Consistent virtual work approach for the nonlinear and postbuckling analysis of steel frames under thermal and mechanical loadings

The aim of this paper is to provide a consistent virtual work formulation for the nonlinear and postbuckling analysis of steel frames at high temperatures. Central to this study is the derivation of the virtual work terms for the thermal stage, in addition to those for the loading stage, based on the updated Lagrangian formulation. The incremental stiffness equation derived for the beam element, considering both the geometrical and thermal effects, is qualified by the rigid body test. The generalized displacement control (GDC) method is adopted as the path-tracing scheme for postbuckling response. Eurocode-3 reduction factors and transformed section method are both adopted for steel I-sections. Two loading cases are studied. For structures loaded gradually under constant temperature, the critical or ultimate loading strength is obtained from the load-deflection curve. For structures heated gradually under constant loading, the critical or maximum temperature that can be sustained by the structure is computed. Conclusions are drawn for the examples studied in this paper.