Reliability based determination of material partial safety factors for cast iron beams in jack arched construction exposed to standard and natural fires

Cast iron beams were extensively used in many 19th century structures, especially in fireproof flooring systems (such as jack arch). Many such structures are still in use today and it is important that they fulfil the current requirements of fire resistance when there is a change of use. These structures are out of scope of modern design codes and old design codes do not provide guidance for fire resistance design. Furthermore, cast iron is a brittle material weak in tension, and there are many uncertainties in its mechanical properties at ambient and elevated temperatures due to material flaws. It is necessary to quantify the probability of structural failure and to introduce safety factors to reduce the probability of structural failure in fire to an acceptable level. This paper presents the results of a detailed study whose purpose is to derive appropriate safety factors to achieve different levels of reliability, for fire safety design of cast iron beams. In this study, a fibre analysis method has been used to calculate the moment capacity of four different types of cast iron cross section. Using randomized stress-strain-temperature relationships, based on variability of the different governing parameters (under tension: maximum stress, 0.2% proof stress, corresponding strains at maximum stress (strength) and failure; under compression: Young's modulus, proportional limit, 0.2% proof stress and the maximum stress), the probability distribution of moment capacity has been calculated. Based on the criterion of cast iron beam failure not exceeding probabilities of 10⁻¹, 10⁻² and 10⁻³, material safety factors of 1.5, 3.0 and 5.0 respectively have been obtained.