07.06: Numerical determination of plastic collapse loads for sections under concentrated transverse forces

Structural steel design codes generally use design methods requiring the determination of two key reference loads: (i) the plastic collapse load and (ii) the elastic buckling load. Using these two key reference loads, the element slenderness can be determined and member resistances can be obtained through buckling curves. Both of these reference loads can be estimated either through simplified analytical expressions or numerical analysis. In the cases of uniform loading, regular geometry and straightforward boundary conditions, the former approach is well suited, while for problems leading to complex non-uniform stress distributions, such as members under concentrated transverse loading, numerical solutions are often necessary. Using numerical methods, the plastic collapse loads can be obtained through Materially Nonlinear Analyses (MNA). However, since the development of a plastic collapse mechanism brings about large localised strains and extensive plasticity, a MNA can abort prematurely due to its failure to satisfy the necessary convergence criteria or the obtained load-deformation path can flatten out only after unrealistically large deformations, resulting in misleading predictions of the plastic collapse loads. In this paper, an extrapolation technique is recommended for the determination of plastic collapse loads from MNA for plate elements and cold-formed sections under concentrated transverse loading. The proposed procedure is based on the Modified Southwell (MS) Plot, originally proposed for the identification of critical loads.