Some concern has been expressed that the load capacity of corner columns might be reduced in fire due to the expansion of unprotected fire-exposed connected beams, even through the columns themselves are protected from fire. A structural analysis program VULCAN has been used to perform a series of parametric studies on corner sub-frames. In order to obtain the best possible representation of the column cross- section, the formulation of beam-column elements was developed to allow the cross- section to be divided into large numbers of segments. The analyses indicate that the existing fire design codes, such as BS5950: Part 8, give an un-conservative result. The finite element method is shown to be capable of modelling this type of sub- frame, but is too complex to be used routinely. As an alternative, a generalised simplified approach to enable a rapid assessment of the sub-frame by hand or spreadsheet calculation has been developed. The results, in comparison with the finite element analyses, give some confidence in the use of this approach. The beam-column elements of the program VULCAN were further developed to model the three-dimensional behaviour of asymmetric steel beams for fire conditions. The general approach, including the principles and details of the modifications to the formulation for asymmetric cross-sections, together with the refinement of the cross- section, are presented. The modified program has been validated by comparison with classical analytical results and test results at ambient and high temperatures. A new generalised beam model has been developed, which can model not only reinforced concrete sections but also steel sections of different shapes including hollow sections, for three-dimensional composite structures at ambient and high temperatures. The method currently includes both geometrical and material non linearities and considers the cracking and crushing of concrete. Several material models have been included, especially for concrete in tension which shows significant effects on the results. The thermal expansion and degradation of both steel and concrete materials with elevated temperatures are also included. The cross- section is divided into an appropriate number of segments so that non-uniform temperature profiles, and variations of strain and stress across the section, can be represented with more accuracy. The formulation is used to further develop the program VULCAN, and is then validated by comparison with theoretical and experimental results.