This paper presents a simplified mathematical model for modeling the flexible bottom plate in an unanchored cylindrical liquid storage tank partially uplifted under the static tilt condition. In this model, the cylindrical tank is divided into substructures according to the deformation-resistant mechanisms involved. The modeling of each substructure is based on the Ritz formulation. Numerical results are presented and compared with reported experimental measurements. The results show that the simplified mathematical model is efficient. Practical and accurate results can be obtained using the model leading to a better understanding of the uplift mechanism. The relationship of the uplift behavior with the static tilt angle is also presented and discussed.

1.
American Petroleum Institute, 1979, “Welded Steel Tanks for Oil Storage,” API Standard 650, 6th Edition, Revision 3, Washington, DC.
2.
American Water Works Association, 1984, “AWWA Standard for Welded Steel Tanks for Water Storage,” AWWA D100-84, Denver, CO.
3.
Auli
W.
,
Fischer
F. D.
, and
Rammerstorfer
F. G.
,
1985
, “
Uplifting of Earthquake Loaded Liquid-Filled Tanks
,” Proceedings, Pressure Vessels and Piping Conference, New Orleans, LA,
ASME PVP
-Vol.
98-7
, pp.
71
85
.
4.
Barton
D. C.
, and
Parker
J. V.
,
1987
, “
Finite Element Analysis of the Seismic Response of Anchored and Unanchored Liquid Storage Tanks
,”
Earthquake Engineering and Structural Dynamics
, Vol.
15
, pp.
299
322
.
5.
Clough, R. W., and Niwa, A., 1979, “Static Tilt Tests of a Tall Cylindrical Liquid Storage Tank,” Report No. UCB/EERC-79/06, Earthquake Engineering Research Center, University of California, Berkeley, CA.
6.
Fischer
F. D.
,
1979
, “
Dynamic Fluid Effects in Liquid-Filled Flexible Cylindrical Tanks
,”
Earthquake Engineering and Structural Dynamics
, Vol.
7
, pp.
587
601
.
7.
Flu¨gge, W., 1960, Stresses in Shells, Springer-Verlag OHG., Berlin/Go¨ttingen/ Heidelberg, Germany.
8.
Hanson, R. D., 1973, “Behaviour of Liquid-Storage Tanks, The Great Alaska Earthquake of 1964,” Engineering Section, National Academy of Sciences, Washington, DC, pp. 331–339.
9.
Haroun
M. A.
,
Badawi
H. S.
, and
Nanda
C. B.
,
1987
, “
Nonlinear Uplift Analysis of Crescent-Shaped Plate
,” Seismic Engineering, Proceedings, Pressure Vessels and Piping Conference, San Diego, CA,
ASME PVP
-Vol.
127
, pp.
317
324
.
10.
Haroun
M. A.
, and
Housner
G. W.
,
1981
, “
Earthquake Response of Deformable Liquid Storage Tanks
,”
ASME Journal of Applied Mechanics
, Vol.
48
, pp.
411
417
.
11.
Haroun
M. A.
, and
Tayel
M. A.
,
1985
a, “
Axisymmetrical Vibrations of Tanks—Numerical
,”
Journal of Engineering Mechanics
, ASCE, Vol.
111
, pp.
329
345
.
12.
Haroun
M. A.
, and
Tayel
M. A.
,
1985
b, “
Axisymmetrical Vibrations of Tanks—Analytical
,”
Journal of Engineering Mechanics
, ASCE, Vol.
111
, pp.
346
358
.
13.
Ishida
K.
, and
Kobayashi
N.
,
1988
, “
An Effective Method of Analyzing Rocking Motion for Unanchored Cylindrical Tanks Including Uplift
,”
ASME JOURNAL OF PRESSURE VESSEL TECHNOLOGY
, Vol.
110
, pp.
76
87
.
14.
Housner
G. W.
,
1963
, “
The Dynamic Behavior of Water Tanks
,”
Bulletin of Seismic Society of America
, Vol.
53
, pp.
381
387
.
15.
Jablonski, A. M., Law, K. T., Lau, D. T., Pierre, J., and Tang, J. H. K., with collaboration of Rainer, J. H., and Allen, D. E., 1990, “The 1989 Loma Prieta (San Francisco Area) Earthquake: Site Visit Report,” Internal Report No. 594, National Research Council Canada.
16.
Lau, D., and Clough, R. W., 1989, “Static Tilt Behavior of Unanchored Cylindrical Tanks,” Report No. UCB/EERC-89/11, Earthquake Engineering Research Center, University of California, Berkeley, CA.
17.
Leon
G. S.
, and
Kausel
E. A. M.
,
1986
, “
Seismic Analysis of Fluid Storage Tanks
,”
Journal of Structural Engineering
, ASCE, Vol.
112
, No.
1
, pp.
1
18
.
18.
Liu
W. K.
, and
Lam
D.
,
1983
, “
Nonlinear Analysis of Liquid-Filled Tanks
,”
Journal of Engineering Mechanics
, ASCE, Vol.
109
, No.
6
, pp.
1344
1357
.
19.
Ma
D. C.
,
Gvildys
J.
,
Chang
Y. W.
, and
Liu
W. K.
,
1982
, “
Seismic Behavior of Liquid-Filled Shells
,”
Nuclear Engineering and Design
, Vol.
