Design of steel arches against in-plate instability

Abstract

Steel arches may be subject to instability caused by in-plane buckling or out-of-plane flexural torsional buckling. Steel arches are deployed in engineering structures over a long period of time, yet the analysis of their in-plane behavior is quite complex and surprisingly little understood. This chapter addresses the in-plane buckling of flat steel arches, where the method of virtual work is used to determine the buckling loads of circular arches with either pinned or fixed ends, and subjected to a uniform loading distributed radially around the arch, and to a point load at the crown. The formulation includes the nonlinear prebuckling configuration of the arch in deference to the classical stability formulations that treat the prebuckling response as being linear. Design formulae for the elastic buckling loads of arches are derived, as are the limits of the arch modified slenderness that delineates between antisymmetric and symmetric (snap-through) buckling modes. The analytical treatment of buckling considered in the chapter produces design equations for the elastic in-plane buckling of shallow arches.