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
flexural-torsional 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.
