This work aimed to analyze the reliability of a steel hall that was recently erected in central Poland subjected to dynamic wind excitation using the stochastic finite element method. Reliability analysis was completed using the relative entropy concept delivered by Bhattacharyya and contrasted with the first-order reliability method recommended by the engineering design codes. Bhattacharyya probabilistic relative entropy was additionally rescaled in this study to fit the demands and recommended admissibility intervals given in Eurocode 0. The finite element method study was carried out thanks to a discrete model created in the system ABAQUS 2019, while all further statistical and probabilistic computations were programmed and completed in the symbolic environment of MAPLE 2019. Contrary to most engineering analyses in steel structure areas, this study included the important warping effect while designing the hall ridges and the purlins. Dynamic structural responses were determined via the Hilber-Hughes-Taylor algorithm and their series were numerically obtained for a series of input uncertainty parameters representing several mechanical and environmental quantities. The generalized 10th order iterative stochastic perturbation technique was contrasted in this context with statistical estimators from the Monte Carlo simulations and numerical integration resulting from the semi-analytical approach. The key research finding of this study was an extremely good coincidence between the FORM indices and the rescaled relative probabilistic entropies for the given stochastic excitations, which additionally did not depend on a choice of one of the three proposed numerical approaches.

An efficiency of the generalized tenth order stochastic perturbation technique in determination of the basic probabilistic characteristics of up to the fourth order of dynamic response of Euler-Bernoulli beams with Gaussian uncertain damping is verified in this work. This is done on civil engineering application of a two-bay reinforced concrete beam using the Stochastic Finite Element Method implementation and its contrast with traditional Monte-Carlo simulation based Finite Element Method study and also with the semi-analytical probabilistic approach. The special purpose numerical implementation of the entire Stochastic perturbation-based Finite Element Method has been entirely programmed in computer algebra system MAPLE 2019 using Runge-Kutta-Fehlberg method. Further usage of the proposed technique to analyze stochastic reliability of the given structure subjected to dynamic oscillatory excitation is also included and discussed here because of a complete lack of the additional detailed demands in the current European designing codes.

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