Law, J. R (1997) Time varying probability of failure of steel floor beams subjected to real fire. Research Master thesis, Victoria University of Technology.

Abstract

A model for estimating the time-dependent reliability of steel beams under real fire conditions has been developed. It gives a more rational basis than time of failure modelling does for design. From risk modelling, some small resistance time from the probabilistic distribution times of failure can be deduced, which gives an acceptably small risk of failure. Time of failure modelling by itself can only give the mean time failure which could lead to excessive risk if the variability of time of failure is large. The model comprises submodels for fire severity, heat transfer, mechanical properties, loads, structural analysis and reliability. Simple submodels have been adopted commensurate with the level of accuracy of other models in fire safety engineering. The submodel for real fire severity is Lie's. Heat transfer submodels have been adopted for three and four sided exposure and have been taken from work by the European Regional Organisation for Steel Construction and the French Technical Centre for Steel Construction. Three sided arises when the beam supports a concrete slab. The mechanical properties submodel was derived from an empirical fit to available test data. It gave better results than the current model in AS4100. It is appropriate for the model but is too complex for replacing the model in AS4100. The structural model four sided exposure was developed from simple plastic theory. For three sided exposure, discrete element analysis was adopted. The load submodels were lognormal for dead load and Weibull arbitrary point in time values for live load. The Monte Carlo method was adopted for the reliability submodel. The overall model was used to obtain the following sensitivities. An increase of lOkg.m-2 in fire load density can increase the risk of failure by 40%. In relation to the sensitivity of risk to ventilation, a reduction of the opening factor from 0.12 to 0.04 m0.5 increases the risk of failure approximately 200 times. Doubling the insulation thickness reduces the risk of failure by a factor ten. Increasing the live load has less effect on the risk of failure than increasing the dead load. If the load present predominantly live load, there is much less risk of failure than if the load is predominantly live load. Four sided exposure has ten times the risk of failure compared with three sided exposure. Accepting larger proof strains reduces the risk of failure; for example, increasing proof strain from 0.2% to 1% reduces the risk of failure by 50%.

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