Optimal Design of Funicular Arches Under Equally Spaced Point Loads for Maximum Buckling Load

Abstract

This paper presents the optimal designs of pinned supported funicular arches under equally spaced point loads for maximum in-plane buckling load. Under such loading conditions, the funicular arch shapes comprise straight arch members between the point loads, that is, following the shape of the bending moment diagram of an equivalent simply supported beam under the same loading condition. Two classes of funicular arch optimization problems are considered herein. The first class of funicular arches imposes a constraint on the cross-sectional area to be uniform throughout the entire arch length. The second class of funicular arches allows the cross-sectional area to be different from one straight arch member to another member. To facilitate the buckling analysis, the Hencky bar-chain model (HBM) is adopted. This discrete structural model simplifies the optimization process as the decision variables are the HBM rotational spring stiffnesses that define the cross-sectional areas and the horizontal force that controls the arch shape. Presented herein are new optimal funicular arch shapes under various numbers of equally spaced point loads. By increasing the number of point loads, the optimal solution approaches the solution of a parabolic arch under a uniformly distributed load.