FYI -- The Gateway Arch, as does any hanging chain, has a horizontal force component which has to be handled by the foundations of the arch. The concept of using hanging chains with weights attached goes back to Hooke, at least, and for some strange reason this concept of the equivalence of chains and arches through this inversion is called "funicular" by structural engineers. So if you want to know more, include "funicular" in your Google searches. Osserman, Robert. "Mathematics of the Gateway Arch". Notices of the AMS 57, 2, Feb. 2010, 220-229. http://www.ams.org/notices/201002/rtx100200220p.pdf Also, Osserman, Robert. "How the Gateway Arch Got Its Shape": www.msri.org/people/staff/osserman/papers/NNJ_v12n2_Osserman_pp167-189.pdf At 08:38 AM 11/12/2012, Cordwell, William R wrote:

Isn't there a shape that has purely compressional tension? The St. Louis arch? It does not have a vertical tangent, as you note.