Volume/thrust optimal shape criteria for arches under static vertical loads

Arches are widely used when large spans are necessary, e.g. to overpass large rivers, and further possess unquestioned aesthetics advantages. Their structural efficiency depends primarily on optimal material exploitation, i.e. minimization of internal stress eccentricity, and on minimization of structural material volume. An efficient structure, under these terms, further requires simpler and lighter scaffolding, contributing in minimizing construction costs. Although arches have millenary use and many researches dealing with this typology are available in literature, there is still scope for design optimization. The proposed study is framed within this context. Investigation is limited to statically determinate plane arches under vertical load. The problem of finding the profile of an equal strength catenary subjected to its self-weight is spread out to the case of an inverted catenary of equal strength under its self-weight and an external constant load. In the first optimization step, constant normal stress is imposed at all sections, to maximize material exploitation, and the resulting arch centerline shape is computed in closed form. In the second step, the ensemble of foundations and arch is considered and optimized, taking the linear combination of arch weight and thrust as objective function. The linear combination is dependent on a single variable, and minima of the objective function (i.e. optimal geometric shape parameters) are computed and charted to be simply used in the design process.