New Idea to Enhance Better Understanding of Free Body Diagrams in Solid Mechanics Course

Abstract

Historically, majority of students taking solid mechanics course at my university find it confusing and even challenging to draw free body diagrams (FBDs) and to compute the internal forces correctly. Many instructors teach those topics in typical statics course and review the same principles in solid mechanics and design courses. However, many students either do not still fully understand the topic or have forgotten the concepts during the time gap between taking statics and the follow on courses. This is also true for colleges such as ours with mandatory co-op education in which students alternate between school and work terms. With incorrect calculation of internal loads (or load in each section of a member), the next steps of calculating the stress and deflection of members will go wrong. In a recent solid mechanics course taught by the author, 60 to 70 percent of the students could not correctly compute the internal forces within each section of an axially loaded member. Although majority of students drew the free body diagram of the entire system correctly, only a few could realize or interpret the correct values of forces within each section of a member. Others drew incorrect FBDs that do not satisfy static equilibrium.The author came up with an idea (alternative approach or method) to teach free body diagrams that partially address the above-mentioned difficulties that many students face. Similar to axial loading, students find it difficult to determine the internal loads for torsional members. Determining the internal loads for beams subjected to complex loading is even more confusing and challenging to these students. Although the new method proposed in this paper is not fully assessed for its effectiveness, it was used during the Fall 2018 (September to December) and Winter 2019 (January to March) solid mechanics classes. The total number of students was around 50 in both academic terms. The students viewed this new method as one of the potential approaches to understand the equilibrium concepts. Same course will be taught by the author during Spring 2019 term to assess the effectiveness of the proposed method 'before and after' by giving the same problems to students using the old approach and to students using the new approach. Preliminary assessment results based on the students' performance on in-class, homework, quizzes and exams will be available by the end of Winter 2019 term. Active learning activities are being used to help teach the method. It is hoped that this alternative method will be an effective approach for instructors teaching statics and solid mechanics courses to make the struggling students better understand the concepts of static equilibrium. Details of this approach will be discussed in detail in this paper along with several numerical examples.