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Session 1368

Teaching Students Work and Virtual Work Method in Statics: A Guiding Strategy with Illustrative Examples

Ing-Chang Jong University of Arkansas

Abstract A virtual displacement is an imaginary differential displacement that may not really take place. A virtual displacement may be either consistent with constraints at supports or inconsistent with constraints at supports. A virtual work is the work done by force or moment during a vir- tual displacement of the system. The virtual work method can be applied to solve problems in- volving either machines (structures with movable members) or frames (structures with no mov- able members). By letting the free body of a system undergo a strategically chosen compatible virtual displacement in the virtual work method, we can solve for one specified unknown at a time in many complex as well as simple problems in mechanics without having to solve coupled simultaneous equations. The virtual work method may initially appear as a magic black box to students, but it generally kindles great curiosity and interest in students of statics. This paper pro- poses an approach consisting of three major steps and one guiding strategy for implementing the virtual work method. It results in great learning of the virtual work method for students.

I. Introduction

Work is energy in transition to a system due to force or moment acting on the system through a displacement of the system, while heat is energy in transition to a system due to temperature dif- ference between the system and its surroundings. Work, as well as heat, is dependent on the path of a process. Like heat, work crosses the system boundary when the system undergoes a process. Unlike kinetic energy and potential energy, work is not a property possessed by a system. Many textbooks in statics show the use of virtual work method to solve problems involving mainly machines, where the virtual displacements are usually chosen to be consistent with constraints at supports. The virtual work method can equally be used to solve problems involving frames in statics. Readers may refer to textbooks by Beer and Johnston,1-2 Huang,3 Jong and Rogers,4 etc., where virtual displacements inconsistent with constraints at supports are strategically chosen to solve equilibrium problems of frames, which are fully constrained at supports.

This paper is aimed at doing the following: (a) sharpen the concept of work for students, (b) compare head to head the virtual work method with the conventional method using an example, (c) use displacement center5 and just algebra and geometry as the prerequisite mathematics to compute virtual displacements, (d ) propose three major steps in the virtual work method, (e) propose a guiding strategy for choosing the virtual displacement that is the best for solving one specified unknown, and ( f ) demonstrate (in Appendix A) the evidence that the conventional method (without displacement center) requires using differential calculus in determining a cer- tain virtual displacement. For benefits of a wider range of readers having varying familiarity with the subject, this paper contains illustrative examples with different levels of complexity.

Proceedings of the 2005 American Society for Engineering Education Annual Conference & Exposition Copyright © 2005, American Society for Engineering Education

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Jong, I. (2005, June), Teaching Students Work And Virtual Work Method In Statics: A Guiding Strategy With Illustrative Examples Paper presented at 2005 Annual Conference, Portland, Oregon. 10.18260/1-2--15341