Elasto-plastic buckling and postbuckling of arches subjected to a central load

Abstract

This paper presented a rational finite curved beam-element model for 3D nonlinear elasto-plastic analysis of arches. The finite element model incorporates the effects of large twist rotations of the cross-section and has consistent sampling scheme of sampling points over the cross-section and so it can perform the elastic and elasto-plastic flexural–torsional buckling and postbuckling analysis of arches in combined bending and compression actions. Elastic and elasto-plastic flexural–torsional buckling and postbuckling behaviour of arches that are subjected to a central concentrated load has been investigated using the rational finite element model. It has been found that the slenderness, included angle, and the torsional parameter of an arch play important roles in the elastic and elasto-plastic buckling. In addition, the number of the inflexion points is important for the elastic and elasto-plastic buckling of fixed arch. Yielding is a significant factor for the elasto-plastic buckling and postbuckling behaviour. When the included angle of a stocky arch is not large, its elasto-plastic buckling load is much lower than its elastic buckling load. When the included angle a stocky arch is large, the end support condition plays an important role in the buckling and postbuckling behaviour of the arch. The elasto-plastic buckling load of a stocky pin-ended arch with a large included angle is equal to its elastic counterpart. The elasto-plastic buckling load of a stocky fixed arches with a large included angle is lower than its elastic counterpart. For a slender arch, its elasto-plastic buckling load is also equal to its elastic buckling load. In general, the elasto-plastic postbuckling load carrying capacity of an arch decreases when the arch continues to deform while its elastic postbuckling load carrying capacity can increase. For slender shallow arches, the elastic postbuckling response is stiffer because of the relaxation of axial load and moment distribution.