Stochastic finite element methods for the reliability-based fire-resistant design of structures

A reliability-based design methodology is needed to reconcile the uncertainty and ensure a consistent level of safety is provided in engineered structural fire designs. This paper presents the application of two stochastic finite element methods, namely the First- and Second-Order Reliability Methods and Monte Carlo Simulation, to the design of structures subjected to fire. An example of a protected steel column subjected to natural fire is presented. A numerical investigation of the evolution of the failure probability with time demonstrates that analytical reliability methods improve the efficiency of the simulation, although significant errors arise when treating the fuel load as a random parameter. Further analysis reveals a “kink” in the response surface due to the lack of sensitivity to the fuel load during the heating phase of fire development. Utilization of an alternative fire model overcomes this limitation