In experimental and analytical studies of the rocking response of a circular cylindrical tank under the action of the purely horizontal and translational ground motion, the author analogically quantified the mass of fluid contributing to both bulging and rocking motion of the tank. It was called “the effective mass of fluid for the rocking-bulging interaction.” Its dynamical role in the rocking motion of the tank was thoroughly investigated. However, applying it to design process requires us to use its rigorous definition. To date, the fluid pressure on the tank induced by the impulsive (= bulging) motion and the rocking motion and their effective masses of fluid for each motion were mathematically defined, respectively. Therefore, this paper tries to define the effective mass of fluid for the rocking-bulging interaction based on the fluid pressure on the tank mathematically. The effective mass of fluid for the rocking-bulging interaction is understood as a part of the effective mass of fluid for the bulging motion that is also under the action of the rotational inertia. The influence of the rotational inertia on the effective mass of fluid for the bulging motion is measured by a ratio of the apparent density of fluid contributing to the rocking motion to the original density of fluid. The distribution of the apparent density of fluid contributing to the rocking-bulging interaction is drawn for the various aspects of tanks. The ratio of the effective mass of fluid for the rocking-bulging interaction to the total mass of fluid of the tank is given as the function of the aspect ratio of the tank and the ratio of the uplift width of the tank bottom.

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