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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. [ABSTRACT FROM AUTHOR]