Optimization of flat arches under uniformly distributed load considering in-plane buckling

Abstract

The optimization of shallow two hinged arches is studied in this work. Specific problem investigated are sinusoidal or segmental arch, with an arbitrary section, under uniformly distributed load. Arches resist general loading by a combination of axial compression and bending actions and an arch which is braced by lateral restraints that prevents lateral buckling, nevertheless, may still suffer in-plane buckling. Shallow arches stability is studied under an energy method to establish the critical load, considering the shortening of its center line, but simplifying the curvature change. Approximations to the symmetric buckling of shallow arches are demonstrated. Analytical solutions for buckling loads and the compressive stress on the section under an uniaxial stress state are reviewed and used for efficiently evaluation of the constraints in the optimization problem. In a volume minimization model of the arch the design variables are continuous, consisting of the section dimensions and arch rise. Three types of sections are investigated: circular, rectangular and I-shaped. Others shapes can be considered but constraints to prevent local buckling must be applied, as in the case of the I-section. Results for the optimal section dimensions and arch rise are obtained using Microsoft Excel's Solver tool.