Probabilistic models of combinations of stochastic loads for limit state design

Abstract

When more than one load act on a structure, the maximum intensity of the combined load effect needs to be evaluated. Turkstra's rule is often used in reliability-based limit state design because of its simplicity; however, the approximation is unconservative. This paper presents the theoretical expressions of the cumulative distribution function (cdf) of the maximum intensity during a reference period taking the temporal variation of load intensity into account. Theoretical investigation and numerical examples show that the theoretical expression provides a fairly good estimate regardless of the statistical characteristics of the load processes. To avoid considering time-dependency in determining a design point, it is proposed to consider the intensities of the load processes at the time when the combination takes its maximum value. Based on the observation that the cross section of the joint probability density function (pdf) of these intensities cut by the limit state surface is similar to that of the joint pdf of the basic random variables, the design point is determined in the basic variable space using AFOSM.