In-plane nonlinear analysis and buckling of tied circular arches

A nonlinear theory is developed in this paper to investigate the elastic in-plane buckling of shallow tied circular arches under uniformly distributed radial loading, in which the effects of the prebuckling deformation and geometric nonlinearity are included. Prescriptive formulae for the elastic buckling loads of tied arches are derived, as well as the critical stiffness that delineates between the possibility that the arch will buckle, or that it will not buckle, in its plane of loading. The relationship between the buckling load and a modified slenderness parameter of the arch is also discussed. The paper also includes the results of two short-term tests undertaken on shallow reinforced concrete tied arches, and the solutions are also analysed using the well-known ABAQUS software. The consistency of the critical loads and the load versus deflection responses demonstrates the accuracy and practicability of the analytical results derived in the paper.