Earthquakes and Structures

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Buckling conditions and strengthening by CFRP composite of cylindrical steel water tanks under seismic load

  • Ali Ihsan Celik (Kayseri University, Tomarza Vocational High School) ;
  • Mehmet Metin Kose (Kahramanmaras Sutcu Imam University, Civil Engineering) ;
  • Ahmet Celal Apay (Duzce University/Faculty of Art, Design and Architecture/Department of Architecture)
  • Received : 2023.11.04
  • Accepted : 2024.05.07
  • Published : 2024.08.25
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Abstract

In this paper, buckling conditions and retrofitting of cylindrical steel water storage tanks with different roof types and wall thicknesses were investigated by using finite element method. Four roof types of cylindrical steel tanks which are open-top, flat-closed, conical-closed and torispherical-closed and three wall thicknesses of 4, 6 and 8 mm were considered in FE modeling of cylindrical steel tanks. The roof shapes significantly affect load distribution on the tank shell under the seismic action. Composite FRP materials are widely used for winding thin-walled cylindrical steel structures. The retrofitting efficiency of cylindrical steel water tank is tested under the seismic loading with the externally bonded CFRP laminates. In retrofitting of cylindrical steel tank, the CFRP composite material coating method was used to improve of seismic performance of cylindrical steel tanks. ANSYS software was used to analyze the cylindrical steel tanks and maximum equivalent (von-Mises) and directional deformation were obtained. Equivalent (von-Mises) stresses significantly decreased due to the coating of the tank shell with FRP composite material. In thin-walled steel structures, excessive stress causes buckling and deformations. Therefore, retrofitting led to decrease in stress, reductions in directional and buckling deformation of the open-top, flat-closed, conical-closed and torispherical-closed tanks.

Keywords

References

  1. Aksoylu, C., Yazman, S., Ozkilic, Y.O., Gemi, L. and Arslan, M.H. (2020), "Experimental analysis of reinforced concrete shear deficient beams with circular web openings strengthened by CFRP composite", Compos. Struct., 249, 112561. https://doi.org/10.1016/j.compstruct.2020.112561.
  2. Alliance, A. (2001), Seismic Fragility Formulations for Water Systems, Part I-Guideline, American Society of Civil Engineers, Reston, VA, USA.
  3. Bakalis, K., Kohrangi, M. and Vamvatsikos, D. (2018), "Seismic intensity measures for above-ground liquid storage tanks", Earthq. Eng. Struct. Dyn., 47(9), 1844-1863. https://doi.org/10.1002/eqe.3043.
  4. Bakalis, K., Vamvatsikos, D. and Fragiadakis, M. (2017), "Seismic risk assessment of liquid storage tanks via a nonlinear surrogate model", Earthq. Eng. Struct. Dyn., 46(15), 2851-2868. https://doi.org/10.1002/eqe.2939.
  5. Balendra, T., Ang, K., Paramasivam, P. and Lee, S.J.I.J.o.M.S. (1982), "Free vibration analysis of cylindrical liquid storage tanks", Int. J. Mech. Sci., 24(1), 47-59. https://doi.org/10.1016/0020-7403(82)90020-0.
  6. Bauer, H.F. (1964), Fluid Oscillations in the Containers of a Space Vehicle and Their Influence upon Stability, National Aeronautics and Space Administration, Washington, D.C., USA.
  7. Brebbia, C.A., Popov, V. and Popov, V. (2011), Boundary Elements and Other Mesh Reduction Methods XXXIII, Wit Press, Southampton, UK.
  8. Brunesi, E., Nascimbene, R., Pagani, M. and Beilic, D. (2014), "Seismic performance of storage steel tanks during the May 2012 Emilia, Italy, earthquakes", J. Perform. Constr. Facil., 29(5), 04014137. https://doi.org/10.1061/(ASCE)CF.1943-5509.0000628.
  9. Buratti, N. and Tavano, M. (2014), "Dynamic buckling and seismic fragility of anchored steel tanks by the added mass method", Earthq. Eng. Struct. Dyn., 43(1), 1-21. https://doi.org/10.1002/eqe.2326.
  10. Burkacki, D. and Jankowski, R. (2019), "Experimental study on models of cylindrical steel tanks under mining tremors and moderate earthquakes", Earthq. Struct., 17(2), 175-189. https://doi.org/10.12989/eas.2019.17.2.175.
  11. Burkacki, D. and Jankowski, R. (2020), "Response of cylindrical steel tank under stochastically generated non-uniform earthquake excitation", 4th Polish Congress of Mechanics and the 23rd International Conference on Computer Methods in Mechanics, Krakow, Poland, September.
