# Monthly Mechanics: Arches

I like when things balance, and maybe that’s why I’m fond of structural mechanics. We learned last month that some materials work only in tension: the strings and wires that weave together to form cables, ropes, and fabrics. So it’s fitting that there are also materials which work only in compression. These materials include unreinforced concrete, stone masonry, and a lot of alternative building materials like strawbales.

Similarly, just as the smiley shape of a cable carries loads in pure tension, the frowny shape of an arch carries loads in pure compression. An arch is a cable turned upside down.

If you recognize this bridge, you are more than likely a structural engineer. (creative commons – flickr)

It’s not quite a perfect balance, though. Whereas cables bend and stretch and automatically assume the most efficient shape, arches pretty much stay whatever shape you build them. A goal of arch design is to determine the line of pure compression, called the thrustline, and then make sure your stones or concrete completely encase the thrustline.

Thrustlines (dashed) for different load combinations on the same arch.

In fact, there might be many possible thrustlines – the concentrated weight of a heavy truck creates a very different load path from the uniform weight of a big snowstorm – and the designer’s challenge is to encase them all.

Most engineers determine the load paths mathematically, but there’s a cool tactile way to do it, too. Remember how an arch is a cable turned upside down? You can build a model out of cables, placing weights at the same points where your arch will get loaded; the resulting shape (turned upside down) is EXACTLY the shape you should build your arch! The architect Gaudi used this property of cables to build string models of some of his wildest structures, including the Sagrada Familia in Barcelona.