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Elastic Deformation

Part of the APT conference that just ended was the preservation engineering Student Competition, which this year was about masonry arches. See here. The team from McGill University won, but their phase 3 arch – the one they built for load testing at the conference, was able to carry no basically no load but its own weight. The picture above shows the McGill team (in red) with their phase 3 arch at the conference. (Note that all of the teams built much more serious arches at their schools, and all carried significant load before failure.) 

The low capacity of the McGill arch was not a mistake. Three of the four teams had designs that could carry little load, which was the result of the students carefully reading the design spec and figuring out that speed of construction and total arch weight mattered more than carrying capacity. When you optimize for one design criterion, others typically take a hit. The McGill arch was fast to build and lightweight because it was made from foam board.

The video below shows the arch moving under light finger pressure. If you watch closely, you see the joints between voussoirs open up on the outside face between blocks 15 and 16 and on the inside face between the keystone and block 12. Those are characteristic of a classic four-hinge arch failure. It’s just that you don’t normally see them under a few ounces of pressure. The dead load of this arch is so small that those few ounces are a significant percentage of the total load.

One of the issues in physical modeling for structural engineers is that you need to play with the parameters to make things clear. If you build a three-foot-span masonry arch using the same materials that would go into a fifteen-foot-span and with scaled-down geometry, the small arch is proportionally much stronger and stiffer than the large one. This is the scale problem in reverse. If you use a material that is lighter and weaker for a model, you get a more realistic view. In this case, the material and geometry were so much less stiff that the model was less strong and less stiff than its real-life, full-size counterpart.