Statics for dummies by James H Allen

388 Pages·2012·4.78 MB·English

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James H. Allen III, PE, PhD, is a registered professional engineer who ISBN 978-0-470-59894-8
teaches courses in the areas of statics, mechanics, structural engineering,
and steel design.
James H. Allen III, PE, PhD,
Assistant Professor of Civil Engineering
Allen University of Evansville
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Statics
FOR
DUMmIES
‰
by James H. Allen III, PE, PhD
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Statics For Dummies®
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Library of Congress Control Number: 2010930963
ISBN: 978-0-470-59894-8
Manufactured in the United States of America
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About the Author
James H. Allen III, PE, PhD, serves on the civil engineering faculty at the
University of Evansville, where he teaches statics, structural analysis, and
structural design courses. Dr. Allen received his PhD from the University of
Cincinnati in structural engineering and performed his undergraduate work
at the University of Missouri-Rolla (now the Missouri University of Science
and Technology).
Dedication
To my wife Miranda for her unconditional love and support.
Author’s Acknowledgments
I wish to thank all of the many people that have worked so hard to make
this book a reality. Thanks especially to my senior project editor, Alissa
Schwipps, for her patience and guidance, and to all of the others who have
made this project possible, including Mike Baker, Megan Knoll, and Wiley’s
Composition Services department. Thanks for all you do!
01_598948-ffirs.indd iii01_598948-ffirs.indd iii 7/28/10 10:54 PM7/28/10 10:54 PM
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Contents at a Glance
Introduction ................................................................ 1
Part I: Setting the Stage for Statics .............................. 7
Chapter 1: Using Statics to Describe the World around You .......................................9
Chapter 2: A Quick Mathematics Refresher .................................................................17
Chapter 3: Working with Unit Systems and Constants ...............................................31
Part II: Your Statics Foundation: Vector Basics ............ 39
Chapter 4: Viewing the World through Vectors...........................................................41
Chapter 5: Using Vectors to Better Defi ne Direction ..................................................51
Chapter 6: Vector Mathematics and Identities ............................................................69
Chapter 7: Turning Multiple Vectors into a Single Vector Resultant ........................79
Chapter 8: Breaking Down a Vector into Components ...............................................95
Part III: Forces and Moments as Vectors .................... 107
Chapter 9: Applying Concentrated Forces and External Point Loads.....................109
Chapter 10: Spreading It Out: Understanding Distributed Loads ............................123
Chapter 11: Finding the Centers of Objects and Regions .........................................135
Chapter 12: Special Occasions in the Life of a Force Vector:
Moments and Couples ................................................................................................149
Part IV: A Picture Is Worth a Thousand Words
(Or At Least a Few Equations): Free-Body Diagrams ..... 167
Chapter 13: Anatomy of a Free-Body Diagram ...........................................................169
Chapter 14: The F.B.D.: Knowing What to Draw and How to Draw It ......................185
Chapter 15: Simplifying a Free-Body Diagram ............................................................199
Part V: A Question of Balance: Equilibrium ................ 207
Chapter 16: Mr. Newton Has Entered the Building: The Basics of Equilibrium .....209
Chapter 17: Taking a Closer Look at Two-Dimensional Equilibrium:
Scalar Methods ............................................................................................................219
Chapter 18: Getting Better Acquainted with Three-Dimensional Equilibrium:
Vector Methods ..........................................................................................................229
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Part VI: Statics in Action ......................................... 241
Chapter 19: Working with Trusses ..............................................................................243
Chapter 20: Analyzing Beams and Bending Members ...............................................259
Chapter 21: Working with Frames and Machines ......................................................279
Chapter 22: A Different Kind of Axial System: Cable Systems .................................293
Chapter 23: Those Darn Dam Problems: Submerged Surfaces ................................309
Chapter 24: Incorporating Friction into Your Applications .....................................321
Part VII: The Part of Tens ......................................... 339
Chapter 25: Ten Steps to Solving Any Statics Problem .............................................341
Chapter 26: Ten Tips for Surviving a Statics Exam ...................................................347
Index ....................................................................... 353
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Table of Contents
Introduction ................................................................. 1
About This Book ..............................................................................................1
Conventions Used in This Book .....................................................................2
What You’re Not to Read ................................................................................3
Foolish Assumptions .......................................................................................3
How This Book Is Organized ..........................................................................3
Part I: Setting the Stage for Statics ......................................................4
Part II: Your Statics Foundation: Vector Basics .................................4
