A Transformational Approach to Teaching Matrix Structural Analysis, and Visual Implementation using Mathcad

At most universities, matrix methods of structural analysis are taught in the senior year, or in the first year of graduate study. For students taking the course, the material may be very challenging because it has been several semesters since they have taken the prerequisite courses (generally linear algebra and theory of structures). More problematically the course is challenging because many of the students have had little exposure to computer programming. At Virginia Tech, the course Computer Methods of Structural Analysis I (CEE 4404) has been designed to minimize these challenges, but still provide a firm theoretical basis in matrix structural analysis. The theoretical basis of the course is rooted in the concepts of equilibrium, compatibility, and superposition (requiring linear-elastic constitutive laws), and is presented in the context of four different levels of "Scope" within a structure. A key aspect of the course is a heavy reliance on a variety of mathematical transformations that relate the levels of scope to each other. Because of the reliance on transformations, the methodology described in this paper is termed the "Transformational Approach" to teaching matrix structural analysis. The implementation of the method is facilitated through the use of the commercial mathematics program Mathcad. Mathcad is used in two ways; first as a visual matrix manipulation tool, and second, as a framework for writing complete structural analysis programs. While a variety of programming platforms could be used (e.g. C++, C#, Visual Basic, Matlab, Mathematica) Mathcad was chosen because it is highly visual, relatively easy to learn, and is widely used in the structural engineering profession. By the end of the semester, quite complex problems may be solved with Mathcad, including any two-dimensional structure incorporating frame or truss elements. Practically any type of loading may be considered; shear deformations, rigid ends, and member end-releases may be included; and a variety of constraints may be modeled. Aside from Mathcad, no commercial structural analysis software is used in the course.