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Graphical Statics Redux

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2016 ASEE Annual Conference & Exposition


New Orleans, Louisiana

Publication Date

June 26, 2016

Start Date

June 26, 2016

End Date

August 28, 2016





Conference Session

Teaching & Learning Statics and Mechanics of Materials

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Paper Authors


Sarah Baxter University of St. Thomas

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Dr. Baxter is a Professor of Mechanical Engineering in the School of Engineering at the University of St. Thomas in St. Paul, MN. She received her PhD in Applied Mathematics from the University of Virginia School of Engineering and Applied Science.

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Bethany Fralick University of South Carolina, Aiken

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Dr. Fralick is an Assistant Professor of Engineering in the Department of Mathematical Sciences at the University of South Carolina Aiken in Aiken, SC. She received her Ph.D. in Mechanical Engineering from the University of South Carolina College of Engineering and Computing.

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There are two fundamental challenges to imbedding active learning in a classroom. The first is coming up with the format for an activity that is appropriate for the class and learning objectives; the second is developing content that can be effectively cast in this format throughout the course.

These two challenges are particular stumbling blocks for Statics, where the list of appropriate in-class activities often reduces to working homework problems; where collaborative activities reduce to students working together on homework problems; and where cooperative activities reduce to teams working on homework problems.

Similarly, the subject matter in Statics does not lend itself to discussions. It is hard to discuss the answer to a problem that is clearly right or wrong, and the availability of different ways to arrive at a solution is usually based on trivial differences in the sequence of algebraic steps. Case studies at this level are usually not involved enough to allow students to contribute intuition and/or apply real-world experience to problem solving.

In previous work, the authors proposed enhancing the Graphical Statics component in Statics classes. Most current textbooks include explanations and problems on how to add vectors graphically and/or the use of funicular polygons for the solution of hanging cables; but in the authors’ personal and anecdotal experience, neither are emphasized to any degree in classrooms. The hypothesis posed in this work was that adding additional Graphical Statics components would help build visualization skills, encourage drawing as a conceptual aid, and help reinforce the concepts. As authors, we found it challenging to develop ways to assess these high level outcomes. Our audience, however, while admitting the potential for these outcomes, was more interested in specific problems that could be directly inserted into the class as active learning exercises. From a practical perspective, they suggested that a framework and progression of Graphical Statics examples, that could become a consistent active component of the class, would be useful and motivate their use of this approach.

In this work, we return to Graphical Statics in the context of a foundation for a series of active learning components for a Statics class. The aims of the paper are threefold: (1) to review the fundamental techniques of graphical statics, including force triangles and funicular polygons, (2) to outline a series/progression of concepts, in the order they appear in Statics curriculum, that can be solved using graphical techniques, and (3) to discuss how Graphical Statics fits into the context and criteria of active learning, and how it’s effects could be realistically assessed, based on definitions and existing research in the literature.

In companion work, sample problems, for each topic/concept presented in this outline, have been assembled into a mini-textbook to facilitate the use of novel, and concept-emphasis heavy, applications of Graphical Statics. This textbook will be available at a poster presentation that illustrates key components of the graphical approach, as well as from the authors by email. The textbook includes theoretical and applied problems with graphical and mathematical solutions.

Baxter, S., & Fralick, B. (2016, June), Graphical Statics Redux Paper presented at 2016 ASEE Annual Conference & Exposition, New Orleans, Louisiana. 10.18260/p.27306

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