Uniform shallow arches of minimum weight and minimum maximum deflection

Abstract

The present paper serves several purposes. Besides presenting closed-form solutions to the problems in the title, it serves to illustrate the deduction of existence and nonexistence of solutions in this context, to point out some of the more or less known inadequacies of these design criteria and, finally, to provide the basis for a comparison with the natural structural shapes of shallow arches presented in another reference. The minimum weight and minimum maximum deflection criteria both yield, as one possible optimal design, an arch on the verge of failure. This is consequence of the fully-stressed design aspects of these criteria which, in this case, correspond to the maximum possible axial load. However, meaningful results are obtained for a prescribed axial load in the minimum weight problem and for a given weight in the minimum of the maximum deflection problem.