Elastic Flexural-Torsional Buckling and Postbuckling of Arches subjected to a Central Concentrated Load

Abstract

This paper investigates the elastic buckling and postbuckling behaviour of arches that are subjected to a central concentrated load, using a finite element model developed by authors. Comparisons with existing experimental and analytical results demonstrate that the model is effective and efficient in terms of accuracy, the number of elements needed for convergence, and the ability to perform a postbuckling analysis. It is found that under a central concentrated load, the elastic buckling and postbuckling behaviour of a simply supported arch is similar to that of an arch in unform bending or in uniform axial compression. The slenderness of a simply supported arch has almost no effect on its buckling behaviour. However, the slenderness of all but very stocky pin-ended arches has significant effects on their buckling behaviour. For shallow pinended arches, the elastic flexural-torsional buckling load is reduced significantly by the large axial compression developed in the arch prior to buckling. As the included angle increases, the buckling load of the pin-ended arch decreases significantly until a minimum value of the buckling load is reached, and then increases. The increase of the buckling load stops at a certain value of the included angle, and thereafter the buckling load steadily decreases with the increase of the included angle. For stocky pin-ended arches, the buckling load decreases steadily with the increase of the included angle. The slenderness of deep pin-ended arches has a very small effect on their buckling behaviour. There is a substantial postbuckling response for shallow pin-ended arches, due to relaxation of the axial compression after buckling. The slenderness of fixed arches has a significant effect on their buckling behaviour. The large axial compression developed in shallow fixed arches reduces the elastic flexural-torsional buckling loads significantly. Shallow fixed arches also have a substantial postbuckling response due to the relaxation of the axial compression and the moment redistribution in the postbuckling range. For slender fixed arches with moderate or large included angles, four inflexion points can be developed in their deformed profile, which reduces their effective length and leads to a significant increase of their flexural-torsional buckling load. After buckling, a redistribution of bending moment takes place which increases the moments at the supports and decreases the moment at mid-span, thereby increasing the postbuckling strengths. For stocky fixed arches, however, only two inflexion points can be developed in their deformed profile prior to buckling and the buckling load decreases slightly as the included angle increases.