On the Optimality Criteria for Archgrids

Abstract

The optimization of an archgrid consisting of a system of parallel arches running in a number of arbitrary directions is presented. It is established that the archgrid must finish with a single middle surface in the optimal solution even though the possibility of separate layers of arches is allowed in the formulation. The possibility of some arches becoming vanishing ones (of zero m cross sections) is also taken into account. It is shown that mean square slopes of vanishing arches are not to exceed unity for any one arch, while those of nonvanishing ones are equal to unity. Implicit in the derivation of these conditions are: (1) The loading system is perpendicular to the reference plane containing the support of all arches: and (2) any one arch is contained in the plane of the loading system, and its reaction component parallel to the reference plane is constant along its entire length. Two examples of optimal shapes of archgrids over square and rectangular domains consisting of arches running in four equally inclined directions are presented.