As I watch students working toward mastering the principles of statics, I find myself frequently answering some of the same basic questions. Despite countless hours of working through examples and homework problems from their textbooks, students often seem to be confused on the same several topics.
The problem isn't that the material in a typical statics class is overly difficult; I think the issue is just several simple misconceptions that manifest themselves through poorly written examples and unnecessarily complex wording in conventional statics textbooks.
That's why I've written Statics For Dummies — to help students of the subject get a better understanding than they may otherwise get in a classic textbook. In this book, my goal is to answer those basic questions by using simple explanations and eliminating a lot of the extra technical jargon.
No statics book can tell you how to solve every possible problem you encounter. What Statics For Dummies tells you is what you need to know and why you need to know it. Why are three-dimensional problems easier to solve with vector formulations than with scalar methods? What exactly is equilibrium, and how do Newton's laws guarantee it? How do you know the difference between a truss and frame? All of these topics are at the heart of understanding statics; after you've got these basics down, actually solving a statics problem is a snap!
In statics, one of the most important habits to form is being as methodical as possible, which means that statics lends itself very nicely to a large number of checklists or simple steps to remember and follow. Throughout this book, I try to organize certain techniques by outlining the steps that you need to follow. Just like when you go grocery shopping, the checklists help you remember what fruits and vegetables (or equations or free-body diagrams) you need to put in your basket.
The best part of this book is that you have complete control on where you want to start. If you just want the tips for solving specific problems, jump to Part VI. If you find you need a bit of a refresher on vectors, that's in Part II. Let the table of contents and index be your guides.
I use the following conventions throughout the text to make things consistent and easy to understand:
New terms appear in italic and are closely followed by an easy-to-understand definition.
Bold is used to highlight the action parts of numbered steps, as well as keywords in bulleted lists.
I also use other, statics-specific conventions that I may not explain every time, so following is a brief list of concepts and terms that I use frequently throughout the book.
Decimal places: I try to carry at least three decimal places in all my calculations in this book. This move helps ensure enough precision in my calculations to demonstrate the fundamental principles without getting bogged down in the pesky numerical accuracy issues I cover in Chapter 2.
Vector variables: The most important aspect of statics is that you take all effects into consideration; if you forget even the smallest behavior on an object, solutions in statics can become impossible to accurately calculate. To help keep track, I usually use F or P to indicate force vectors, and M to indicate a moment vector. I also use i, j, and k to represent those common unit vectors in the text; in equations, they appear as
.
Bold (not in steps): Aside from its use in numbered steps and bulleted lists, I also use bold text to represent a vector equation. If you see a bolded variable, that indicates a vector is lurking in the discussion. This convention is common to most classical textbooks, so I replicate it here just for the sake of consistency with vectors you may have already been exposed to in a conventional statics or physic class.
Arrows on top of vector names: Another method of denoting a vector is to use the label or name of the vector with an arrow over the top such as
or
. If you see an arrow on top of a letter or word in an equation, you know that I'm working with vectors.
Italics (not as definitions): I also adopt a second sign convention from other textbooks: When I talk about a vector's magnitude (length) in the text, I use the name or label of the vector in italics.
Absolute value brackets: To represent the magnitude of a vector in an equation, I surround it with absolute value brackets, such as |
Because magnitudes are properties of vectors, I still include the vector arrow over the label. Just remember that the absolute value brackets take precedence, so if you see those, you know I'm primarily talking about a scalar magnitude.
Plus signs (+) with vector senses: Although it's not required, I use the plus symbol before positive numbers in some vector calculations as a visual reminder that I have in fact considered the sense (direction) of the vector on the Cartesian plane.
Origin: I assume that the origin of any given Cartesian plane is (0,0) for two-dimensional problems and (0,0,0) for three-dimensional ones unless otherwise noted.
Although I hope you're interested in every word I've painstakingly inscribed in this book, I admit that there are a few things you can skip over if you're short on time or just after the most important and practical stuff.
Text in sidebars: Sidebars are the shaded boxes that provide extra information, such as history or trivia, about the chapter topic.
Anything with a Technical Stuff icon: The in-depth info tagged by this icon is useful, but it may not be entirely necessary to solve day-to-day problems. It may also include information that shows how the information being discussed was developed or how the formulations came about.
As I wrote this book, I made a few assumptions about you, my beloved reader.
You're any college student taking an engineering statics class or studying Newtonian mechanics in your physics classes, or are at least familiar with those basic concepts.
You remember some math skills, including algebra and basic calculus topics such as differentiation and simple integration.
You have proficiency in geometry and trigonometry. The basic rules governing sines, cosines, and tangents of angles (both in degrees and radians) prove invaluable as you work a statics problem.
You're willing to practice the techniques that I show you. Remember all those problems your math teachers made you work back in school? Statics may require a similar effort. Practice makes perfect!
This book starts with a basic review of units and math and goes through vectors, forces, free-body diagrams, equilibrium, and practical statics applications. Here's the lowdown on each part.
