On the fire resistance of structural steel elements derived from standard fire tests or by calculation

Due to high costs, a fire resistance test of a load-bearing structural element is usually limited to one test specimen — in a few countries, to two test specimens. Accordingly, there are no possibilities of evaluating the test results statistically.For a single test specimen, the actual quality of the structural material represents a random sample from a wide variety. This applies also to the initial imperfections of the structural elements. In consequence of this, a standard fire resistance test is generally carried out on a test specimen with a load-bearing capacity which is greater — most often significantly greater — than the load-bearing capacity related to the characteristic values of the mechanical material strength and of the imperfections of the structural member. In current practice, no corrections of the test results with respect to this are made.In a conventional analytical design, a determination of the load-bearing capacity of a structure at room temperature conditions is based on the characteristics values of the strength and imperfections. Extended to a structural fire engineering design, this procedure will give an analytically determined fire resistance of a load-bearing structural element which is lower — normally essentially lower — than the corresponding value derived from a standard fire resistance test.Available methods for a simplified calculation of the temperature of fire exposed steel structures are, as a rule, based on the assumption of a uniformly distributed temperature structure at each time of fire exposure. The ECCS Recommendations for an analytical design of steel structures exposed to a standard fire follow this kind of approach. For certain types of steel structures, for example, beams with a slab on the upper flange, a considerable temperature variation arises over the cross section as well as in the longitudinal direction during a fire resistance test. A simplified, analytical method, which neglects this influence, gives a further underestimation of the fire resistance in relation to the corresponding result obtained in a standard fire resistance test.The described discrepancies between an analytical and an experimental determination of the fire resistance are further discussed and analysed in Sections 2 and 3, with particular reference to different types of steel structures. The discussion is focussed on the loading and restraint conditions, the scatter of material properties and geometrical imperfections, and the temperature variation over the structure or structural element. The discussion is summarized in Section 4 and alternative methods of correction are outlined briefly for obtaining an improved consistency between the analytical and the experimental approaches.In Section 5, one of these methods is further developed to a design basis which can be applied easily in practice. Principally, the method is characterized by a correction of the analytically determined load-bearing capacity, based on the characteristic value of the structural material properties, the characteristic value of the imperfections of the structure, and a uniformly distributed steel temperature across and along the structure. Two different sequences of the design procedure are dealt with, defined according to Figs. 10 and 11. The resultant correction factors, ? and κ, belonging to the respective sequences, are given by Figs. 8 and 12 for columns, isostatic beams, and hyperstatic beams. The straight line curves in Figs. 9 and 13 show corresponding, simplified relationships for the ? and κ factors.The derived method of correction must be characterized as an approximate approach. This is in consequence of the present state of knowledge, which does not allow a solution of high accuracy. The task to develop a correction procedure which leads to improved consistency between an analytically and an experimentally determined fire resistance, should also be seen in the context of the inadequate reproducibility of the standard fire resistance test.