Residual stresses in cold-formed steel sections and their effect on column behaviour

Abstract

The cold-bending operations required in manufacturing cold-formed steel columns have a significant effect on their structural behaviour. This effect has traditionally been assessed using idealized residual stress distributions based on limited laboratory measurements in conjunction with separate specifications of mechanical properties for the flat portions and the corner regions, or using whole section mechanical properties obtained from stub column tests. These conventional approaches are highly empirical and do not provide an accurate description of the co-existent residual stresses and strain hardening of the material arising from the manufacturing process. This thesis is concerned with the theoretical modelling of the manufacturing process of press-braked carbon and stainless steel sections for the prediction of the resulting residual stresses and equivalent plastic strains. The residual stresses in such cold- formed sections are derived from two sources: the coiling, uncoiling and flattening process (referred to simply as the coiling-uncoiling process) and the cold-forming process. A series of analytical solutions are presented in this thesis to predict the residual stresses and the associated equivalent plastic strains in steel sheets as a result of cold bending, covering both processes. These solutions are verified using finite element simulations of cold bending of steel sheets. For the modelling of cold bending of stainless steel sheets, a new stress-strain relationship was established to overcome significant deficiencies of existing stress-strain relationships. On the basis of these analytical solutions, two alternative approaches for the prediction of residual stresses and equivalent plastic strains in press-braked sections are presented and verified: (a) a finite element-based method in which a finite element simulation of the cold-forming process is carried out with its initial state being defined by an analytical solution for the coiling-uncoiling process; and (b) a complete analytical model in which the residual stresses and equivalent plastic strains from both processes are given by analytical solutions. A parametric study employing the finite element-based method was conducted to study the effect of forming parameters on the resulting residual stresses in cold-formed sections. The complete analytical model provides an attractive approach for defining the initial state of a section in a column nonlinear buckling analysis. The thesis next presents an advanced numerical approach to predict the buckling behaviour of cold-formed columns in which the effect of the manufacturing process is explicitly and accurately accounted for. In this approach, the complete analytical model for residual stresses is employed together with an appropriate imperfection model. Using this finite element method, the effect of cold work on buckling behaviour was examined. Based on results from the present study, it can be concluded that the through- thickness variation of residual stresses in cold-formed sections is nonlinear, and thus the traditional assumption of linear variation is inappropriate. The distributions of residual stresses in the flat portions of a cold-formed section are highly dependent on the initial coil diameter of the metal sheet used for fabrication, so very different residual stresses can arise in the flat portions of otherwise identical cold-formed sections as a result of different initial coil diameters, which are unknown to designers and users of these sections. This may have been a major factor responsible for the significant scatter in test load capacities of cold-formed members. It is also shown that whether the buckling strength of a cold-formed column can be enhanced or reduced by cold work is a result of the combined effect of the residual stresses and the equivalent plastic strains in the member, and this effect varies depending on the initial material properties and the forming parameters.