Elastic flexural-torsional buckling of continuously restrained arches

Arches are often connected to other members which influence the structural behaviour of the arch. These members induce restraining actions during flexural-torsional buckling which restrict the buckled shapes of the arch and may significantly influence its buckling response. This paper uses an energy method to study the elastic flexural-torsional buckling of continuously restrained arches of doubly symmetric open thin-walled cross-section in uniform bending and in uniform axial compression. Closed form solutions for the flexural-torsional buckling moment of restrained arches in uniform bending and for the flexural-torsional buckling load of restrained arches in uniform axial compression are obtained. It is found that the elastic continuous restraints are more effective in increasing the buckling resistance for arches with a large included angle than for arches with a small included angle. The first buckling mode may not correspond to the lowest buckling moment or load for arches restrained by minor axis rotational or lateral-translational restraints. It is also found that the number of half sine waves corresponding to the lowest buckling moment or load increases with the stiffness of the restraints. For restrained arches in uniform axial compression, when the restraining stiffness exceeds a limiting value, the buckling mode may change from flexural-torsional to torsional