A reformulation of the stochastic load combination problem. (July 2021)

• Record Type: Journal Article
• Authors: Pandey, Mahesh D.; van der Weide, J.A.M.; Manzana, N.
• Is Part Of: Structural safety. Volume 91(2021)
• Publication Date: 2021-07
• Subjects: Stochastic renewal process -- Pulse and shock processes -- Load combination -- Distribution of maximum load -- Turkstra's rule -- Load coincidence method; Structural stability -- Periodicals; Safety factor in engineering -- Periodicals; Reliability (Engineering) -- Periodicals; Constructions -- Stabilité -- Périodiques; Coefficient de sécurité en ingénierie -- Périodiques; Fiabilité -- Périodiques; 620.86
• DOI: 10.1016/j.strusafe.2021.102094
• Languages: English
• ISSNs: 0167-4730

Abstract

Abstract: 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. Highlights: A new formulation of the load combination problem based on the theory of renewal processes. An original solution of the combination of renewal pulse and shock processes. An efficient numerical solution by integral equation method. A comparative evaluation of popular approbations of the load combination problem.