To protect flat-bottom cylindrical tanks against severe damage from uplift motion, accurate evaluation of accompanying fluid pressures is indispensable. This paper presents a mathematical solution for evaluating the fluid pressure on a rigid flat-bottom cylindrical tank in the same manner as the procedure outlined and discussed previously by the authors (Taniguchi, T., and Ando, Y., 2010, “Fluid Pressures on Unanchored Rigid Rectangular Tanks Under Action of Uplifting Acceleration,” ASME J. Pressure Vessel Technol., 132(1), p. 011801). With perfect fluid and velocity potential assumed, the Laplace equation in cylindrical coordinates gives a continuity equation, while fluid velocity imparted by the displacement (and its time derivatives) of the shell and bottom plate of the tank defines boundary conditions. The velocity potential is solved with the Fourier–Bessel expansion, and its derivative, with respect to time, gives the fluid pressure at an arbitrary point inside the tank. In practice, designers have to calculate the fluid pressure on the tank whose perimeter of the bottom plate lifts off the ground like a crescent in plan view. However, the asymmetric boundary condition given by the fluid velocity imparted by the deformation of the crescent-like uplift region at the bottom cannot be expressed properly in cylindrical coordinates. This paper examines applicability of a slice model, which is a rigid rectangular tank with a unit depth vertically sliced out of a rigid flat-bottom cylindrical tank with a certain deviation from (in parallel to) the center line of the tank. A mathematical solution for evaluating the fluid pressure on a rigid flat-bottom cylindrical tank accompanying the angular acceleration acting on the pivoting bottom edge of the tank is given by an explicit function of a dimensional variable of the tank, but with Fourier series. It well converges with a few first terms of the Fourier series and accurately calculates the values of the fluid pressure on the tank. In addition, the slice model approximates well the values of the fluid pressure on the shell of a rigid flat-bottom cylindrical tank for any points deviated from the center line. For the designers’ convenience, diagrams that depict the fluid pressures normalized by the maximum tangential acceleration given by the product of the angular acceleration and diagonals of the tank are also presented. The proposed mathematical and graphical methods are cost effective and aid in the design of the flat-bottom cylindrical tanks that allow the uplifting of the bottom plate.

1.
Shibata
,
H.
, 1972, “
Seismic Damages of Industrial Facilities
,”
JSME
0855-1146,
75
(
643
), pp.
13
22
.
2.
Clough
,
D. P.
, 1977, “
Experimental Evaluation of Seismic Design Methods for Broad Cylindrical Tanks
,” Report Nos. UCB/EERC-77/10 and PB-272 280,
University of California
, Berkeley, CA.
3.
Niwa
,
A.
, 1978, “
Seismic Behavior of Tall Liquid Storage Tanks
,” Report Nos. UCB/EERC-78/04 and PB-284 017,
University of California
, Berkeley, CA.
4.
Cambra
,
F. J.
, 1982, “
Earthquake Response Considerations of Broad Liquid Storage Tanks
,” Report Nos. UCB/EERC-82/25 and PB83–251 215,
University of California
, Berkeley, CA.
5.
Manos
,
G. C.
, and
Clough
,
R. W.
, 1982, “
Further Study of the Earthquake Response of a Broad Cylindrical Liquid-Storage Tank Model
,” Report No. UCB/EERC-82/07 and PB83–147 744,
University of California
, Berkeley, CA.
6.
Clough
,
R. W.
, and
Niwa
,
A.
, 1979, “
Static Tilt Tests of a Tall Cylindrical Liquid Storage Tank
,” Report Nos. UCB/EERC-79/06 and PB-301 167,
University of California
, Berkeley, CA.
7.
Isoe
,
A.
, 1994, “
Investigation on the Uplift and Slip Behavior of Flat-Bottom Cylindrical Shell Tank During Earthquake
,” Ph.D. thesis, University of Tokyo, Tokyo, Japan.
8.
Veletsos
,
A. S.
, and
Tang
,
Y.
, 1987, “
Rocking Response of Liquid Storage Tanks
,”
J. Eng. Mech.
0733-9399,
113
(
11
), pp.
1774
1792
.
9.
Malhotra
,
P. K.
, and
Veletsos
,
A. S.
, 1994, “
Uplifting Response of Unanchored Liquid-Storage Tanks
,”
J. Struct. Eng.
0733-9445,
120
(
12
), pp.
3525
3547
.
10.
Taniguchi
,
T.
, 2004, “
Experimental and Analytical Studies of Rocking Mechanics of Unanchored Flat-bottom Cylindrical Shell Model Tanks
,”
Seismic Engineering
,
PVP
,
ASME
, Vol.
486-1
, pp.
119
127
.
11.
Taniguchi
,
T.
, 2005, “
Rocking Mechanics of Flat-Bottom Cylindrical Shell Model Tanks Subjected to Harmonic Excitation
,”
ASME J. Pressure Vessel Technol.
0094-9930,
127
(
4
), pp.
373
386
.
12.
Taniguchi
,
T.
and
Ando
,
Y.
, 2007, “
Fluid Pressure on Rectangular Rigid Tanks Due to Uplift Motion
,”
ASME
Paper No. PVP2007-26447.
13.
Taniguchi
,
T.
, and
Ando
,
Y.
, 2010, “
Fluid Pressures on Unanchored Rigid Rectangular Tanks Under Action of Uplifting Acceleration
,”
ASME J. Pressure Vessel Technol.
,
132
(
1
), p.
011801
0094-9930.
14.
Lamb
,
H.
, 1932,
Hydrodynamics
,
6th ed.
,
Cambridge University Press
,
New York
, pp.
8
9
.
You do not currently have access to this content.