Study on Fundamental Frequencies of Cylindrical Storage Tanks Obtained from Codes and Finite Element Method

Document Type : Research Papers


1 Ahvaz



In the case of study on the seismic behavior of tanks, one of the most important subjects is selection of convective and impulsive frequencies for storage tanks. These two frequencies are defined by Housner. The major utility of these frequencies is for Rayleigh damping which is a must for time history analysis. API 650, EUROCODE 8 have suggested some analytical solutions for finding convective and impulsive frequencies and other parameters. In addition, these frequencies can be obtained from modal analysis by finite element software. In current study, these frequencies are obtained using Finite Element (FE) software and performing modal analysis. In the next stage, these modes are compared with analytical methods from standards. To compare tanks with different (H/R) ratios, all these tanks are modeled with the same volume and weight. This study showed that there is a good agreement between convective frequencies extracted from Finite Element method and those from standards. Furthermore, an increase in liquid level led to a rise and dip in convective and impulsive frequencies, respectively. In addition, results show that a 1.47 times increase in the viscosity leads to a 17 percent decrease in the values of impulsive frequencies.


Main Subjects

ACI Committee 350.3-06. (2006). Seismic design of liquid-containing concrete structures (ACI 350.3-06) and commentary (ACI 350.3R-06), Farmington Hills (MI, USA), American Concrete Institute.
Amiri, M. and Sabbagh-Yazdi, S.R. (2012). “Influence of roof on dynamic characteristics of dome roof tanks partially filled with liquid”, Thin-Walled Structures, 50(1), 56-67.
ANSYS, Inc. (2014). ANSYS release 15.0 Documentation, USA,
API Standard 650. (2008). Welded steel tanks for oil storage, 11th Ed., American Petroleum Institute, Washington, D.C.
Barton, DC. and Parker, JV. (1987). “Finite Element analysis of the seismic response of anchored and unanchored liquid storage tanks”, Earthquake Engineering and Structural Dynamics, 15(3), 299-322.
Bayraktar, A., Sevim, B., Altunışık, A. and Türker, T. (2010). “Effect of the model updating on the earthquake behavior of steel storage tanks”, Journal of Constructional Steel Research, 66(3), 462-469.
Chen, JZ. and Kianoush, MR. (2005). “Seismic response of concrete rectangular tanks for liquid containing structures”, Canadian Journal of Civil Engineering, 32, 739-52.
Chopra, AK. (2000). Dynamics of structures: Theory and applications to earthquake engineering, 2nd Ed., Prentice-Hall.
Epstein, H.I. (1976). “Seismic design of liquid storage tanks”, Journal of the Structural Division, ASCE, 102(9), 1659-1673.
Eskandari-Ghadi, M., Rahimian, M., Mahmoodi, A., and Ardeshir-Behrestaghi, A. (2013). “Analytical Solution for Two-Dimensional Coupled Thermoelastodynamics in a Cylinder”, Civil Engineering Infrastructures Journal, 46(2), 107-123.
Eurocode 8. (2003). Design of structures for earthquake resistance, Part 1: General rules seismic action and general requirements for structures, Part 4: Silos, tanks and pipelines, European Committee for Standardization.
Ghaemmaghami, A. (2010). “Dynamic time-history response of concrete rectangular liquid storage tanks”, Dissertation Abstracts International, 72(08).
Ghateh, R., Kianoush. M.R. and Pogorzelski, W. (2015). “Seismic response factors of reinforced concrete pedestal in elevated water tanks”, Engineering Structures, 87, 32-46.
Ghateh, R., Kianoush, M. R., and Pogorzelski, W. (2015). “Seismic response factors of reinforced concrete pedestal in elevated water tanks”, Engineering Structures, 87, 32-46.
Gnitko, V., Marchenko, U., Naumenko, V., and Strelnikova, E. (2011). “Forced vibrations of tanks partially filled with the liquid under seismic load”, In Proceedings of XXXIII Conference “Boundary Elements and other mesh reduction methods”, WIT Press, Transaction on Modeling and Simulation, pp. 285-296.
González, E., Almazán, J., Beltrán, J., Herrera, R., and Sandoval, V. (2013). “Performance of stainless steel winery tanks during the 02/27/2010 Maule Earthquake”, Engineering Structures, 56, 1402-1418.
Hosseinzadeh, N., Kazem, H., Ghahremannejad, M., Ahmadi, E., and Kazem, N. (2013). “Comparison of API650-2008 provisions with FEM analyses for seismic assessment of existing steel oil storage tanks”, Journal of Loss Prevention in the Process Industries, 26(4), 666-675.
