Finite Element Applications: Trusses and Beams

Abstract

We now turn to illustrating how we can implement the principles detailed in Chap. 10. In particular, and following to a large extent the historical development of these methods, we will now describe the implementation of matrix methods and FEA. Thus, we will first introduce finite elements (literally!) and matrix methods for trusses. We will use a matrix formulation of trusses to introduce the direct stiffness method as a way to solve truss problems, as well as to set the stage for formulating and solving structures problems generally. We then follow that with FEA of the bending of beams by expanding our notion of finite elements to describe, formulate, and solve beam problems. Our emphasis here will be on the hand calculations that, in practice, we would nowadays do with a finite element software package, because it is always important to keep in mind exactly what the computer is doing on our behalf: With this understanding, we are better able to both obtain valid and verifiable results and to interpret correctly whether we are actually solving the problem we set out to solve.