June 12, 2005
June 12, 2005
June 15, 2005
10.1114.1 - 10.1114.11
Statics is an early, critical step in preparing engineers, persons who can bridge the gap between fundamental concepts of physics and the analysis and design of real mechanical and structural systems. Students struggle with many concepts in Statics. We propose here that the modeling of supports, joints or connections between bodies is one of the most difficult and important ideas to be grasped in Statics. Moreover, it is probably at the core of linking physics with real mechanical and structural systems. The notions of force and equilibrium can be dealt with in purely mathematical ways, until one is compelled to associate forces with the actual interactions between particular bodies. Doing that correctly is not easy for students, and yet it is critical. We suspect that continuing difficulties in applying Statics in upper level design courses is at least partially tied to weaknesses in this area. We have previously criticized various aspects of traditional instruction in Statics. The subject of connections, in particular, typically receives cursory treatment in textbooks, as exemplified by the tables showing idealized drawings of joints and the unknown “reactions”. Traditional statics courses and textbooks are essentially teaching the analysis of forces for “pre-modeled”, simplified situations. Moreover, these situations are neatly separated into two- and threedimensional cases often covered in separate chapters. In reality, all mechanical and structural systems are three-dimensional; it is up to the engineer to decide if a two-dimensional analysis is warranted. To its detriment, we believe, traditional instruction in Statics also tends to minimize any reference to motion. Clearly, motion is tacitly present in problems that are often legitimately analyzed using Statics, including, for example, slowly moving mechanisms, and gears and shafts rotating steadily at high speeds. Reference to motion is clearly necessary if we are to explain to students the purpose of many connections: to accommodate certain motions between parts while precluding other motions. Noting the relative motions that are allowed and prohibited is also obviously one way of tracking and rationalizing which reactions can be present in different types of connections. Only if students are familiar with the essential features of connections, we would argue, can they: (i) recognize the various physical realizations of connections, (ii) understand the possible forces acting between connected members, and (iii) model the forces appropriately. With this premise, we propose significant enhancements to instruction pertaining to connections. These enhancements highlight the various roles that connections play in machines and structures, rationalize in a deeper way the relation between possible forces and physical characteristics of connections, and even empower students to draw their own conclusions regarding the virtues of certain designs over others. We fully recognize that most instructors devote relatively modest time to connections, probably referring students to the tables in books. For the reasons suggested above, however, we suggest that mechanics instructors reconsider this allotment of instructional time. To make enhanced attention to practical connections, we have begun to devise appropriate elements of instructional content. This content is suitable for a Statics course, and could allow for the generation of specific educational materials, such as textbooks and in-class instructional materials. In the following sections of the paper we address earlier experiences in our Statics sequence that can prepare students for understanding connections, followed by excerpts from the newly developed content.
Steif, P. S., & Dollar, A. (2005, June), Sharpening Statics As A Tool For Design: Demystifying The Modeling Of Forces At Connections Paper presented at 2005 Annual Conference, Portland, Oregon. https://peer.asee.org/15322
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