FORM-based structural design parameters considering nonstationary conditions

The reliability-based design of structures based on the first-order reliability method (FORM) offers a method of determining the design parameters of the semi-probabilistic safety concept. If time dependent loads and resistances are considered, the safety verification should cover related effects on the design parameters. In this paper, an efficient approximation method based on the FORM and extreme value theory is proposed, which allows the consideration of several nonstationary time-dependent variables. Next to the time-cumulated failure probability, the proposed method advantageously allows an efficient approximation of the associated design point as well. For this purpose, the parameters of time-cumulative extreme value distributions and their dependencies for all relevant random variables are approximated based on time-interval FORM analyses. The time-cumulated extreme value distributions are represented as mixture distributions whose components correspond to the individual time intervals. The design point associated with the greatest probability density of the multivariate mixture distribution in the failure range is determined by reapplying the FORM. In the present study, the developed method is presented and subsequently applied, validated and discussed based on examples and comparative Monte Carlo simulations.