Elastic analysis of straight members at elevated temperatures

The inherent expense of conducting full-scale experiments on steel members at elevated temperatures reinforces the need for accurate and reliable theoretical modelling, in order to assess their structural response under fire loading. The behaviour of steel members at elevated temperatures is quite complex and often counter-intuitive, and hitherto advanced finite element packages have been preferred over more generic or analytical solutions. Because of this, the significance of some parameters that influence the behaviour greatly may be lost. This article presents a generic modelling of the behaviour of a restrained beam member in a compartment fire, using the philosophy of a sub-assembly approach in lieu of a global modelling of the structure, which is allowed by the Eurocode standard. The analysis is elastic and therefore ignores yielding and the catenary effects that result at higher temperatures, and is based on the theorems of virtual work which allows for the prescription of governing differential equations of equilibrium and of the static boundary conditions. The equations of equilibrium are solved for some specific cases of restraint, and it is shown how the analytical solutions lead directly to prescriptive modelling of the structural behaviour, and importantly these equations lend themselves readily to codification in fire engineering design.