactions
        2. 14.1.2. Including more than the required info on your F.B.D.
      2. 14.2. Zooming In with Isolation Boxes
        1. 14.2.1. Unveiling internal forces
        2. 14.2.2. Applying rules of application
        3. 14.2.3. Avoiding problems with incorrect isolation techniques
      3. 14.3. Using Multiple F.B.D.s
    3. 15. Simplifying a Free-Body Diagram
      1. 15.1. Presenting the Principle of Superposition
      2. 15.2. Centering on Centerlines and Lines of Symmetry
      3. 15.3. Equivalent Systems: Forces on the Move
        1. 15.3.1. Moving a force: The space potato analogy
        2. 15.3.2. Moving a moment
  10. V. A Question of Balance: Equilibrium
    1. 16. Mr. Newton Has Entered the Building: The Basics of Equilibrium
      1. 16.1. Defining Equilibrium for Statics
        1. 16.1.1. Translational equilibrium
        2. 16.1.2. Rotational equilibrium
      2. 16.2. Looking for Equilibrium with Newton's Laws
        1. 16.2.1. Reviewing Newton's laws of motion
        2. 16.2.2. The scalar equations that make it happen: The big three
          1. 16.2.2.1. In two dimensions
          2. 16.2.2.2. In three dimensions
      3. 16.3. Identifying Improper Constraints: When Equilibrium Equations Are Insufficient
        1. 16.3.1. Concurrent force systems
        2. 16.3.2. Parallel force systems
    2. 17. Taking a Closer Look at Two-Dimensional Equilibrium: Scalar Methods
      1. 17.1. Tackling Two-Dimensional Statics Problems in Three Basic Steps
      2. 17.2. Calculating Support Reactions with Two-Dimensional Equilibrium Equations
        1. 17.2.1. First things first: Creating the F.B.D.
        2. 17.2.2. Writing the equilibrium equations
          1. 17.2.2.1. Adding helpful notation
          2. 17.2.2.2. Summing forces first: Writing two translational equilibrium equations
          3. 17.2.2.3. Summing moments: Writing the rotational equilibrium equation
          4. 17.2.2.4. Solving for the unknown reactions
      3. 17.3. Choosing a Better Place to Sum Moments
    3. 18. Getting Better Acquainted with Three-Dimensional Equilibrium: Vector Methods
      1. 18.1. Finding a Starting Point
      2. 18.2. Seeing Equilibrium within Vector Notation
        1. 18.2.1. Equilibrium in translational behaviors
        2. 18.2.2. Rotational components
      3. 18.3. Figuring Support Reactions with Three-Dimensional Equilibrium Equations
        1. 18.3.1. Establishing the F.B.D.
          1. 18.3.1.1. Sketching the loads on the F.B.D.
          2. 18.3.1.2. Writing each load in vector form
        2. 18.3.2. Writing the equilibrium equations
          1. 18.3.2.1. Summing forces
          2. 18.3.2.2. Summing moments
          3. 18.3.2.3. Setting up to complete the cross product
  11. VI. Statics in Action
    1. 19. Working with Trusses
      1. 19.1. Identifying Truss Members
      2. 19.2. The Method of Joints: Zooming In on One Panel Point at a Time
        1. 19.2.1. Step 1: Drawing isolation boxes
        2. 19.2.2. Step 2: Applying the equations of equilibrium
        3. 19.2.3. Step 3: Review and repeat
      3. 19.3. Drawbacks to the Method of Joints
      4. 19.4. And Now for My Next Trick: Slicing through the Method of Sections
        1. 19.4.1. Step 1: Cutting the truss
        2. 19.4.2. Step 2: Drawing the F.B.D. for the two remaining truss pieces
        3. 19.4.3. Step 3: Applying the equations of translational equilibrium
        4. 19.4.4. Step 4: Applying the equation of rotational equilibrium
        5. 19.4.5. Step 4, continued: Identifying the instantaneous center
      5. 19.5. Shortcutting the Equation Writing: Zero-Force Members
    2. 20. Analyzing Beams and Bending Members
      1. 20.1. Defining the Internal Bending Forces
        1. 20.1.1. And then there were three: Internal forces of two-dimensional objects
        2. 20.1.2. Strange new three-dimensional effects
          1. 20.1.2.1. Translation: Another shear force
          2. 20.1.2.2. Rotation: Torsion and another bending moment
      2. 20.2. Calculating Internal Loads at a Point
        1. 20.2.1. Positive moments make you happy!: Yet another two-dimensional sign convention
        2. 20.2.2. Using the sign convention
        3. 20.2.3. Computing internal force magnitudes
      3. 20.3. Writing Generalized Equations for Internal Forces
        1. 20.3.1. Defining the critical points
        2. 20.3.2. Establishing the regions of your generalized equations
        3. 20.3.3. Discovering other useful tricks from generalized equations
          1. 20.3.3.1. Defining the relationship between shear and moment
          2. 20.3.3.2. Calculating maximum and minimum shear and moments with calculus
          3. 20.3.3.3. Plotting a system's internal forces
      4. 20.4. Creating Shear and Moment Diagrams by Area Calculations
        1. 20.4.1. Rules to remember when working with area methods
        2. 20.4.2. Constructing the shear diagram
        3. 20.4.3. Creating the moment diagram
    3. 21. Working with Frames and Machines
      1. 21.1. Identifying a Frame and Machine System