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 ........................................5
Part VI: Statics in Action .......................................................................5
Part VII: The Part of Tens ......................................................................6
Icons Used in This Book .................................................................................6
Where to Go from Here ...................................................................................6
Part I: Setting the Stage for Statics ............................... 7
Chapter 1: Using Statics to Describe the World around You. . . . . . . . .9
What Mechanics Is All About .......................................................................10
Putting Vectors to Work ...............................................................................10
Peeking at a few vector types .............................................................11
Understanding some purposes of vectors........................................11
Defi ning Actions in Statics ............................................................................12
Sketching the World around You: Free-Body Diagrams ...........................13
Unveiling the Concept of Equilibrium .........................................................14
Applying Statics to the Real World .............................................................14
Chapter 2: A Quick Mathematics Refresher . . . . . . . . . . . . . . . . . . . . . .17
Keeping Things Accurate and Determining What’s Signifi cant ...............18
Nomenclature with Little Superscripts: Using Scientifi c and
Exponential Notation .................................................................................19
Recalling Some Basic Algebra ......................................................................20
Hitting the slopes of functions and lines ..........................................21
Rearranging equations to solve for unknown variables .................22
Sigma notation......................................................................................22
Getting into Shapes with Basic Geometry and Trigonometry .................23
Getting a handle on important geometry concepts ........................24
Tackling the three basic identities of trigonometry ........................26
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viii
Statics For Dummies
Brushing Up on Basic Calculus ....................................................................27
The power rule: Differentiation and integration of polynomials ......27
Using calculus to defi ne local maximum and minimum values .....29
Chapter 3: Working with Unit Systems and Constants . . . . . . . . . . . . .31
Measuring Up in Statics ................................................................................31
The metric system ...............................................................................32
U.S. customary units ............................................................................34
The kip: One crazy exception .............................................................35
Never the twain shall meet: Avoiding mixing unit systems............35
Looking at Units of Measure and Constants Used in Statics ....................37
Constants worth noting ......................................................................37
Three common statics units for everyday life .................................37
All the derived units you’ll ever need ...............................................38
Part II: Your Statics Foundation: Vector Basics ............. 39
Chapter 4: Viewing the World through Vectors . . . . . . . . . . . . . . . . . . .41
Defi ning a Vector ...........................................................................................41
Understanding the difference between scalars and vectors ..........42
Taking a closer look at vectors ..........................................................42
Applying vector basics ........................................................................43
Drawing a Vector’s Portrait ..........................................................................45
The single-headed arrow approach ...................................................45
A two-headed monster: The double-headed arrow approach .......47
Exploring Different Types of Vectors ..........................................................48
Fixed vector ..........................................................................................48
Free vector ............................................................................................49
Sliding vector ........................................................................................49
Chapter 5: Using Vectors to Better Defi ne Direction. . . . . . . . . . . . . . .51
Taking Direction from the Cartesian Coordinate System .........................51
As a Crow Flies: Using Position Vectors to Determine Direction ............53
Describing direction in detail .............................................................54
Moving from Point A to Point B and back again ..............................54
A First Glance at Determining a Vector’s Magnitude ................................56
Recognizing the notation for magnitude...........................................56
Computing the magnitude of a position vector: Pythagoras
to the rescue! ....................................................................................56
Unit Vectors Tell Direction, Too! .................................................................59
Cartesian-vector notation ...................................................................59
Using unit vectors to create position vectors ..................................60
Creating Unit Vectors from Scratch ............................................................62
Shrinking down position vectors .......................................................62
Using angular data and direction cosines ........................................63
Utilizing proportions and similar triangles ......................................65
Knowing which technique to use .......................................................67
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