Housner GW. (1963). “The dynamic behavior of water tanks”, Bulletin of the Seismological Society of America, 53(2), 381-387.
Haroun, MA. and Tayel, MA. (1985). “Response of tanks to vertical seismic excitations”, Earthquake Engineering and Structural Dynamic, 13, 583-595.
Hariri Ardebili, M.A., Mirzabozorg, H., Kolbadi, S., and Mahdi, S. (2013). “Are there any differences in seismic performance evaluation criteria for concrete arch dams?”, Civil Engineering Infrastructures Journal, 46(2), 233-240.
Jaiswal, O.R., Kulkarni, S., and Pathak, P. (2008). “A study on sloshing frequencies of fluid-tank system”, In Proceedings of the 14th World Conference on Earthquake Engineering, pp. 12-17.
Kazem, H., and Mehrpouya, S. (2012). “Estimation of sloshing wave height in broad cylindrical oil storage tanks using numerical methods”, Journal of Structural Engineering and Geo-Techniques, 2(1), 55-59.
Kianoush, M.R. and Chen, J.Z. (2006). “Effect of vertical acceleration on response of concrete rectangular liquid storage tanks”, Engineering Structures, 28(5), 704-15.
Kianoush, M.R. and Ghaemmaghami, A.R. (2011). “The effect of earthquake frequency content on the seismic behavior of concrete rectangular liquid tanks using the finite element method incorporating soil–structure interaction”, Engineering Structures, 33(7), 2186-2200.
Korkmaz, K.A., Sari, A., and Carhoglu, A.I. (2011). “Seismic risk assessment of storage tanks in Turkish industrial facilities”, Journal of Loss Prevention in the Process Industries, 24(4), 314-320.
Livaoglu, R., Cakir, T., Dogangun, A., and Aytekin, M. (2011). “Effects of backfill on seismic behavior of rectangular tanks”, Ocean Engineering, 38(10), 1161-1173.
Maekawa, A., Shimizu, Y., Suzuki, M., and Fujita, K. (2010). “Vibration test of a 1/10 reduced scale model of cylindrical water storage tank”, Journal of Pressure Vessel Technology, 132(5), 051801.
Malhotra, P. K., Wenk, T., and Wieland, M. (2000). “Simple procedure for seismic analysis of liquid-storage tanks”, Structural Engineering International, 10(3), 197-201.
Moslemi, M. and Kianoush, M.R. (2012). “Parametric study on dynamic behavior of cylindrical ground-supported tanks”, Engineering Structures, 42, 214-230.
Ormeño, M., Larkin, T. and Chouw, N. (2015). “Evaluation of seismic ground motion scaling procedures for linear time-history analysis of liquid storage tanks”, Engineering Structures, 102, 266-277.
Ranjbar, M.M., Bozorgmehrnia, S. and Madandoust, R. (2013). “Seismic behavior evaluation of concrete elevated water tanks”, Civil Engineering Infrastructures Journal, 46(2), 175-188.
Ruiz, D.P. and Gutiérrez, S.G. (2015). “Finite Element methodology for the evaluation of soil damping in LNG tanks supported on homogeneous elastic half space”, Bulletin of Earthquake Engineering, 13(3), 755-775.
Ruiz, R.O., Lopez-Garcia, D. and Taflanidis, A.A. (2015). “An efficient computational procedure for the dynamic analysis of liquid storage tanks”, Engineering Structures, 85, 206-218.
Sezen. H., Livaoglu. R. and Dogangun, A. (2008). “Dynamic analysis and seismic performance evaluation of above-ground liquid containing tanks”, Engineering Structures, 30, 794-803.
Shahmardani, M., Mirzapour, J. and Tariverdilo, S. (2014). “Dynamic response of submerged vertical cylinder with lumped mass under seismic excitation”, International Journal of Engineering, Transactions A: Basics, 27(10), 1547-1556.
Tedesco, J.W. (1982). “Vibrational characteristics and seismic analysis of cylindrical liquid storage tanks”, Dissertation Abstracts International Part B: Science and Engineering [DISS. ABST. INT. PT. B- SCI. & ENG.], 43(3).
Virella, J.C., Godoy, L.A. and Suárez, L.E. (2006). “Fundamental modes of tank-liquid systems under horizontal motions”, Engineering Structures, 28(10), 1450-1461.
Nicolici, S. and Bilegan, R.M. (2013). “Fluid structure interaction modeling of liquid sloshing phenomena in flexible tanks”, Nuclear Engineering and Design, 258, 51-56.
 Yazdanian, M., Razavi, S.V. and Mashal, M. (2016a) “Seismic analysis of rectangular concrete tanks by considering fluid and tank interaction”, Journal of Solid Mechanics, 8(2), 435-445.
Yazdanian, M., Razavi, S.V. and Mashal, M. (2016b). “Study on the dynamic behavior of cylindrical steel liquid storage tanks using finite element method”, Journal of Theoretical and Applied Vibration and Acoustics, 2(2), 144-165.