2025 ASEE Annual Conference & Exposition

Equivalent systems, distributed loads, and reactions are often treated as highly theoretical and largely disconnected concepts by Statics students. Integrated learning objectives, basic theory, real world scenarios, and low-cost 3D printed beam model demonstrations connect all three major topics. The beam model employs two low-cost kitchen scales, a small set of gram weights, and a 3D-printed, simply supported beam model. In the first class, after the instructor introduces equivalent systems, students set up a particular loading scenario with multiple weights at several locations along a beam. They then calculate the resultant force and moment and the resultant force at a location, noting that for each of the three equivalent systems the kitchen scales show the same reactions. In a second class on distributed loads, students approximate a triangular distributed load on the same model beam and then experimentally determine the location of the resultant force that results in an externally equivalent system (i.e. identical reactions). Students then compare this location to the location of the centroid of the distributed load. In a final class on reactions, students again model a unique multi-force load combination including both point and distributed loads. Students then compare the reactions predicted by the rigid body equations of equilibrium with the reactions measured on the scales. Using low-cost, hands-on models, students gain the opportunity to build better mental models associated with engineering analysis tools, to recognize the variations between idealized models and the natural variability of reality, and to engage with the challenges of comparing theoretical predictions with measured values. By reusing the same beam model multiple times, students draw connections between equivalent systems, distributed loads, centroids, and reactions. Real world scenarios encourage curiosity about the world and demonstrate how statics is an important first step toward creating value for others. Faculty eager to teach these topics will find comprehensive coverage of the topics and the use of the beam model to teach the topics. Thoroughly demonstrated applications of John Milton Gregory’s Seven Laws of Teaching [1] should also be helpful to the engineering educator.