Feel the Force! An Inquiry-based Approach to Teaching Free-body Diagrams for Rigid-body Analysis

Eric Davishahl; Todd Haskell; Lee W. Singleton

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Conference: 2020 ASEE Virtual Annual Conference Content Access
Location: Virtual On line
Publication Date: June 22, 2020
Start Date: June 22, 2020
End Date: June 26, 2021
Conference Session: Making Mechanics Courses Fun and More Effective
Tagged Division: Mechanics
Page Count: 22
DOI: 10.18260/1-2--34669
Permanent URL: https://strategy.asee.org/34669
Download Count: 1054

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Paper Authors

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Eric Davishahl Whatcom Community College orcid.org/0000-0001-9506-2658

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Eric Davishahl holds an MS degree in mechanical engineering and serves as associate professor and engineering program coordinator at Whatcom Community College. His teaching and research interests include developing, implementing and assessing active learning instructional strategies and auto-graded online homework. Eric has been a member of ASEE since 2001. He currently serves as awards chair for the Pacific Northwest Section and was the recipient of the 2008 Section Outstanding Teaching Award.

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Todd Haskell Western Washington University

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Todd Haskell is a cognitive scientist interested in learning and the development of expertise, especially in STEM fields. He is currently Associate Professor of Psychology at Western Washington University. In previous projects Dr. Haskell has worked on understanding how chemistry novices and experts navigate between macroscopic, symbolic, and small particle representations, and how pre-service elementary teachers translate an understanding of energy concepts from physics to other disciplines.

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Lee W. Singleton Whatcom Community College

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Lee Singleton is a professor at Whatcom Community College, in Bellingham, WA. He holds a BS in mathematics from Harding University, a MS in mathematics and PhD in biomedical mathematics from Florida State University. His current interests include 3D-printing, active learning, and infusing more physical activity into mathematics courses. Recent grant positions include principal investigator on the NSF-funded grant “EAGER: MAKER: Engaging Math Students with 3D-Printing for STEM Success and co-PI on the NSF-funded grant "Collaborative Research: Improving Representational Competence by Engaging with Physical Modeling in Foundational STEM Courses".

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Abstract

Perusal of any common statics textbook will reveal a reference table of standard supports in the section introducing rigid body equilibrium analysis. Most statics students eventually memorize a heuristic approach to drawing a free-body diagram based on applying the information in this table. First, identify the entry in the table that matches the schematic representation of a connection. Then draw the corresponding force and/or couple moment vectors on the isolated body according to their positive sign conventions. Multiple studies have noted how even high performing students tend to rely on this heuristic rather than conceptual reasoning. Many students struggle when faced with a new engineering connection that does not match an entry in the supports table.

In this paper, we describe an inquiry-based approach to introducing support models and free-body diagrams of rigid bodies. In a series of collaborative learning activities, students practice reasoning through the force interactions at example connections such as a bolted flange or a hinge by considering how the support resists translation and rotation in each direction. Each team works with the aid of a physical model to analyze how changes in the applied loads affect the reaction components. A second model of the isolated body provides opportunity to develop a tactile feel for the reaction forces. We emphasize predicting the direction of each reaction component, rather than following a standard sign convention, to provide opportunities for students to practice conceptual application of equilibrium conditions. Students’ also draw detailed diagrams of the force interactions at the mating surfaces in the connection, including distributed loadings when appropriate. We use equivalent systems concepts to relate these detailed force diagrams to conventional reaction components.

Targeted assessments explore whether the approach described above might improve learning outcomes and influence how students think about free-body diagrams. Students use an online tool to attempt two multiple-choice concept questions after each activity. The questions represent near and far transfer applications of the concepts emphasized and prompt students for written explanation. Our analysis of the students’ explanations indicates that most students engage in the conceptual reasoning we encourage, though reasoning errors are common. Analysis of final exam work and comparison to an earlier term in which we used a more conventional approach indicate a majority of students incorporate conceptual reasoning practice into their approach to free-body diagrams. This does not come at the expense of problem-solving accuracy. Student feedback on the activities is overwhelmingly positive.

Citation
Format

Davishahl, E., & Haskell, T., & Singleton, L. W. (2020, June), Feel the Force! An Inquiry-based Approach to Teaching Free-body Diagrams for Rigid-body Analysis Paper presented at 2020 ASEE Virtual Annual Conference Content Access, Virtual On line . 10.18260/1-2--34669

TY - CPAPER
AB - Perusal of any common statics textbook will reveal a reference table of standard supports in the section introducing rigid body equilibrium analysis. Most statics students eventually memorize a heuristic approach to drawing a free-body diagram based on applying the information in this table. First, identify the entry in the table that matches the schematic representation of a connection. Then draw the corresponding force and/or couple moment vectors on the isolated body according to their positive sign conventions. Multiple studies have noted how even high performing students tend to rely on this heuristic rather than conceptual reasoning. Many students struggle when faced with a new engineering connection that does not match an entry in the supports table.

In this paper, we describe an inquiry-based approach to introducing support models and free-body diagrams of rigid bodies. In a series of collaborative learning activities, students practice reasoning through the force interactions at example connections such as a bolted flange or a hinge by considering how the support resists translation and rotation in each direction. Each team works with the aid of a physical model to analyze how changes in the applied loads affect the reaction components. A second model of the isolated body provides opportunity to develop a tactile feel for the reaction forces. We emphasize predicting the direction of each reaction component, rather than following a standard sign convention, to provide opportunities for students to practice conceptual application of equilibrium conditions. Students’ also draw detailed diagrams of the force interactions at the mating surfaces in the connection, including distributed loadings when appropriate. We use equivalent systems concepts to relate these detailed force diagrams to conventional reaction components.

Targeted assessments explore whether the approach described above might improve learning outcomes and influence how students think about free-body diagrams. Students use an online tool to attempt two multiple-choice concept questions after each activity. The questions represent near and far transfer applications of the concepts emphasized and prompt students for written explanation. Our analysis of the students’ explanations indicates that most students engage in the conceptual reasoning we encourage, though reasoning errors are common. Analysis of final exam work and comparison to an earlier term in which we used a more conventional approach indicate a majority of students incorporate conceptual reasoning practice into their approach to free-body diagrams. This does not come at the expense of problem-solving accuracy. Student feedback on the activities is overwhelmingly positive.

AU - Eric Davishahl
AU - Todd Haskell
AU - Lee W. Singleton
CY - Virtual On line
DA - 2020/06/22
PB - ASEE Conferences
TI - Feel the Force! An Inquiry-based Approach to Teaching Free-body Diagrams for Rigid-body Analysis
UR - https://strategy.asee.org/34669
DO - 10.18260/1-2--34669
ER -