Reliability assessment of reinforced concrete columns based on the P–M interaction diagram using AFOSM

Abstract

This paper presents a new approach for evaluating the reliability index and most probable failure point (MPFP) of a reinforced concrete (RC) column using the advanced first-order second-moment reliability method without Monte-Carlo simulations. The P–M interaction diagram (PMID) is selected as the limit state function of an RC column. The strength parameters of an RC column include the material properties and geometric properties of the cross section of an RC column. The strength and load parameters are considered as random variables. An iterative solution scheme with double iteration loops is adopted for obtaining the MPFP and reliability index. The continuous and differentiable PMID is constructed with discretely defined sampling points of the PMID using the cubic spline interpolation. The sensitivities of the PMID are calculated through the direct differentiation of the cubic spline and sampling points of the PMID. Detailed expressions of the sensitivities of the PMID with respect to the random variables are presented. The validity of the proposed method is demonstrated through a simple rectangular column and the pylon of a real cable-stayed bridge. It is shown that the proposed method yields physically meaningful solutions efficiently for the examples presented.