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

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Chapter 18. Getting Better Acquainted with Three-Dimensional Equilibrium: Vector Methods

Statics problems in three dimensions are some of the most intimidating types of problems you encounter. You can easily get lost in all the dimensions, coordinates, and angles in three dimensions. A single force in three dimensions is completely capable of producing moments about three different Cartesian axes (see Chapter 5). And determining whether a rotation is positive or negative by the scalar methods I show in Chapter 17 can be a real challenge (though not impossible with the right-hand rule I describe in Chapter 12). If you choose to work with vectors, a lot of those difficulties are automatically handled for you. And after you've become an old pro at turning forces and distances into vectors, why not let vectors do the work for you?

In this chapter, I show you how to apply all those vector calculations to the free-body diagrams (F.B.D.s) I cover earlier in the book. Then I show you how to write the equations of equilibrium in vector form to solve for unknown support reactions.

Finding a Starting Point

The solution method for solving three-dimensional statics problems is very similar to the solution methods for two-dimensional situations that I describe in Chapter 17. Although it requires a bit more work upfront, the actual ...

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