Generic nonlinear modelling of a steel beam in a frame sub-assembly at elevated temperatures

This paper presents a virtual work formulation that enables the elevated temperature response of a steel beam with translational and rotational restraint, which forms a component of a compartment sub-assembly in a steel frame structure, to be determined in the pre-yielded range of structural response. The differential equations for the temperature-induced transverse and longitudinal deformations are derived, and in particular the static boundary conditions which can sometimes be counter-intuitive in analyses under thermal actions eventuate from the virtual work formulation. In lieu of most advanced finite element packages whose application generally does not permit an overall ‘feeling’ for the underlying structural mechanics, the technique proposed here is generic and leads to solutions in closed form for arbitrary regimes of temperature loading prior to attaining first yield. The technique can further be extended to quantify the post-yield response in a generic fashion. The application of the method is then illustrated with a simple numerical example.