        1. 21.1.1. Defining properties of frames and machines
        2. 21.1.2. Determining static determinacy
      2. 21.2. Using the Blow-It-All-Apart Approach to Solve Frame and Machine Problems
        1. 21.2.1. Breaking it at the hinges
        2. 21.2.2. Knowing where to start solving frame and machine problems
          1. 21.2.2.1. Starting on a member with a load
          2. 21.2.2.2. Solving for the unknown hinge forces as fast as you can
      3. 21.3. Considering Other Useful Approaches to Common Frame and Machine Problems
        1. 21.3.1. When more than two members meet at an internal hinge
        2. 21.3.2. Dealing with pesky pulley problems
          1. 21.3.2.1. Changing force direction with pulleys
          2. 21.3.2.2. Creating mechanical advantage with pulleys
      4. 21.4. Tackling Complex and Unique Assemblies on Machine Problems
        1. 21.4.1. Pistons and slider assemblies
        2. 21.4.2. Slotted holes and unidirectional pins
    4. 22. A Different Kind of Axial System: Cable Systems
      1. 22.1. Defining Nonlinear Structural Behavior
      2. 22.2. Distinguishing among Types of Flexible Cable Systems
        1. 22.2.1. Recognizing cables under concentrated loads
        2. 22.2.2. Picking out parabolic cable systems
        3. 22.2.3. Identifying catenary cable systems
      3. 22.3. Solving for Tension in Flexible Cables
        1. 22.3.1. Concentrated load systems
        2. 22.3.2. Parabolic cable systems
          1. 22.3.2.1. Calculating tension when you know sag
          2. 22.3.2.2. Calculating sag when tension is known
        3. 22.3.3. Catenary cable systems
      4. 22.4. Taking a Shortcut: The Beam Analogy for Flexible Cables
    5. 23. Those Darn Dam Problems: Submerged Surfaces
      1. 23.1. Feeling the Pressure: Understanding Fluid Pressure
        1. 23.1.1. Dealing with hydrostatic pressure
          1. 23.1.1.1. Recognizing why zero pressure isn't exactly zero pressure
          2. 23.1.1.2. Working with a unit width
        2. 23.1.2. Determining effects from the self weight of water
      2. 23.2. Making Calculations under (Fluid) Pressure
        1. 23.2.1. Drawing the fluid F.B.D.
        2. 23.2.2. Creating the hydrostatic pressure distribution
        3. 23.2.3. Finding the dead weight of water and dams
          1. 23.2.3.1. Determining the self weight of water
          2. 23.2.3.2. Establishing the self weight of a concrete dam
        4. 23.2.4. Including base reactions for dam structures
        5. 23.2.5. Applying equilibrium equations
      3. 23.3. Figuring Partial Pressures on Openings and Gates
    6. 24. Incorporating Friction into Your Applications
      1. 24.1. Friction: It's More Than Just Heat!
        1. 24.1.1. Factors affecting friction
        2. 24.1.2. Types of friction
      2. 24.2. A Sense of Impending . . . Motion? Calculating Sense
        1. 24.2.1. Establishing equilibrium when friction is present
        2. 24.2.2. Finding the friction limit FMAX
      3. 24.3. Solving Friction Problems by Using Logic and Equations Together
        1. 24.3.1. Working with friction angles
        2. 24.3.2. Combining friction and normal forces into a single resultant
      4. 24.4. Timber! Exploring Tipping
        1. 24.4.1. Uncovering the tipping point and normal force
        2. 24.4.2. Moving the normal force to prevent tipping
        3. 24.4.3. Establishing which friction phenomenon controls, sliding or tipping
          1. 24.4.3.1. Case 1: Checking sliding before tipping
          2. 24.4.3.2. Case 2: Checking tipping before sliding
      5. 24.5. Examining More Common Friction Applications
        1. 24.5.1. Wedging in on the action
        2. 24.5.2. Staying flexible with belts and pulleys
  12. VII. The Part of Tens
    1. 25. Ten Steps to Solving Any Statics Problem
      1. 25.1. Sketches Come First
      2. 25.2. Determine the Supports
      3. 25.3. Don't Forget the Applied Loads and Self Weight
      4. 25.4. Calculate As Many Unknown Support Reactions As You Can
      5. 25.5. Guess It's a Frame or Machine
      6. 25.6. Get Out the Dynamite: Separating Pieces from the Problem for Internal Analysis
      7. 25.7. Assume Directions of Internal Forces
      8. 25.8. Be Consistent with Your Assumptions
      9. 25.9. Guess That Three (or Six) Equilibrium Equations Are Necessary
      10. 25.10. If Friction Is Involved, Guess That the Object Slides
    2. 26. Ten Tips for Surviving a Statics Exam
      1. 26.1. Find Problems You Know How to Solve
      2. 26.2. State Your Assumptions
      3. 26.3. Relax and Remember Your Basic Steps
      4. 26.4. Identify Your Origin and Coordinate System
      5. 26.5. Remember Your Vectors
      6. 26.6. Write Your Equilibrium Equations
      7. 26.7. Stuck? Draw More Free-Body Diagrams
      8. 26.8. Draw Your Shear and Moment Diagrams Correctly
      9. 26.9. Assess Your Answers
      10. 26.10. Acknowledge Mistakes and Don't Erase

Product information

  • Title: Statics For Dummies
  • Author(s): PE James H. Allen III, PhD
  • Release date: September 2010
  • Publisher(s): For Dummies
  • ISBN: 9780470598948