Fluid pressure on unanchored rigid flat-bottom cylindrical tanks due to uplift motion and its approximation

Abstract

As well as the uplift displacement of the tanks, the fluid pressure accompanying the uplift motion of the unanchored tanks has been considered to contribute toward their various damages. Its accurate estimate is indispensable to secure the safety of the tanks at an earthquake event. Assuming the ideal fluid and velocity potential, a mathematical solution for evaluating the fluid pressure on a rigid flat-bottom cylindrical tank accompanying the angular acceleration that acts on a pivoting bottom edge is derived. In actual case scenarios, practitioners should calculate the fluid pressure accompanying the rocking motion of the tank which possesses a crescent-like uplift region in a plan view of the bottom plate. To satisfy this demand, this paper also proposes an approximation method featuring a rectangular tank with a unit depth off and parallel with the center line of the rigid flat-bottom cylindrical tank, denoted a slice model. The mathematical solution is given by the explicit function of aspect of the tank but is a Fourier series. It well converges with a few first terms of the Fourier series. A comparison with the FE analysis with a three-dimensional half tank model reveals the analytical accuracy for evaluating values of the fluid pressure on the rigid flat-bottom cylindrical tank. In addition, the slice model reasonably approximates the values of the fluid pressure on the shell off and parallel with the center line of the rigid flat-bottom cylindrical tank. For designer’s convenience, diagrams that depict the normalized fluid pressure are also presented. The curved component of the fluid pressure distribution increases as the tank becomes taller or the azimuth angle approaches to 0 or 180 degrees.