Plastic collapse analysis of slender circular tubes subjected to large deformation pure bending

This paper presents a plastic mechanism analysis for thin-walled circular hollow section (CHS) tubes deforming in a multi-lobe or diamond collapse mode under large deformation pure bending. The fold formation process was such that the shell curvature flattened on the compression side transforming into a definite number of flat triangles attached to each other. The collapse proceeded progressively by folding about the base and sides of these triangular planes and over traveling hinge lines. The collapse mechanism was similar to the diamond crush mode. An existing kinematic model for an axially compressed thin-walled circular tube was modified to predict the collapse curve of a thin-walled tube under bending. Inextensional deformation and rigid plastic material behaviour were assumed in the derivation of the deformation energy. Ovalisation was observed during the test and its deformation energy was determined and found significant. An expression for the plastic collapse moment was obtained by equating the total energy absorbed in bending, rolling and ovalisation to the external work carried out during a given cycle of deformation. Comparisons of the predicted post-buckling moments and slopes of the collapse curves with those obtained from experiments carried out by the authors on cold-formed circular hollow sections show very good agreement.