Rocking Mechanics of Flat-Bottom Cylindrical Shell Model Tanks Subjected to Harmonic Excitation

Abstract

The rocking motion of the tanks is complex and not fully understood. Using model tanks that possess concentric rigid-doughnut-shaped bottom plates, this paper tries to clarify its fundamental mechanics through the analog of rocking motion of rigid bodies. Introducing an effective mass for the internal liquid for rocking motion enables the development of a dynamical system including the rocking-bulging interaction motion and the effective mass of liquid for the interaction motion. Since the base shear and uplift displacement observed during shaking tests match well with computed values, the proposed procedure can explain the mechanics of the rocking motion of the model tanks used herein.

Study of rocking motion of rigid body with slide contact

“…1 ρ is the position vector from C P to 1 P on the rigid body, 2 ρ is the position vector from C P to 2 P on the base, and t is the tangential unit vector on the contact point of the rigid body. 1 P and 2 P are the contact points on the rigid body and the base, respectively. Applying the scalar product, the distance d between C P to 1 P can be obtained as,…”

“…To secure their safety and stability, it is also important to make arguments based on theoretical and analytical approaches. The rocking motion of the tanks has also been studied [1]. For that case, a dynamical system of the rocking motion of the tanks was formulated by employing the effective mass of the liquid for rocking motion and the contribution of the rotational inertia forces.…”

Masses of Fluid for Cylindrical Tanks in Rock With Partial Uplift of Bottom Plate

“…Consider a small volume of fluid inside the slice model whose fluid density is specified by Eq. (7). The effective mass of fluid for rocking motion of cylindrical tank M r is given by summing up the mass of all small volumes inside all slice models…”

“…In contrast, presumption of an angular or rocking base motion about a horizontal axis at the tank bottom edge differentiates the present work from the previous work. References [6] and [7] first proposed the use of a dynamical model consisting of a springmass-rigid-body combined system for evaluating the rocking motion of cylindrical tanks about a horizontal axis at the tank bottom edge subjected to horizontal ground acceleration. By analogy with the equivalent mass fastened rigidly to the wall of the container [8], the effective mass of fluid for rocking motion and that for rocking-bulging interaction were predicted and quantified empirically [7].…”

“…References [6] and [7] first proposed the use of a dynamical model consisting of a springmass-rigid-body combined system for evaluating the rocking motion of cylindrical tanks about a horizontal axis at the tank bottom edge subjected to horizontal ground acceleration. By analogy with the equivalent mass fastened rigidly to the wall of the container [8], the effective mass of fluid for rocking motion and that for rocking-bulging interaction were predicted and quantified empirically [7]. Since they play important roles in the tank rocking motion and reach a half of the total mass of the fluid as shown latter, their rigorous quantification is indispensable for accurate evaluation of the tank rocking motion.…”