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Session 3520

An Interactive Graphics Oriented Beam Analysis Program

by Jack Zecher Indiana University - Purdue University at Indianapolis

ABSTRACT An interactive graphics based beam analysis program was developed which automates the analysis of beam problems usually encountered in the undergraduate Strength of Materials course. The program provides a highly intuitive graphical user interface that assists in the definition of supports, loads, length and cross-sectional properties of the beam. The program then automatically calculates shear, moment and deflection values along the length of the beam. The results of the analysis are presented in the form of graphical displays of the shear and moment diagrams as well as the deflection diagram. This paper describes the techniques used in the development of the program, as well as the impact that the use of this program can have when used in conjuction with teaching traditional shear and moment diagram techniques.

INTRODUCTION Techniques for constructing shear and moment diagrams are first introduced during the sophomore level Strength of Materials course. These techniques are then used extensively in the process of calculating stresses and deflections in beams. Students are first introduced to the method of calculating resisting shear and moment values by using the basic principles of static equilibrium. Graphical techniques are then introduced, to further reinforce the relationship between shear and moment values along the beam. When first introduced, students usually struggle to understand the concept. It is almost always necessary to show the students numerous cases involving different loading and support situations until they begin to feel comfortable solving problems on their own.

Beam deflections are calculated using both the moment-area method and the principle of superposition. Although the moment-area method is fairly quick, it is easily prone to errors due to the complicated sign conventions. The principle of superposition is performed by solving for the displacement at a single point along the beam by using formulas which are based on simpler beam problems, and then adding the results. This technique is also prone to arithmetic errors because of the large number of variables involved in the formulas. In addition to these arithmetic problems, students often never get to the stage of constructing moment diagrams or calculating deflections, because they make a mistake at a previous stage. For example, if a mistake is made during the calculation of a reaction forces, it then becomes impossible to proceed with correctly constructing the shear and subsequent moment diagram.

It was decided to develop a computer program which could be used in conjunction with the traditional solution techniques. The objective was to develop a program that would allow concentrated forces and moments as well as linearly distributed loads to be applied anywhere along the length of the beam. Pinned, roller and cantilevered supports would be able to be positioned at any location along the beam. The program

1996 ASEE Annual Conference Proceedings

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Zecher, J. (1996, June), An Interactive Graphics Oriented Beam Analysis Program Paper presented at 1996 Annual Conference, Washington, District of Columbia. 10.18260/1-2--6136