Generic nonlinear modelling of restrained steel beams at elevated temperatures

This paper presents a novel numerical method to describe the nonlinear behaviour of a restrained steel beam at elevated temperatures, which is based on a non-discretisation semi-analytical formulation of a generic steel cross-section with elastic and plastic parts. The model incorporates moderately large displacement effects as well as material nonlinearity to assess the performance of steel beams exposed to thermal loading in a compartment fire, and it considers the yielding and development of catenary action affects with an increase in the temperature. The effects of the thermal gradient along the length of the beam are considered in the formulation, in which the cross-section is subjected to an arbitrary thermal profile. Degradation of the stiffness and yield strength with increasing temperature is simulated using empirical retention functions given elsewhere, and the technique is shown to be part of the class of boundary value problems in engineering mechanics. The generic technique developed in the paper is shown to agree with solutions given by ABAQUS finite element modelling, and it provides a computationally superior formulation to that of commercial finite element packages, and provides a formulation which may be used as a platform for structural design and evaluation.