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Opening the Black Box: The Direct Stiffness Method Uncovered

Ronald W. Welch Stephen J. Ressler United States Military Academy

Abstract

This paper describes our use of common computer tools to help students unlock the mysteries embedded in structural analysis computer programs that are based on the Direct Stiffness Method. The methodology described in this paper is taught in an Advanced Structural Analysis course in the ABET-accredited civil engineering program at the United States Military Academy. This formulation is based on our strong belief that students must understand the basic assumptions inherent in the Direct Stiffness Method before they can confidently and competently perform computer-based structural analyses. We find that students understand these assumptions best when they have an opportunity to work through each major step in the Direct Stiffness Method by hand—aided by appropriate software to perform computations and matrix manipulations.

I. Introduction

In our Advanced Structural Analysis course at the U. S. Military Academy, students learn and apply the Direct Stiffness Method in three different blocks of instruction—Trusses, Beams, and Frames. In each block, we develop the direct stiffness formulation for the appropriate structural element, then have students work through one or more problems involving the analysis of a relatively simple structure. In every case, the students perform the Direct Stiffness Method manually, but use Excel spreadsheet software to perform matrix manipulations and MathCAD computational software to perform mathematical computations. This presented educational methodology is effective for peering inside any type Black Box tool as long as the key learning steps are clearly delineated and common computer tools are used only to perform the mundane, time consuming tasks.

Specifically, students solve each problem as follows:

· Use MathCAD to define local element stiffness matrices. · Use MathCAD to transform the local element stiffness matrices to global element stiffness matrices. · Use Excel to assemble (i.e., stack) the global element stiffness matrices into a global structure stiffness matrix. · Use Excel to reorder the rows and columns of the global structure stiffness matrix to better solve for unknown values of displacements and external forces. · Use MathCAD to solve for reactions and unknown nodal displacements. · Use MathCAD to solve for local internal member forces. · Use a commercial structural analysis software package to analyze the same structure, and compare the displacements and member forces with those obtained through the manual solution.

Proceedings of the 2002 American Society for Engineering Education Annual Conference & Exposition Copyright © 2002, American Society for Engineering Education

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Welch, R., & Ressler, S. (2002, June), Opening The Black Box: Direct Stiffness Method Uncovered Paper presented at 2002 Annual Conference, Montreal, Canada. 10.18260/1-2--10195