Basis and application of simple interaction formula for steel frames under fire conditions

For a long time, the Rankine method has been applied successfully to steel columns and frames subjected to increasing loads but maintained at constant ambient temperature. This paper extends the Rankine formula to frames under fire conditions. An original theoretical derivation of the formula, which is general and based on the virtual work principle, is provided in this paper. A simple expression has also been derived for the buckling coefficient of frames under fire conditions, which takes the deterioration of steel properties at elevated temperature into consideration. Comparison of test results shows that the Rankine formula yields very good predictions of critical temperatures of frames, with a mean value of 1.01 and a coefficient of variation of 9.2% for a total of 18 frames. Most importantly, it is shown that the fire resistance of steel frames can be obtained from the conventional frame analysis performed at ambient temperature.