Sources Of Students’ Difficulties With Couples And Moments In Statics

NOTE: The first page of text has been automatically extracted and included below in lieu of an abstract Sources of Students’ Difficulties with Couples and Moments in Statics Introduction This study was conducted in response to observations of students’ difficulties in understanding and applying moments and couples during our previous work in statics1. Over the past several years, we have been engaged in an interdisciplinary effort to help students understand the proper problem solving skills required to draw free body diagrams, an important element for developing a model of a real problem in statics. Through this effort, we have found that two key problems for students are the conceptual understanding of moments and couples and the ability to apply a moment equation during equilibrium analysis. We believe that part of the confusion for students results from definitions that are inconsistent across textbooks and courses. In sampling a few textbooks, we found that the terms, moment, couple, and torque, have different definitions, some of which are in conflict with each other. For example, Meriam and Kraige define a couple as the moment produced by two equal, opposite, and non-collinear forces2. Other texts define a couple as a pair of equal, opposite, and non-collinear forces whose moment is defined as the moment of a couple3,4. This was the definition used as far back as 1874, and arrived at using analytical geometry5. Another issue that arises in terminology is the use of the same symbol (M) to represent both a moment and a couple across all texts that we sampled. This seems to create confusion about whether the reaction couple should be included in the sum of moments equation, and also what word should be used to describe it, and what symbol should be used to represent it. Compounding the issues that students face in engineering mechanics courses, terms such as force, couple, and moment are used in everyday language with meanings that are often very different than the meaning in the engineering domain6. Adding to the confusion generated by these imprecise terminologies in statics are issues that arise in more advanced mechanics courses. In sampling a few mechanics of materials texts, for example, we found that the descriptions of torque, moment, and couple also vary. The internal reactions resisting ‘twisting’ in shafts are referred to as torques7,8,9,10 and moments7 and couples9. In the beam bending portion of the texts, in all cases the internal force is referred to as a ‘bending moment’7,8,9,10, however during bending stress calculations, the internal load is sometimes referred to as a couple8,9. This potential for confusion is further compounded in introductory physics courses where moments of forces are referred to as torques, a term usually reserved in mechanics for axial moments11. These issues have led us to try and understand why students are confused about the use of moments and couples, and how we might address this in future studies. Here we report on