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A Numerical Approach for Plastic Cross‐Sectional Analyses of Steel Members

Global structural analyses in civil engineering are usually performed considering linear‐elastic material behavior. However, for steel structures, a certain degree of plasticization depending on the member classification may be considered. Corresponding plastic analyses taking material nonlinearities into account are effectively realized using numerical methods. Frequently applied finite elements of two and three‐dimensional models evaluate the plasticity at defined nodes using a yield surface, i.e. by a yield condition, hardening rule, and flow rule. Corresponding calculations are connected to a large numerical as well as time‐consuming effort and they do not rely on the theoretical background of beam theory, to which the regulations of standards mainly correspond. For that reason, methods using beam elements (one‐dimensional) combined with cross‐sectional analyses are commonly applied for steel members in terms of plastic zones theories. In these approaches, plasticization is in general assessed by means of axial stress only. In this paper, more precise numerical representation of the combined stress states, i.e. axial and shear stresses, is presented and results of the proposed approach are validated and discussed.