  12. Cao, Q.S. and Zhao, Y. (2010), "Buckling strength of cylindrical steel tanks under harmonic settlement", Thin Wall. Struct., 48(6), 391-400. https://doi.org/10.1016/j.tws.2010.01.011.
  13. Celik, A.I. and Kose, M.M. (2019) "Dynamic buckling analysis of cylindrical steel water storage tanks subjected to Kobe earthquake loading", Steel Constr., 13(2), 128-138. https://doi.org/10.1002/stco.201900003.
  14. Celik, A.I., Kose, M.M., Akgul, T. and Apay, A.C. (2018), "Strengthening of cylindrical steel water tank under the seismic loading", Kahramanmaras Sutcu Imam Univ. J. Eng. Sci., 21(4), 334-345. https://doi.org/10.17780/ksujes.441831.
  15. Celik, A.I., Zeybek, O. and Ozkilic, Y. (2024), "Effect of the initial imperfection on the response of the stainless steel shell structures", Steel Compos. Struct., 50(6), 705. https://doi.org/10.12989/scs.2024.50.6.705.
  16. Chaulagain, N.R., Sun, C.H. and Kim, I.H. (2019), "Seismic fragility analysis of ground supported horizontal cylindrical tank", J. Korea Inst. Struct. Mainten. Inspect., 23(7), 145-151. https://doi.org/10.11112/jksmi.2019.23.7.145.
  17. Christensen, R.M. (2012), Mechanics of Composite Materials, Courier Corporation, North Chelmsford, MA, USA.
  18. Colombo, J. and Almazan, J. (2017), "Experimental investigation on the seismic isolation for a legged wine storage tank", J. Constr. Steel Res., 133, 167-180. https://doi.org/10.1016/j.jcsr.2017.02.013.
  19. Cortes, G., Nussbaumer, A., Berger, C. and Lattion, E. (2011), "Experimental determination of the rotational capacity of wall-to-base connections in storage tanks", J. Constr. Steel Res., 67(7), 1174-1184. https://doi.org/10.1016/j.jcsr.2011.02.010.
  20. Damatty, A.E., Korol, R.M. and Mirza, F.A. (1997), "Stability of imperfect steel conical tanks under hydrostatic loading", J. Struct. Eng., 123(6), 703-712. https://doi.org/10.1061/(ASCE)0733-9445(1997)123:6(703).
  21. Daniel, I.M., Ishai, O., Daniel, I.M. and Daniel, I. (1994), Engineering Mechanics of Composite Materials, Oxford University Press, New York, NY, USA.
  22. del Rey Castillo, E., Griffith, M. and Ingham, J. (2018), "Seismic behavior of RC columns flexurally strengthened with FRP sheets and FRP anchors", Compos. Struct., 203, 382-395. https://doi.org/10.1016/j.compstruct.2018.07.029.
  23. Dogangun, A. and Livaoglu, R. (2004), "Hydrodynamic pressures acting on the walls of rectangular fluid containers", Struct. Eng. Mech., 17(2), 203-214. https://doi.org/10.12989/sem.2004.17.2.203.
  24. Elgabbas, F., El-Ghandour, A., Abdelrahman, A. and El-Dieb, A. (2010), "Different CFRP strengthening techniques for prestressed hollow core concrete slabs: Experimental study and analytical investigation", Compos. Struct., 92(2), 401-411.
  25. Ergin, A., Temarel, P. and vibration (2002), "Free vibration of a partially liquid-filled and submerged, horizontal cylindrical shell", J. Sound, 254(5), 951-965. https://doi.org/10.1006/jsvi.2001.4139.
  26. Eurocode 8 (2004), Eurocode 8: Design of Structures for Earthquake Resistance, European Commission, Ispra, Italy.
  27. Ewins, D. and Imregun, M. (1986), "State-of-the-art assessment of structural dynamic response analysis methods (DYNAS)", Shock Vib. Bull., 59, 1.
  28. Fan, J. (2018), Modeling of Lightly Confined Reinforced Concrete Columns Subjected to Lateral and Axial Loads, The Ohio State University, Columbus, OH, USA.
  29. Fan, J., Hur, J., Sezen, H., Denning, R. and Aldemir, T. (2020), "Structural modeling and dynamic analysis of condensate storage tanks in nuclear power plants", Nucl. Eng. Des., 363, 110613. https://doi.org/10.1016/j.nucengdes.2020.110613.
