Proposal to compute hydrodynamic pressures and sloshing heights in ground-supported rectangular tanks subjected to earthquakes

Abstract

A proposal to estimate both the hydrodynamic pressures and the maximum wave height of liquids contained in rectangular tanks subjected to earthquake ground motions is presented. The computation procedure, based on the Rayleigh-Ritz method, assumes the fluid as a continuum and it does not use concentrated masses or springs. The solution is achieved by equating the seismic input energy of the system with the total kinetic energy of the fluid assuming liquid velocity fields. The resulting design formulas are simple and they are intended to simplify the seismic design of tanks. Numerical results lead to both the liquid maximum sloshing height and hydrodynamic pressure distributions that are similar to those obtained with other simplified methods and those estimated with the finite element method. Preliminary estimations of shear forces and bending moments for a numerical example resulted 13% and 6% larger (respectively) than the corresponding values obtained with the finite element method.