NATURAL APPROACH FOR THIN-WALLED BEAM-COLUMS WITH ELASTIC-PLASTICITY

In a realistic analysis of thin‐walled steel frames the warping of beam‐columns of open cross‐section must be considered. To model the behaviour of these structures up to collapse load, the plasticity of the material also has to be included in the analysis. This work presents the derivation of a new finite element for three‐dimensional non‐linear analysis of steel frames with bi‐symmetrical cross‐sections that models warping and elastic‐plasticity. The displacement field is described by the Principle of Sectorial Areas and is modelled with Hermitian functions. For the material non‐linearity the Incremental Plasticity Theory in a concentrated plasticity model has been used. The yield surfaces based on the natural stress resultants which include torsion and bimoment are used in the formulation of the element. The matrices of the proposed element are derived explicitly and implemented in a computer program which uses the Natural Approach. The implemented stress recovery process is insensitive to rigid‐body motions. The accuracy of the finite element and the efficiency of the implementation are illustrated through examples. Copyright © 1990 John Wiley & Sons, Ltd