Fatigue Reliability of Parallel Member Systems

A method is developed for calculating the probability of progressive collapse due to fatigue for structural systems in which members are connected in parallel and for parallel member systems connected in series. Formulation of the method is “exact” and is based on the assumptions of equal member load sharing and identically distributed fatigue lives. Numerical integration is used to evaluate the probabilities that also include the effect of statistical correlation between the fatigue lives of different elements. An expression to quantify the degree of correlation is developed. The method is applied to systems of up to eight parallel members, with each member consisting of an arbitrary number of joints of equal fatigue life connected in series. The resulting probabilities are compared to a previously published progressive collapse study, which used a Monte Carlo simulation technique. Insight is provided concerning the importance of correlation effects in systems fatigue analysis. The method can be useful in fatigue design criteria development, since it relates the reliability of an individual element to the reliability of the complete system comprised of the elements. Because the method is “exact,” it can be used as a good test case for future work in the development of system reliability methods for more general applications.