Analysis of Tank Rocking Motion Based on a Spring-Mass-Rigid-Body Combined Model and Magnification Factor

Abstract eng:
For the unanchored flat-bottom cylindrical tanks located in the seismically active area, uplift of the tank bottom plate is inevitable. This paper proposes the use of a mechanical model consisting of a spring-mass-rigid body combined system for analyzing the seismic response of the unanchored flat-bottom cylindrical tank that is set on the almost rigid foundation, pivots on either bottom edge and has a crescent-like uplift region of the tank bottom plate. Since its equation of motion naturally incudes interaction between the fluid moving in unison with the tank rocking motion and that moving in unison with the tank bulging motion, this paper employs the effective mass of fluid for rocking motion, that for bulging motion and that for rocking-bulging interaction derived by solving a boundary-value problem with the boundary conditions corresponding to the tank rocking motion and the tank bulging motion, respectively. The equation of motion is rearranged to include the corresponding effective masses of fluid and a response magnification factor. By ordering some terms of it, the simplified calculation that enables to approximate the maximum angular acceleration of the tank rocking motion, the absolute maximum response acceleration of the tank bulging motion, the maximum base shear and the maximum reactions at a pivoting bottom edge is derived. Consider a tank with the undeformable cylindrical shell subjected to the harmonic base excitation whose driving period is the same as the natural period of the tank bulging motion, the analytical accuracy of the proposed method is examined. Although out-of-round deformation of the tank shell enlarges the uplift displacement of tanks, its consideration remains as future work. Comparison between results of the proposed method and that of the explicit finite element analysis reveals that the proposed method may approximate the angular acceleration accompanying the tank rocking motion, if de-amplification of the tank rocking motion due to landing of the tank bottom plate on the foundation is properly taken into account.

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