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What is the physics behind an arch?


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March 21, 2008 8:43AM

Picture the arch. It resists the pull of gravity. The force of gravity is a constant, and it wants to pull the center of the span down. But the materials distribute some of the force sideways. The sides of the arch support much of the weight of the structure, but they have to be designed to resist being "pushed apart" by the arch as well as to hold it up. Take two sticks and a smooth table top. Stand the sticks a little apart and tip them to where the tops touch. Put just a bit of tape there to keep the sticks touching and pushing on each other. With a smooth table and a goodly space between the bottoms of the sticks, the sticks will slip sideways and fail to stand up. That's the "down" force of gravity acting along the stick. It pushes down, and the sticks resist. And some of the force is vectored "along" the stick and causes an "outward" push. It's an experiment that shows the "down and outward" force on the sticks, and the arch experiences similar forces. There are some other considerations that must be looked at in arch construction, but those two are the primary ones. It is the "down" and the "out" forces that are greatest in the arch. Links are provided to relevant Wikipedia posts. One is to a nice drawing, and the second is to the article on the arch. If pictures are worth a thousand words, there is a book here. And there are arches that have been standing for a thousand years, too!