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Revisiting Graphical Statics

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2015 ASEE Annual Conference & Exposition


Seattle, Washington

Publication Date

June 14, 2015

Start Date

June 14, 2015

End Date

June 17, 2015





Conference Session

Statics and Finite Element Analysis

Tagged Division

Mechanical Engineering

Page Count


Page Numbers

26.1344.1 - 26.1344.10



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Paper Authors


Sarah C. 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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Ann Johnson University of South Carolina

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Ann Johnson holds a joint appointment as an associate professor in the departments of history and philosophy at the University of South Carolina. Her main research interests lie in studying the profession work practices of engineers, with particular attention to the ways the produce knowledge and the role of mathematical modeling.

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Bethany S. Fralick University of South Carolina

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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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Revisiting Graphical StaticsUp until the 1950’s a significant part of static analyses and design was done using the tools ofgraphical statics. These methods use scaled representations of force vectors to calculate themagnitude and direction of a resultant combination of forces. The roots of these graphicalmethods can be traced back to Leonardo da Vinci and Galileo Galilei, however German engineerKarl Culmann, (1821-1881) is generally considered the father of graphical statics.The methods remained a pedagogical technique, particularly in architecture schools, until the1990’s when, with the accessibility of desk-top computing and relatively inexpensive software,computer-aided drawing began to dominate and hand drawing disappeared from the engineeringcurriculum. Visualization and analysis can be done more quickly and accurately using CADprograms. In addition CAD addresses a more diverse range of problems, including those inthree-dimensions. As a result, returning to hand drawing in order to solve statics problems is nota move anyone would make for engineering reasons. However, it has been hypothesized thatdrawing on a computer lessens the reflective component of the design thought process. Students,in particular, aren’t thinking “visually” when they “draw” on a computer screen.To re-engage students in visual thinking we propose a return to graphical statics as modules inthe traditional undergraduate statics class. The motivation is to improve student visualizationcapabilities, for example to develop their abilities to correctly interpret three dimensional imagesviewed in a text or on a screen, and to enhance their ability to think critically about whether ananswer makes sense.In this preliminary work, two small modules were inserted into two statics classes taught tosophomore mechanical engineering students at_______ and _________. The first modulefocused on the analysis of two-dimensional particle equilibrium problems using force polygons.The second module used force polygons, and their extension to funicular polygons to determinethe magnitude and location of an equivalent resultant force. In this paper, some of thebackground, history and theory of these methods are discussed and the first generation of thesespecific modules presented. Additionally, the results of an end-of-course Statics ConceptInventory Exam, developed by Steif, Hansen and Dantzler, (2005, 2007), given to each of thegraphical statics classes, as well as to two other sections of statics at _________that did notinclude the graphics modules, are presented. While these inventory exams do not specificallyassess visualization or critical thinking skills, they do provide a preliminary look at whether theability to visualize two-dimensional problems graphically contributes to a better understandingof the concepts in Statics. The paper concludes with a discussion of extensions/modifications tothe modules and consideration of future assessment tools that could be used to evaluatevisualization or critical thinking skills more directly.

Baxter, S. C., & Johnson, A., & Fralick, B. S. (2015, June), Revisiting Graphical Statics Paper presented at 2015 ASEE Annual Conference & Exposition, Seattle, Washington. 10.18260/p.24681

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