70
, pp.
437
455
.
20.
Malhotra
P. K.
, and
Veletsos
A. S.
,
1994
a, “
Uplifting Analysis of Base Plates in Cylindrical Tanks
,”
Journal of Structural Engineering
, ASCE, Vol.
120
, No.
12
, pp.
3489
3505
.
21.
Malhotra
P. K.
, and
Veletsos
A. S.
,
1994
b, “
Uplifting Response of Unanchored Liquid-Storage Tanks
,”
Journal of Structural Engineering
, ASCE, Vol.
120
, No.
12
, pp.
3525
3547
.
22.
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, Earthquake Engineering Research Center, University of California, Berkeley, CA.
23.
Manos, G. C., and Talaslidis, D., 1988, “Response of Cylindrical Tanks Subjected to Lateral Loads Correlation Between Analytical and Experimental Results,” Proceedings, Ninth World Conference on Earthquake Engineering, Tokyo-Kyoto, Japan, Vol. VI, pp. 667–672.
24.
Natsiavas
S.
,
1988
, “
An Analytical Model for Unanchored Fluid-Filled Tanks Under Base Excitation
,”
ASME Journal of Applied Mechanics
, Vol.
55
, pp.
648
653
.
25.
Peek
R.
,
1988
, “
Analysis of Unanchored Liquid Storage Tanks Under Lateral Loads
,”
Earthquake Engineering and Structural Dynamics
, Vol.
16
, Oct., pp.
1087
1100
.
26.
Peek
R.
, and
Jennings
P. C.
,
1988
, “
Simplified Analysis of Unanchored Tanks
,”
Earthquake Engineering and Structural Dynamics
, Vol.
16
, Oct., pp.
1073
1085
.
27.
Rammerstorfer
F. G.
,
Auli
W.
, and
Fischer
F. D.
,
1985
, “
Uplifting and Stability of Wind-Loaded Vertical Cylindrical Shells
,”
Engineering Computations
, Vol.
2
, No.
3
, pp.
170
180
.
28.
Sakai
F.
, and
Isoe
A.
,
1989
, “
Computation and Experiment on Base-Uplift Behavior of Cylindrical Oil Storage Tanks During Earthquakes
,” Sloshing and Fluid Structure Vibration—1989, Proceedings, Pressure Vessels and Piping Conference, Honolulu, Hawaii,
ASME PVP
-Vol.
157
, pp.
9
14
.
29.
Sakai
F.
,
Isoe
A.
,
Hirakawa
H.
, and
Mentani
Y.
,
1989
, “
Large-Scale Tilt Tests of Seismic Behavior of Flat-Bottomed Cylindrical Liquid Storage Tanks
,” Sloshing and Fluid Structure Vibration—1989, Proceedings, Pressure Vessels and Piping Conference, Honolulu, Hawaii,
ASME PVP
-Vol.
157
, pp.
69
74
.
30.
Shaaban, S. H., and Nash, W. A., 1976, “Finite Element Analysis of a Seismically Excited Cylindrical Storage Tank, Ground Supported and Partially Filled with Liquid,” Report No. NSF/RA-760261, Univ. of MA.
31.
Shih, C. F., and Babcock, C. D., 1981, “Failure of Liquid Storage Tanks Due to Earthquake Excitations,” Report No. 81/04, Earthquake Engineering Research Laboratory, California Institute of Technology, Pasadena, CA.
32.
Timoshenko, S., and Woinowsky-Krieger, S., 1960, Theory of Plates and Shells, 2nd Edition, McGraw-Hill, New York, NY.
33.
Uras
R. A.
, and
Liu
W. K.
,
1989
, “
Dynamic Stability Characteristics of Liquid-Filled Shells
,”
Earthquake Engineering and Structural Dynamics
, Vol.
18
, pp.
1219
1231
.
34.
Veletsos
A. S.
, and
Tang
Y.
,
1990
, “
Soil-Structure Interaction Effects for Laterally Excited Liquid Storage Tanks
,”
Earthquake Engineering and Structural Dynamics
, Vol.
19
, pp.
473
496
.
35.
Veletsos, A. S., and Yang, J. Y., 1977, “Earthquake Response of Liquid-Storage Tanks,” Advances in Civil Engineering Through Engineering Mechanics, Proceedings, Second Annual Engineering Mechanics Division Specialty Conference, Raleigh, NC, pp. 1–24.
36.
Wozniak, R. S., and Mitchell, W. W., 1978, “Basis of Seismic Design Provisions for Welded Steel Oil Storage Tanks,” Proceedings, Session of Advances in Storage Tank Design, API Refining Dept., pp. 485–493.
37.
Zeng, Xianguang, 1993, “Earthquake Response Analysis of Unanchored Cylindrical Liquid Storage Tanks,” Ph.D. dissertation, Carleton University, Ottawa, Ontario, Canada.
38.
Zui
H.
, and
Shinke
T.
,
1985
, “
Seismic Deformation Analysis of Unanchored Cylindrical Tanks Accompanied With the Uplift of the Bottom Plate
,”
Proceedings, Japan Society of Civil Engineering and Structural Engineering
, Vol.
31A
, pp.
537
550
.
This content is only available via PDF.
You do not currently have access to this content.