Statics For Dummies

Chapter 15. Simplifying a Free-Body Diagram

In This Chapter

• Understanding the principle of superposition

• Relocating forces and moments

• Determining equivalent systems with the space potato analogy

Chapters 13 and 14 equip you with the countless tools and equations to create, calculate, and depict the behaviors of vectors on objects by using free-body diagrams (F.B.Ds). F.B.D.s can be complex, intimidating, and a bit overwhelming because you often have an object that is subjected to distributed loads, concentrated forces, and applied moments applied at multiple locations, all acting simultaneously. (Flip to the chapters of Part III for more on these concepts.) Figuring out where to begin in tackling these diagrams can be quite a task.

One of the first steps you want to perform after making your sketch is to look for ways to simplify your F.B.D. In this chapter, I show you several handy simplifying techniques that you can utilize on a regular basis.

Presenting the Principle of Superposition

The principle of superposition basically states that multiple actions on an object are equivalent to the sum of the effects of each action applied individually. The principle of superposition allows you to quickly compute behaviors (such as reactions, displacements, and internal forces) from combined multiple load cases by simply adding together the responses of the individual cases.

Note

I assume that all objects in this book are rigid bodies, which are objects that aren't deformed by the forces acting ...