The Strongest Circular Arch—A Perturbation Solution

Abstract

We consider the problem of determining that shape of circular arch which has the largest critical buckling pressure of all circular arches of given radius, central angle, and volume. The problem is formulated exactly and solved approximately by a perturbation procedure with the corresponding column problem as the fundamental solution. This latter problem was solved exactly by Keller and Tadjbakhsh and Keller. For hinged-hinged circular arches having rectangular cross sections of constant width, the best shaping is found to increase the buckling pressure by approximately 40 percent over that of a uniform arch.