TEACHER NOTES

ISSUES RELATED TO THE PROBLEM

The purpose of this problem is to illustrate a very useful application of the calculus. The issue is the extent of the knowledge that the student must acquire before working the problem. Although a serious attempt has been made to supply this background material, this problem may not be for the average calculus student. It might be assigned as a project to students who are oriented towards mechanical and civil engineering.

Prerequisites

A knowledge of integration is essential to carrying out the manipulations needed to work the problem.

Time allotment - time management

This is a project which will need some "soak" time. It should be assigned over a period of several days. Even with a computer algebra system, the solution to the problem is quite lengthy.

Expectations

Students will have questions like, "Where does this theory come from?" What is presented here is a simplified special case of Euler bending theory. The references cited should help curious students. The important thing to remember is that the problem is focused more on the calculus than on the mechanics.

Future payoffs

The problem is a good preparation for the study of mechanics of materials. A student who masters the problem should feel comfortable applying calculus in a new, unknown technical area.

Extensions

Extensions could be created in which different types of loading or supports were used. For some of these problems it would be possible to search for the points where deflection or slope was at a maximum.

References and Sources

Mechanics of Materials, by Ferdinand P. Beer and Russell Johnston, Jr. McGraw-Hill, 1992, ISBN 0-07-004340-X