  30. Gamage, J., Wong, M.B. and Al-Mahaidi, R. (2005). "Performance of CFRP strengthened concrete members under elevated temperatures", Proceedings of the International Symposium on Bond Behaviour of FRP in Structures (BBFS 2005), Hong Kong, China, December.
  31. Gemi, L. (2018), "Investigation of the effect of stacking sequence on low velocity impact response and damage formation in hybrid composite pipes under internal pressure. A comparative study", Compos. Part B: Eng., 153, 217-232. https://doi.org/10.1016/j.compositesb.2018.07.056.
  32. Gemi, L., Aksoylu, C., Yazman, S., Ozkilic, Y.O. and Arslan, M.H. (2019), "Experimental investigation of shear capacity and damage analysis of thinned end prefabricated concrete purlins strengthened by CFRP composite", Compos. Struct., 229, 111399. https://doi.org/10.1016/j.compstruct.2019.111399.
  33. Gemi, L., Kayrici, M., Uludag, M., Gemi, D.S. and Sahin, O .S. (2018), "Experimental and statistical analysis of low velocity impact response of filament wound composite pipes", Compos. Part B: Eng., 149, 38-48. https://doi.org/10.1016/j.compositesb.2018.05.006.
  34. Gemi, L., Morkavuk, S., Koklu, U. and Gemi, D.S. (2019), "An experimental study on the effects of various drill types on drilling performance of GFRP composite pipes and damage formation", Compos. Part B: Eng., 172, 186-194. https://doi.org/10.1016/j.compositesb.2019.05.023.
  35. Gemi, L., Morkavuk, S., Koklu, U. and Yazman, S. (2020), "The effects of stacking sequence on drilling machinability of filament wound hybrid composite pipes: Part-2 damage analysis and surface quality", Compos. Struct., 235, 111737. https://doi.org/10.1016/j.compstruct.2019.111737.
  36. Gemi, L., Sahin, O.S. and Akdemir, A. (2017), "Experimental investigation of fatigue damage formation of hybrid pipes subjected to impact loading under internal pre-stress", Compos. Part B: Eng., 119, 196-205. https://doi.org/10.1016/j.compositesb.2017.03.051.
  37. Godoy, L.A. (2016), "Buckling of vertical oil storage steel tanks: Review of static buckling studies", Thin Wall. Struct., 103, 1-21. https://doi.org/10.1016/j.tws.2016.01.026.
  38. Goudarzi, M.A., Moosapoor, M. and Nikoomanesh, M.R. (2020), "Seismic design loads of cylindrical liquid tanks with insufficient nfreeboard", Earthq. Spectra, 36(4), 1844-1863. https://doi.org/10.1177/8755293020926191.
  39. Hamdan, F. (2000a), "Seismic behaviour of cylindrical steel liquid storage tanks", J. Constr. Steel Res., 53(3), 307-333. https://doi.org/10.1016/S0143-974X(99)00039-5.
  40. Hamdan, F. (2000b), "Seismic behaviour of cylindrical steel liquid storage tanks", J. Constr. Steel Res., 53(3), 307-333.
  41. Hashemi, S., Saadatpour, M.M. and Kianoush, M. (2013b), "Dynamic analysis of flexible rectangular fluid containers subjected to horizontal ground motion", Earthq. Eng., 42(11), 1637-1656. https://doi.org/10.1002/eqe.2291.
  42. Hashemi, S., Saadatpour, M.M. and Kianoush, M.R. (2013a), "Dynamic analysis of flexible rectangular fluid containers subjected to horizontal ground motion", Earthq. Eng., 42(11), 1637-1656. https://doi.org/10.1002/eqe.2291.
  43. Hernandez-Hernandez, D., Larkin, T., Chouw, N. and Banide, Y. (2020), "Experimental findings of the suppression of rotary sloshing on the dynamic response of a liquid storage tank", J. Fluid. Struct., 96, 103007. https://doi.org/10.1016/j.jfluidstructs.2020.103007.
  44. Housner, G.W. (1954), "Earthquake pressures on fluid containers", California Institute of Technology, Earthquake Research Laboratory, Pasadena, CA, USA.
  45. Housner, G.W. (1957), "Dynamic pressures on accelerated fluid containers", Bull. Seismol. Soc. Am., 47(1), 15-35.
  46. Housner, G.W. (1963), "The dynamic behavior of water tanks", Bull. Seismol. Soc. Am., 53(2), 381-387.
  47. Kashani, B.K. and Sani, A.A.J.E.J.o.M.-A.S. (2016), "Free vibration analysis of horizontal cylindrical shells including sloshing effect utilizing polar finite elements", Eur. J. Mech. A/Solids, 58, 187-201. https://doi.org/10.1016/j.euromechsol.2016.02.002.
