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Statics For Dummies by James H. Allen, III, PE, PhD

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Chapter 17. Taking a Closer Look at Two-Dimensional Equilibrium: Scalar Methods

The equilibrium equations I present in Chapter 16 give you the tools you need to begin studying the effects of behaviors on structures. You're well on your way to determining support reactions, calculating internal forces, and solving specific application problems with either scalar or vector techniques. For two-dimensional problems, scalar solution techniques are much more efficient, and that's what I show you in this chapter. But never fear — I show you the vector methods (which you almost always need for three-dimensional problems) in Chapter 18. In this chapter, I show you how to use your free-body diagrams (F.B.D.s — see Part IV) to determine the magnitude and sense of unknown support reactions. I start the chapter by outlining the three basic steps that you follow when working a scalar statics problem and then I show you how to create the translational and rotational equilibrium equations in two-dimensional situations. Finally, I highlight a few considerations for selecting points for moment equilibrium equations.

Tackling Two-Dimensional Statics Problems in Three Basic Steps

As you start to analyze a system or object, keep in mind that you're always using the concepts of static equilibrium to determine the unknown forces and behaviors. Although some problems (such as those defined ...

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