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Using Engineering Mathematics to Learn Structural Analysis

Abstract

Engineering students by the junior year are required to be proficient in mathematics. At this stage, the students have taken many of the introductory STEM (Science, Technology, Engineering, and Mathematics) courses. However, many students do not see nor appreciate the relevance of their mathematics courses to their major field of study. Beginning in structural analysis and in fluid mechanics in the junior year, the need for students to apply advanced mathematics becomes apparent. Students tend to want the calculator to do the math but many times fail to realize that calculators only generate numbers. Faculty must stand firm to motivate the students to learn and appreciate how to apply mathematical concepts to engineering problems and technology is helping to make this a reality.

This paper discusses how some of the fundamental content in a structural analysis course is presented and learned by the students. The content is presented in such a way that students must readily apply concepts learned in previous mathematics courses to be successful in the course. Students use technology such as a software package called Mathcad to help visualize the principles and applications that are discussed in the course.

I. Introduction

Engineers are technical problem solvers. From a historical perspective of the mid 20th century and after, engineers have been trained to be number “crunchers” due to significant changes in engineering education and technology as a result of the post World War II era1-4. From high school math and science courses through college engineering courses, engineers have been “molded” to crunch numbers. Here is a problem with all the associated numerical information. Now, solve for the solution.

The practice of number crunching has not only been ingrained in our engineering youth but also in our technology. Computers and now calculators have been developed which can rapidly crunch numbers5. In terms of analyses, numerical based methods such as difference methods and finite element methods have been developed to approximate differential equations. Such solutions, even if the exact differential equations are known, generate only an approximate solution. And in the case of finite element analyses, the solutions are not conservative.

In engineering practice, number crunching has become routine. However, solutions are generated and constantly modified to meet unforeseen changes. After the solution has been calculated, modifying it is often done at considerable time and expense depending on the complexity of the problem and the dependency of the variable to other related system variables. It would be beneficial to teach engineers to develop general solutions which can be more routinely modified due to changes in constraints of variables or boundary conditions. Such solution strategies can be developed by solving problems symbolically in terms of variables rather than numerically.

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Palmquist, S. (2007, June), Using Engineering Mathematics To Learn Structural Analysis Paper presented at 2007 Annual Conference & Exposition, Honolulu, Hawaii. 10.18260/1-2--2039