Part I: Setting the Stage for Statics
In Part I, I give you some basic refresher information, such as working with units, while reviewing some of the basic math that provides the foundation for statics. Chapter 1 introduces the concept of statics while Chapter 2 provides you with a brief refresher about a wide range of mathematics topics, including basic algebra and polynomials, trigonometric relationships, and basic integration and differentiation of polynomials. Chapter 3 highlights the two major systems of units that you encounter in statics and shows you the base units for a wide range of values in statics.
Part II: Your Statics Foundation: Vector Basics
Part II introduces some basic vector principles. Chapter 4 shows you the three basic characteristics of vectors and how you can depict them graphically. Chapter 5 describes how to define your first vector, describing direction from one point to another. I also show you several alternative ways to define direction by using vectors. In Chapter 6, I explain the basics of vector mathematics and explore several useful identity relationships that come in handy. Chapter 7 demonstrates how to create one vector from multiple other vectors. I explain several basic techniques and show you how to apply basic formulas for calculations of each technique. Chapter 8 shows you the opposite information from Chapter 7: how you can split a single vector into multiple vectors acting in different directions.
Part III: Forces and Moments as Vectors
In Part III, I explore how load effects are created. In Chapter 9, I illustrate single concentrated loads (or point loads) and introduce you to the concept of self weight as a single value. Chapter 10 covers loads acting over an area or a distance and shows you how to turn a distributed load into an equivalent concentrated load as well. In Chapter 11, I show you how to calculate the different centroids (geometric centers, such as center of area and center of mass/gravity) of different geometric shapes, which proves useful for helping you to locate the single equivalent force of a distributed load. Chapter 12 is where I introduce rotational effects known as moments, explaining how to draw and calculate them.
Part IV: A Picture Is Worth a Thousand Words (Or At Least a Few Equations): Free-Body Diagrams
Part IV shows you how to draw the pictures necessary to solve statics problems. In Chapter 13, I give you the basic checklist of items to include on a free-body diagram (F.B.D.) and then explain how to define supports in terms of forces and moments. Chapter 14 shows you what to draw and how to work with multiple free-body diagrams at the same time. In Chapter 15, I give you some guidance on several ways to simplify some of the more complex diagrams that you create.
Part V: A Question of Balance: Equilibrium
In Part V, I introduce you to the concept of stability or equilibrium in statics. Chapter 16 defines the different types of equilibrium by explaining Newton's three laws of motion and the basic assumptions behind the governing equations of statics. In Chapters 17 and 18, I show you how to apply the basic equations of equilibrium to solve for unknown support reactions in two- and three-dimensional problems, respectively.
Part VI: Statics in Action
In Part VI, I show you how to identify the major categories of problems you come across in the real world. I also highlight several tips and techniques to speed up your solution process. Chapter 19 introduces you to trusses and simple axial members. I show you the basic techniques for solving for internal forces in the members of the trusses. Chapter 20 shows you that for many members in statics, additional internal forces exist beyond just the simple axial cases. I show you how to write equations for these internal forces and how to draw a graph of their values. In Chapter 21, you discover how to deal with frames and machine structures. Chapter 22 provides you with tools necessary to solve for internal forces of systems whose internal forces vary with geometry; I explain the concepts of sag and tension and then provide a useful shortcut technique known as the beam analogy.
In Chapter 23, you sink to new depths by exploring the behavior of fluids on submerged surfaces. I explain the concept of pressure and unit width in your calculations, and how to apply the equations of equilibrium. Things really heat up in Chapter 24 as I introduce friction to the problems. I explain the logic needed to determine if an object is prone to tipping or sliding and how to mathematically prove that.
Part VII: The Part of Tens
Part VII includes helpful top-ten lists. Chapter 25 provides you with ten important statics ideas to remember even if you forget everything else, and Chapter 26 gives you ten tips to survive a statics exam.
To make this book easier to read and simpler to use, I include some icons that can help you find and identify key ideas and information.
Tip
This icon appears whenever an idea or item can save you time or simplify your statics experience.
Note
Any time you see this icon, you know the information that follows points out a key idea or concept, greatly increasing the number of statics tools you have at your disposal.
Warning
This icon flags information that highlights dangers to your solution technique, or a common misstep that statics practitioners make but you should avoid.
Note
This icon appears next to information that's interesting but not essential. Don't be afraid to skip these paragraphs.
You can use Statics For Dummies either as a supplement to a course you're currently taking or as a stand-alone volume for understanding the basic concepts of statics.
If you're taking a statics course or studying Newtonian mechanics in physics, hopefully you find the organization to be very familiar. I follow the basic topics sequence that you experience in a class. However, unlike a classical text, if you want to skip a chapter, feel free.
If you're studying on your own or have never had a statics class, I strongly urge you to start at the beginning with Chapter 1 and read the chapters in order. The techniques in the later chapters do build on concepts of early chapters. That being said, this book isn't a mystery novel. If you want to skip ahead to the topics at the end, go right ahead; you won't ruin the ending. And if you get really lost, you can always fall back to an earlier chapter for a quick refresher!