Numerical method for the primary torsional capacity of arbitrary steel cross sections considering nonlinear plastic behaviour

Abstract

In structural design, plastic capacities of cross sections are of great importance for evaluating the capacity of steel members. Moreover, when it comes to problems of member stability, states of partial plasticisation are of interest as well. Depending on the cross section geometry and the material law to be considered, the determination can be challenging. This particularly applies to load conditions characterised by shear stress states, as for instance in the case of primary torsion (St. Venant's torsion). Simplifications are therefore often made with regard to the cross section geometry and engineering models are applied if the plastic limit moment of primary torsion Mpl,xp is to be determined. However, numerical methods allow a precise determination of properties and stress distributions of arbitrary cross section. In the present study, corresponding finite element formulations are combined with a plasticity algorithm for torsional analysis considering effects of nonlinear isotropic hardening. The approach approximates the nonlinear material law by a multilinear curve, which is stepwise evaluated based on linear hardening formulations. It allows determining states of partial cross section plasticisation for any strain or deformation state as well as the identification of the plastic limit capacity of the cross section. Results of the implemented algorithm are presented and verified for different common steel profiles showing excellent agreement to comparative studies.