*Int.J.Press.Vessels and Piping* **76**, 693-709,
1999

### A REFINED ANALYSIS OF SLOSHING EFFECTS

IN SEISMICALLY EXCITED TANKS

F.D. Fischer¹ and F.G. Rammerstorfer²

¹Institute of Mechanics,

University of Mining and Metallurgy, Leoben, Austria

²Institute of Lightweight Structures and Aerospace
Engineering,

TU Wien,
Vienna, Austria

**Abstract** -
Sloshing in terms of liquid surface displacement in vertical liquid-filled
cylindrical tanks under earthquake excitation is a well studied phenomenon.
Various design rules exist for liquid storage tanks to sustain the
corresponding liquid pressure due to seismic excitation and to take into
account the necessary freeboard.
However, usually the sloshing motion is considered under the assumption of
a rigid tank with an earthquake excitation at the base circle.
The arguments used so far in justifying this assumption are of rather
qualitative but not of quantitative nature.
Since it is important to have a quantitative measure of that what is
neglected it is the intention of this paper to show if this engineering
approach is based on rigorous theoretical quantitative results. u
Therefore, in this paper coupling of sloshing with the deformations of a
flexible tank wall during earthquake excitation is investigated in a refined
analysis.
In contrast to former papers which have studied the negligible influence of
the wall deformations due to sloshing itself, in this paper the more
important coupling including the wall deformations caused by the impulsive
effect of the contained liquid is taken into account.
An analytical procedure is presented which allows to study explicitly the
influence of the wall deformations on both the liquid pressure and the
surface elevation for typical wall deformation shapes, i.e. vibration modes.
From the rather complex mathematical derivations a simple formula is drawn
which enables the engineer to get a quick guess of the magnitude of the
influence of the wall deformations on the convective pressure contributions
due to sloshing and hence to decide whether or not the assumption of a rigid
tank wall is suitable.
It is shown that for tanks made of less stiff materials, such as for instant
polymers, this rigid wall assumption which is suitable for steel tanks may
become questionable.

(hjb,990830)