Inelastic local and lateral buckling of thin-walled steel members

Abstract

The finite element method has been used to develop a numerical model for simulating the observed behaviour of structural steel members subjected to the large inelastic deformations which may occur during severe earthquakes.. Such behaviour includes interaction between local buckling deformations and Iateral-torsional buckling, with cyclic strength degradation, and the strain hardening behaviour of steel peculiar to cyclic stress reversals. A hybrid thin-walled beam and thin shell finite element model where rectangular shell elements are linked to the thin-walled beam axes was adopted in order to preserve the advantages of a one dimensional beam element. The result is a general open-section thin-walled beam model with local deformations of the cross-section. Large displacements are considered by using a Total Lagrangian formulation with axis updating, second order displacement equations and the semi-tangential definition for moments and finite rotations. The local displacement fields are measured with respect to the convected thin-walled beam axes and use bicubic hermitian functions for the plate bending deformations, with lower order fields for the membrane displacements. In addition to the IocaI buckling thin-walled beam element, a conventional thin-walled beam element and a rectangular shell element with complete bicubic displacement interpolation functions were developed using the same basic formulation. All three elements have been added to the ANSR-III nonlinear finite element analysis program which includes a material constitutive model for cyclic stress-strain behaviour of steel. Other facilities provided by the thin-walled beam elements include residual stresses, initial deflections, eccentric loads and elastic restraints. Several trial analyses of simple problems with known theoretical solutions or previously published results have demonstrated the accuracy of the formulations for a wide range of instability modes. The experimental results for a series of three cyclically loaded steel portal frame knee joints where member local and Iateral-torsional buckling dominated the behaviour, are also presented. Comparisons between a finite element analysis and one of test specimen beams showed that a finite element model using a rather crude discretisation could predict the general behaviour of the real member but further work is needed to improve the ultimate strength and strength degradation predictions.