Reliability assessment of a planar steel frame subjected to earthquakes in case of an implicit limit-state function

Abstract

This study determines the probability of failure of a planar steel frame using a proposed framework and Monte Carlo simulation (MCS) considering the uncertainties of the material and cross-section parameters. A new framework (O-FCD method) is proposed by combining the OpenSees software for structural analysis and the first-order reliability method (FORM) implemented using MATLAB for analyzing the structural reliability to determine the failure probability of a case study structure with the implicit limit-state function. The limit-state conditions of this case study structure are defined by the limitations in two scenarios: the total drift defined as the ratio of the maximum top displacement to the building height of 3%, and the maximum interstory drift of 5%. Both static and dynamic loads are applied to compare the results of the O-FCD method and MCS. The investigations show that the O-FCD method can determine well the probability of failure of this case study structure. The absolute errors of the proposed framework and MCS are slightly different under both static and dynamic loads. In addition, the O-FCD method can solve the computationally expensive part of MCS in the case of a lower failure probability. Finally, the O-FCD method uses the finite central difference method to calculate the gradient vector in FORM numerically. The proposed framework can reach the convergence criteria with numerous random variables compared with a framework using the forward finite difference method.