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Learning the Virtual Work Method in Statics: What Is a Compatible Virtual Displacement?

Abstract Statics is a course aimed at developing in students the concepts and skills related to the analysis and prediction of conditions of bodies under the action of balanced force systems. At a number of institutions, learning the traditional approach using force and moment equilibrium equations is followed by learning the energy approach using the virtual work method to enrich the learning of students. The transition from the traditional approach to the energy approach requires learning several related key concepts and strategy. Among others, compatible virtual displacement is a key concept, which is compatible with what is required in the virtual work method but is not commonly recognized and emphasized. The virtual work method is initially not easy to learn for many people. It is surmountable when one understands the following: (a) the proper steps and strategy in the method, (b) the displacement center, (c) some basic geometry, and (d ) the radian measure formula to compute virtual displacements. For learning and pedagogical purposes, this paper includes seven examples with various levels of challenge.

I. Introduction

More often than not, it is manifested that the virtual work method is used to treat problems in- volving mainly machines. This manifestation comes about as a consequence of focusing on the determination of the equilibrium configuration of a series of pin-connected members by restrict- ing virtual displacements to be consistent with constraints at the supports. In general, such a re- striction is too strong and is an over restriction. It prevents the virtual work method from being effectively used to treat problems involving beams and frames, and it diminishes the usefulness of the virtual work method in Statics. As a result, some feel that the virtual work method lacks broad appeal in Statics. Nonetheless, the virtual work method is a standing topic contained in most textbooks of Statics. By and large, such a topic is covered in Statics at the discretion of the instructors to enrich the learning of students.

Both the traditional method and the virtual work method equally require and emphasize the drawing of free-body diagrams, although the former involves more algebra and the latter uses more geometry in solving problems. Most students find that learning the virtual work method is challenging, since they are generally better at algebra than geometry. It is not the intent of this paper to urge anyone to teach the virtual work method or to upstage the time-honored traditional method in Statics. Rather, this paper is mainly aimed at being an extension to previous efforts1-9 of mechanics educators and textbook authors who included the virtual work method in Statics. In particular, this paper identifies key concepts, steps, and strategy that have been helpful to stu- dents in learning the virtual work method. Readers, who are familiar with this method, may skip the refresher on the rudiments included in the early part of this paper.

A displacement of a body is a change of position of the body. A rigid-body displacement of a body is a change of position of the body without inducing any strain in the body. A virtual dis-

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Jong, I. (2006, June), Learning The Virtual Work Method In Statics: What Is A Compatible Virtual Displacement? Paper presented at 2006 Annual Conference & Exposition, Chicago, Illinois. 10.18260/1-2--466