The analysis of building frames under thermal loading is an important task in structural engineering. Two types of thermal effects need to be considered, namely:

1. Thermal effects under normal daily temperature ranges, and

2. Thermal effects under elevated temperatures, such as fire conditions.

In the first case, the material properties can be considered to be essentially unchanged due to the temperature changes. However, thermal effects may still have detrimental effects on a structure due to the expansion and contraction of the members. An example of this is thermal buckling, such as in the case of railway tracks under high daily temperatures. The second case is more complicated because the material properties can no longer be considered constant. In particular, steel loses both rigidity and strength at high temperatures, and any analysis under these conditions must take these effects into account.

Linear analysis is generally inadequate in both cases, and nonlinear analysis is essential to correctly model the behaviour of the structure. Various nonlinear models are used in practice and these models usually involve some form of approximation of the nonlinear effects. In this case, it is not often clear what effects the approximations have on the analysis. Hence, it is important to study the effects of the approximations on the analysis, since significant differences in results are possible using different approximations.

Therefore, this paper details a general approach for the nonlinear analysis of steel frames under thermal loading. In particular, we consider the role of approximations in the governing equations of the structure and the effects of the changes in material properties at high temperatures. We start with a fully nonlinear model for the member behaviour and then systematically consider the effects of simplifying approximations on the results of the analysis. The nonlinear and simplified models are combined with the changes in the material properties to explore the failure condition of a structure, which we conservatively assume occurs at the point of first yield, at elevated temperatures.

Several examples are given in the paper that demonstrate the various effects of the simplifying approximations on the results, and recommendations are provided to accurately deal with this class of problems.