Plastic Buckling of Unanchored Roofed Tanks under Dynamic Loads
Publication: Journal of Engineering Mechanics
Volume 124, Issue 6
Abstract
Cylindrical tanks that are not anchored effectively to their foundations often rock during seismic loading. Vertical compressive forces in the tank wall that are required to resist seismic overturning moments then tend to be concentrated over a small portion of the circumference of the tank, where the tank wall remains in contact with the foundation. This together with the effect of internal pressures often leads to plastic buckling of the tank wall at the base or the so-called elephant foot bulge. This paper aims at predicting not only whether elephant foot bulging will occur, but also the extent of elephant foot bulging. This is done by means of a nonlinear dynamic time history analysis on a simplified rigid cylinder model, in which equivalent springs are used to represent elastic tank deformations, as well as nonlinear effects including geometric and plastic shortening of the tank wall caused by elephant foot bulging, and the resistance to uplift provided by the hold-down action of the floor plate. A physically based approach is provided to calculate the properties and location of the equivalent springs using finite-element analyses of the tank that can be performed with minimal computational effort. This leads to a simplified model for which key aspects of the behavior (dynamic as well as static) match that of the real tank. The approach is applied to a tank that was damaged during the 1977 San Juan earthquake. Although field measurements of the amount of elephant foot bulging are not available, photographs taken after the earthquake show an amount of bulging that is consistent with the predictions.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Auli, W., Fisher, F. D., and Rammerstorfer, F. G. (1985). “Uplifting of earthquake loaded liquid filled tanks.” 1985 Pressure Vessels and Piping (PVP) Conf., ASME, New York, N.Y., 71–85.
2.
El-Bkaily, M. (1993). “Plastic buckling of unanchored liquid storage tanks under dynamic loads,” PhD thesis, Department of Civil and Environmental Engineering, University of Michigan, Ann Arbor, Mich.
3.
El-Bkaily, M., and Peek, R.(1992). “Load shortening in plastic buckling of cylinders.”J. Engrg. Mech., ASCE, 118(9), 1892–1906.
4.
Graham, E. W., and Rodriguez, A. M.(1952). “Characteristics of fuel motion which affect airplane dynamics.”J. Appl. Mech., 19(3), 381–388.
5.
Hanson, R. D. (1973). “Behavior of liquid storage tanks.” The Great Alaska Earthquake of 1964, Engineering, National Academy of Sciences, Washington, D.C., 331–339.
6.
Haroun, M. A. (1980). “Dynamic analyses of liquid storage tanks.”Rep. No. EERL 80-4, Earthquake Engrg. Res. Lab., California Inst. of Technol., Pasadena, Calif.
7.
Housner, G. W.(1957). “Dynamic pressures on accelerated fluid containers.”Bull. Seismological Soc. of Am., 47(1), 15–35.
8.
Housner, G. W.(1963). “The dynamic behavior of water tanks.”Bull. Seismological Soc. of Am., 53(1), 381–387.
9.
Jennings, P. C., ed. (1971). “Engineering features of the San Fernando Earthquake, February 9, 1971.”Rep. No. EERL 71-02, Earthquake Engrg. Res. Lab., Pasadena, Calif.
10.
Manos, G. C.(1991). “Evaluation of the earthquake performance of anchored wine tanks during the San Juan, Argentina, 1977 Earthquake.”Earthquake Engrg. and Struct. Dynamics, 20, 1099–1114.
11.
Natsiavas, S. (1987). “Response and failure of fluid-filled tanks under base excitation,” PhD thesis, Graduate Aeronautical Laboratories, California Institute of Technology, Pasadena, Calif.
12.
Natsiavas, S.(1988). “An analytical model for unanchored fluid-filled tanks under base excitation.”J. Appl. Mech., 55, 648–653.
13.
Peek, R. (1986). “Analysis of unanchored liquid storage tanks under seismic loads.”Rep. No. EERL 86-01, Earthquake Engrg. Res. Lab., California Inst. of Technol., Pasadena, Calif.
14.
Peek, R.(1988). “Analysis of unanchored liquid storage tanks under seismic lateral loads.”Earthquake Engrg. and Struct. Dynamics, 16(7), 1087–1100.
15.
Peek, R. (1989). “Buckling criteria for earthquake-induced overturning stresses in cylindrical liquid-storage tanks.” ASCE Structures Congress, San Francisco, May 1989.
16.
Peek, R., and El-Bkaily, M.(1991). “Postbuckling behavior of unanchored steel tanks under lateral load.”J. of Pressure Vessel Technol., 113(3), 423–428.
17.
Peek, R., and El-Bkaily, M.(1997). “Mechanical analogies for liquid storage tanks and action of eccentric gravity loads.”J. Engrg. Mech., ASCE, 123(6), 561–567.
18.
Peek, R., and Jennings, P. C.(1988). “Simplified analysis of unanchored liquid storage tanks.”Earthquake Engrg. and Struct. Dynamics, 16(7), 1073–1086.
19.
Rammerstorfer, F. G., Scharf, F. D., and Fisher, F. D.(1990). “Storage tanks under earthquake loading.”Appl. Mech. Rev., 43(11), 261.
20.
Rotter, J. M.(1990). “Local collapse of axially compressed pressurized thin cylinders.”J. Struct. Engrg., ASCE, 116(7), 1955–1970.
21.
Scharf, K., Rammerstorfer, F. G., and Fischer, F. D. (1989). “Elastic plastic stability analysis of earthquake loaded tanks.”“Nichtlineare Berechnungen im Konstruktiven Ingenieurbau,” Springer-Verlag, Berlin (in German).
22.
Veletsos, A. S., and Tang, Y.(1987). “Rocking response of liquid storage tanks.”J. Engrg. Mech., 113(11), 1774–1792.
23.
Zui, H., and Shinke, T. (1985). “Seismic deformation analysis of cylindrical tanks accompanied with the uplift of the bottom plate.”Proc., JSCE Structural Engineering, 31A, 537–550 (in Japanese).
Information & Authors
Information
Published In
Journal of Engineering Mechanics
Volume 124 • Issue 6 • June 1998
Pages: 648 - 657
Copyright
Copyright © 1998 American Society of Civil Engineers.
History
Published online: Jun 1, 1998
Published in print: Jun 1998
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.