One-Dimensional Fourth-Order Moment Approximation to Reliability Analysis of Structural Systems

Abstract

This paper proposes a method to evaluate the reliability of structures by using moments up to the fourth-order, which are the minimum number of terms reflecting the shape of probability distributions. The one-dimensional cumulative distribution function (c.d.f.) is asymptotically expanded into Edgeworth's series expressed in terms of moments up to the fourth-order. The expanded c.d.f. gives a negative value at the tail of the distribution for some cases of the combination of skewness and kurtosis. Modification is made in the approximation formula to remedy this draw-back, thus making it possible to evaluate any general non-Gaussian c.d.f.
The proposed method is applied to the reliability analysis of typical frame structures where the random variables follow non-Gaussian probability distributions. It is shown that the proposed method is very effective for evaluating quantitatively the effects of probability distributions on the resulting structural reliability or failure probability.