A reformulation of the stochastic load combination problem

This paper revisits a classical problem of stochastic load combination, in which the maximum load generated by combinations of various types of stochastic processes are analysed. This paper takes a fresh look at the combination of a renewal pulse with a homogeneous Poisson shock process, and proves that the problem can be transformed into an equivalent renewal process. This approach leads to an accurate solution for the distribution of maximum combined load in the form of an integral equation, which can be solved by a trapezoidal integration scheme. The proposed solution is accurate for all small and large load levels and time intervals, since this approach does not rely on any asymptotic arguments. This paper also analyses various assumptions and relative accuracies of popular approximations of the load combination problem reported in literature. The proposed formulation advances the understanding of the load combination problem and provides an accurate and original solution for an important problem of structural reliability analysis.

Automated summary

This paper revisits a classical problem of stochastic load combination, providing an accurate solution for the distribution of maximum combined load through an integral equation method. The proposed approach is accurate for all small and large load levels and time intervals, without relying on any asymptotic arguments.