Volume optimization of end-clamped arches

Abstract

Even if arch arised as structural system more than two thousand years ago, this structural typology is still not widely diffused and is mainly adopted when large spans have to be covered. The structural efficiency of arches primarily depends on optimal material exploitation, i.e. minimization of internal stress eccentricity that reduces structural material volume and weight. An efficient structure, under these terms, implies simple and light scaffolding, so contributing in minimizing construction costs. Although very abundant knowledge and literature on arches, there is still scope for design optimization. This study is framed within this context and deals with the structural analysis of end-clamped plane circular arches under uniformly distributed vertical load and self weight. In the first step, the analytical solution of arch static and kinematic behaviour is derived by the force method. In the second step, the arch shape is optimized, by assuming the arch volume, and thus the weight, as objective function. Finally minima of the objective function (i.e. optimal geometric shape parameters) are computed and charted in order to be used for practical purposes.