Hands-On Beam Models and Matching Spreadsheets Enhance Perceptual Learning of Beam Bending

This evidence-based practice paper explores the use of a physical beam model and an accompanying spreadsheet that plots deflection, slope, shear, moment, and loading diagrams as teaching tools.These tools were used to reinforce engineering theory as part of a second year civil engineering statics and solid mechanics course.The models consisted of three beams of known cross-section and stiffness, two supports which could be altered to provide clamped or simple support, and two dial gauges to measure beam deflection, all of which could be affixed to a base delineated with markings to quantify the distances between individual model components.Steel weights could be placed at any portion along the beam to apply vertical point loads to the beam.The physical model was accompanied by an electronic spreadsheet that back-calculated diagrams for slope, curvature, shear, moment, and loading.This was done based on the beam geometry, Young's modulus, and boundary conditions, as well as the measured deflections at the loaded points.In the first of two exercises students examined clamped, simple, and free boundary conditions.They also observed linearity between loading and deflection, and used statics to calculate shear and moment diagrams.Students compared their calculations and plotted diagrams with a spreadsheet that plotted a full set of beam diagrams.The goal of this exercise was to encourage students to start thinking about the notion that deflection, slope, and curvature are related to loading and boundary conditions.In a second session, after the students had been taught methods for calculating deflections in statically determinate beams, they examined model beams with various strategic boundary conditions and load patterns, looking for physical manifestations of deflection, slope, and curvature (moment) within those beams.As part of this exercise, students chose a particular beam design and loading, and used a version of the spreadsheet that could plot all of the beam diagrams based on geometric and boundary condition information and measured deflections at the loaded points.By comparing their model beam with the spreadsheet diagrams, students were able to make and strengthen their connections between mathematical, visual, and kinesthetic representations of beam bending.After each exercise, students were asked to provide written feedback on the effectiveness of the exercise through questions such as: "What are three specific things you learned about beams today?", "Which observations were unexpected or in conflict with your intuition?",and "How did the physical model and spreadsheet enable you to better understand the operation of beams?"The students noted that the exercise helped them understand how the different support conditions, material properties, and applied loads affect the deflection of the beam.They also stated that the spreadsheet helped them understand the relationship between deflection, slope, and curvature.After changing the support conditions of the beam, the students mentioned that some of their observed beam deflections conflicted with their intuition, which made them question why the beam behaved this way.This exercise helped the students think about how the theory relates to actual beam behavior and vice-versa.

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