Trusses, Matrix MethodEdit
The Truss is a commonly studied structure and serves as a good example for illustrating many concepts, such as the Finite Element Method (FEM). While a truss is usually defined by three or more beams comprising one or more triangular elements, the analysis of the structure in Figure 1 below follows that of a truss due to its constraints at points 1 and 3.
The structure above is statically determinate, and therefore does not require the FEM. However it was the example used in class to demonstrate a few key concepts. The first, although a review from statics, was the free body diagram (FBD). First the global FBD, which includes the entire structure, was drawn. This was followed by a local FBD of each beam. In addition, a numbering scheme was introduced to avoid confusion in more difficult problems to be encountered later. This includes using numbers enclosed by: circles for nodes (joints), and triangles for beams.
In addition, the force displacement relation based on the model of a 1-D spring was introduced. Also, it was shown how matrices can be used to solve multiple degree of freedom (dof) systems.