I’m filling in for Rob Whitehead this year as designated structures professor for our SCI-TECH sequence (he’s got a well-deserved internal fellowship to teach the rest of the University how to do project-based learning–or, as we call it, learning), and like any good substitute I’m calling a few audibles. For a while now, the final structures module in our five-course sequence has covered long spans, and for a cumulative assignments students have done a case study on a classic long span project. While that’s paid some dividends, in particular integrating history into our tech coursework, both of us thought that some hands-on summative work might be a good experiment.
Enter the Long Span Steel Cage Match. For five weeks, students have been proposing model structures to meet a very specific set of criteria: carry a 10-pound weight over a 48″ span at a height that allows a regulation soccer ball to pass under its 1/3 points. They were given height limits and a base condition–two 2×4 timbers forming ‘rails’ that were the only things their structures could touch. We also limited the materials they could use, to cardboard (not corrugated), basswood, string, and hot glue. Final models would be tested and ranked, and grades for the final lab (1/4 of the module’s grade) would be based on how much their structures weighed, relative to the rest of the class.
This last bit was critical. In the past, we’d done competitive model testing to see how much a structure could carry, but this invariably led to models that were way, way over designed. Requiring the class to design to the same applied load and judging based on weight allows us to emphasize long span principles–in particular reducing unnecessary or under-stressed material, and using funicular shapes. It also encourages them to work iteratively to gradually remove material or elements until the structure just barely carries the load.
The five week module had four lab periods scheduled. For each of these, we gave students an intermediate assignment that roughly paralleled how a design experiment would actually proceed: Hypothesis, Modeling, Prototype Testing, and Final Testing. In Week 1, students had to propose, on paper, three possible solutions to the problem. For each one, they had to sketch their scheme and predict possible modes of failure. They presented these to the class, and we gave them feedback–without making any overly specific suggestions.
In Week 2, we tested 1/4 scale models of their designs to destruction, asking them to explain in static terms how each of their options failed. Many teams noted that their models performed better than expected–and most teams understood that this wasn’t actually good news. If a structure carried much more than its required load, it meant that the structure was probably over-designed.
The most productive thing we tried was an optional prototyping session two weeks prior to the final test. We provided exactly the conditions under which we’d test the final models, and teams could subject as many options as they wanted during the lab period. Not every team showed up, but those that did were able to see not only how their models performed, but also how every other teams’ worked. Sure enough, after a dozen or so structures that carried the load and weighed between 600 and 1000 grams, one team came in with a simple four-legged structure that carried the load–and weighed in at just 234 grams. Those teams that were there realized that all of the arches, trusses, and cable-structures they’d brought had been the results of over-thinking; the ten-pound weight was a point load, and the funicular shape for a point load at midspan is a simple triangle. Sure enough, the lightweight option, by following the funicular shape in both the longitudinal and the cross-sectional direction, cut more than 2/3 the weight of the next-lightest scheme. We could not have asked for a better demonstration of long span principles.
On testing day, we saw a pretty solid variety of schemes. Many of the teams who had been present for the prototyping session arrived with some version of the funicular pyramid–which we endorsed. There’s no “stealing” in evolutionary design, just “research,” I suggested. But there were plenty of other solutions that worked–the one above, for instance, which used a compression arch formed of truss elements. But, very quickly, a lead pack emerged that was some version of the pyramid:
Once all the schemes had been tested (only two failures!) we had a near tie for first place at 230 grams, and we allowed teams to keep working and testing throughout the two-hour lab. What finally won (above) was the result of a quick bit of structural surgery, with a team cutting one leg off of their pyramid to create a true tripod. At 163 grams, nothing else came close, and they were clever enough to wait until time was nearly up to test it. Noting that the iterative process had cut about 70% of the weight from the initial round of prototyping, we suggested that there were lessons here not only about long spans, but also about adopting a truly experimental process for design; by introducing real competition, we were able to provide an incentive for innovation. By holding the tests in public, the knowledge gained from testing those innovations was diffused throughout the teams, enabling truly iterative testing until the clearly ‘correct’ idea won out. As pedagogical proof, every team in the top five had attended the prototyping session, which meant that they arrived with a clear advantage over those teams testing for the first time.
Beginning this week, I switch from the fifth class in the sequence to the third, which means less exotic topics–instead of truss arches and cable-stayed roofs, we’re going to spend most of our five weeks on basic beam and column theory. But in among the labs on shear-moment diagrams and slenderness ratios there is one open lab period that seems tailor-made for some beam-busting. As Rob’s new book, Structures by Design puts it, “Think, Make, Break, Iterate.” It’s become our version of medical education’s “watch one, do one, teach one,” and I’m convinced it’s the best possible way to build up intuitive knowledge of structural principles…