Elastic flexural-torsional buckling of circular arches under uniform compression and effects of load height

A circular arch with in-plane radial loads uniformly distributed around the arch axis is primarily subjected to uniform compression. Under this action, the arch may suddenly deflect laterally and twist out of the plane of loading and fail in a flexural-torsional buckling mode. In most studies of the elastic flexuraltorsional buckling of arches under uniform compression, the directions of the uniformly distributed loads are assumed to be unchanged and parallel to their initial directions during buckling. In practice, arches may be subjected to hydrostatic or to uniformly distributed directed radial loads. Hydrostatic loads always remain normal to the tangent of the deformed arch axis, while uniformly distributed directed radial loads always remain directed toward a specific point during buckling. These uniform radial loads may act at a load height, such as at the top surface of the cross-section. In this case, the radial loads produce an additional torsional moment during buckling which affects the flexural-torsional buckling of the arch. This paper uses both virtual work and static equilibrium approaches to study the elastic flexural-torsional buckling, effects of the load height on the buckling of circular arches under uniform compression (that is, produced by uniformly distributed dead or by directed radial loads), and closed form solutions for the buckling loads are developed.