Flexural–torsional buckling of fixed steel arches under uniform bending

This paper develops a closed-form solution for the elastic flexural–torsional buckling of a laterally fixed steel circular arch that is subjected to uniform bending. The formulation makes recourse to an orthogonal rotations matrix in order to derive the finite strains and the energy equation for buckling. Whilst the flexural–torsional buckling of pinned arches has received some degree of treatment in the literature, it appears that the flexural–torsional buckling of fixed arches has not been reported openly. The buckling solutions are very different from those of pinned arches, and significantly they illustrate that the concept of an ‘effective length’ approach, that is often useful for determining the buckling response of straight beams or columns, is not applicable for the flexural–torsional buckling of arches. The ramifications of this observation are that design procedures for the out-of-plane buckling of pinned arches cannot be used as a basis for design procedures for fixed arches.