Second mode sloshing motion induces the vertical out-of-plane deformation of deck plate in single deck floating roof (FR) cylindrical storage tanks. This vertical deformation tends to shrink the deck plate in horizontal direction, causing elliptical deformation of pontoon. In order to evaluate seismic stress caused by the second sloshing mode, the relation between out-of-plane vertical deformation of deck plate and the radial shrinkage of pontoon is required. In this study, a simple analytical approach is proposed for calculating the shrinkage of the pontoon. The numerical analysis is also performed for five tanks with various dimensions to assess the effectiveness of introduced new method. The accuracy of proposed formulation is confirmed by comparing its results with the results of both numerical analysis and available experimental measurements. Despite existing empirical formula, geometric characteristics of considered tanks are involved in proposed formulation and it is shown that final relationship could be utilized for various ranges of tank dimensions without scaling or unit limitation. It is also found from the results of numerical analysis that the dynamic characteristics of sloshing modes are not considerably affected by the presence of floating roof.

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