Computationally efficient estimation of the probability density function for the load bearing capacity of concrete columns exposed to fire

Concrete columns are critical for the stability of structures in case of fire. In order to allow for a true Performance Based Design, the design should be based on considerations of risk and reliability. Consequently, the probability density function (PDF) which describes the load-bearing capacity of concrete columns during fire exposure has to be assessed. As second order effects can be very significant for columns, traditional probabilistic methods to determine the PDF become very computationally expensive. More precisely, for most current numerical calculation tools (e.g. Finite Element), the computational requirements are so high that traditional Monte Carlo simulations become infeasible for any practical application. In order to tackle this, a computationally very efficient method is presented and applied in this paper. The method combines the Maximum Entropy Principle together with the Multiplicative Dimensional Reduction Method, and Gaussian Interpolation, resulting in an estimation of the full PDF requiring only a very limited number of numerical calculations. Although the result is necessarily an approximation, it gives very good assessment of the PDF and it is a significant step forward towards true risk- and reliability-based structural fire safety.