Free-body diagrams are commonly used by engineers and physicists as a visual aid in the solution process of many mechanics problems, both simple and complex. In a typical first-year engineering mechanics course, free-body diagrams are used for a variety of problems in particle and rigid body equilibrium including: trusses, frames and machines, friction and wedges, and internal forces in structures.
Although the underlying physics behind each problem type is the same (governed by the equations ∑F=0 and ∑M=0) these topics have evolved into separate teaching modules in a typical first-year engineering statics curriculum due to their distinct conceptual complexities. A review of the literature indicates that research to date has focused on the use of free-body diagrams in only a few of the first-year topics (particle and rigid body equilibrium, electrostatics, and friction). At present the effect of the use of free-body diagrams in the problem solving process for frame and machine type of problems has gone unstudied. This research uses an evidence-based approach to study the impact that free-body diagrams have on solutions developed by first-year engineering students in a statics course.
Using final exams from a first-year statics course, the effectiveness of using free-body diagrams on the problem-solving process for frames and machines type problems was analyzed for two independent cohorts of engineering students in two different years. The specific problems considered were frame type problems which included multiple members (including a two-force member) and different distributed loading configurations of varying difficulty. The free-body diagrams and the resulting equations were evaluated by assessing the accuracy and quality of the drawings using a rubric designed by the researchers. The data collected for the study was then analyzed using statistical methods and the results are discussed with respect to: identifying the common mistakes that students make on frame type problems, quantifying the mistakes that students make when including moment equations, tabulating the common errors made when including two force members, and determining the effect of increasing difficulty level in frame type problems. Results indicate that free-body diagrams become more important for the development of correct equations of a frame and machine type problem as the complexity of the problem increases.
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