A branch-switching procedure for analysing instability of steel structures subjected to fire

The paper describes the development of a two-dimensional (2D) co-rotational nonlinear beam finite element that includes advanced path-following capabilities for detecting bifurcation instability in elasto-plasticity of steel elements subjected to fire without introducing imperfections. The advantage is twofold: i) no need to assume the magnitude of the imperfections and consequent reduction of the model complexity; ii) the presence of possible critical points is checked at each converged time step based on the actual load and stiffness distribution in the structure that is affected by the temperature field in the elements. In this way, the buckling modes at elevated temperature, that may be different from the ones at ambient temperature, can be properly taken into account. Moreover, an improved displacement predictor for estimating the displacement field allowed significant reduction of the computational cost. A co-rotational framework was exploited for describing the beam kinematic. In order to highlight the potential practical implications of the developed finite element, a parametric analysis was performed to investigate how the beam element compares both with the EN1993-1-2 buckling curve and with experimental tests on axially compressed steel members. Validation against experimental data and numerical outcomes obtained with commercial software is thoroughly described.