  48. Ke, L., Li, C., Luo, N., He, J., Jiao, Y. and Liu, Y. (2019), "Enhanced comprehensive performance of bonding interface between CFRP and steel by a novel film adhesive", Compos. Struct., 229, 111393. https://doi.org/10.1016/j.compstruct.2019.111393.
  49. Khalil, M., Ruggieri, S. and Uva, G. (2022). "Assessment of structural behavior, vulnerability, and risk of industrial silos: State-of-the-art and recent research trends", Appl. Sci., 12(6), 3006. https://doi.org/10.3390/app12063006.
  50. Khalil, M., Ruggieri, S., Tateo, V., Nascimbene, R. and Uva, G. (2023), "A numerical procedure to estimate seismic fragility of cylindrical ground-supported steel silos containing granular-like material", Bull. Earthq. Eng., 21, 5915-5947. https://doi.org/10.1007/s10518-023-01751-6.
  51. Kirtas, E., Rovithis, E. and Makra, K. (2020), "On the modal response of an instrumented steel water-storage tank including soil-structure interaction", Soil Dyn. Earthq. Eng., 135, 106-198. https://doi.org/10.1016/j.soildyn.2020.106198.
  52. Kohrangi, M., Bakalis, K., Triantafyllou, G., Vamvatsikos, D. and Bazzurro, P. (2023), "Hazard consistent record selection procedures accounting for horizontal and vertical components of the ground motion: Application to liquid storage tanks", Earthq. Eng. Struct. Dyn., 52(4), 1232-1251. https://doi.org/10.1002/eqe.3813.
  53. Ma, C., Wang, D. and Wang, Z. (2017), "Seismic retrofitting of full- scale RC interior beam-column-slab subassemblies with CFRP wraps", Compos. Struct., 159, 397-409. https://doi.org/10.1016/j.compstruct.2016.09.094.
  54. Madenci, E., Ozkilic, Y.O. and Gemi, L. (2020), "Experimental and theoretical investigation on flexure performance of pultruded GFRP composite beams with damage analyses", Compos. Struct., 242, 112162. https://doi.org/10.1016/j.compstruct.2020.112162.
  55. Mahdavipour, M.A., Eslami, A. and Jehel, P. (2019), "Seismic evaluation of ordinary RC buildings retrofitted with externally bonded FRPs using a reliability-based approach", Compos. Struct., 232, 111567. https://doi.org/10.1016/j.compstruct.2019.111567.
  56. Malhotra, P.K., Wenk, T. and Wieland, M. (2000), "Simple procedure for seismic analysis of liquid-storage tanks", Struct. Eng. Int., 10(3), 197-201. https://doi.org/10.2749/101686600780481509.
  57. Mieda, G., Nakamura, H., Matsui, T., Ochi, Y. and Matsumoto, Y. (2019), "Mechanical behavior of CFRP on steel surface molded and bonded by vacuum-assisted resin transfer molding technology", SN Appl. Sci., 1(6), 601. https://doi.org/10.1007/s42452-019-0603-4.
  58. Miladi, S. and Razzaghi, M.S. (2019), "Failure analysis of an unanchored steel oil tank damaged during the Silakhor earthquake of 2006 in Iran", Eng. Fail. Anal., 96, 31-43. https://doi.org/10.1016/j.engfailanal.2018.09.031.
  59. Moeini, M., Nikomanesh, M.R. and Goudarzi, M.A. (2019), "Vertical isolation of seismic loads in aboveground liquid storage tanks", J. Seismol. Earthq. Eng., 21(1), 45-53.
  60. Mohamadshahi, M. and Afrous, A. (2015), "General considerations in the seismic analysis of steel storage tanks", J. Sci. Res. Develop., 2(6), 151-156.
  61. Molin, B. and Remy, F. (2013), "Experimental and numerical study of the sloshing motion in a rectangular tank with a perforated screen", J. Fluids, 43, 463-480. https://doi.org/10.1016/j.jfluidstructs.2013.10.001.
  62. Morkavuk, S., Koklu, U., Bagci, M. and Gemi, L. (2018), "Cryogenic machining of carbon fiber reinforced plastic (CFRP) composites and the effects of cryogenic treatment on tensile properties: A comparative study", Compos. Part B: Eng., 147, 1-11. https://doi.org/10.1016/j.compositesb.2018.04.024.
  63. Moslemi, M. (2011), "Seismic response of ground cylindrical and elevated conical reinforced concrete tanks", Ph.D. Thesis, Civil Engineering, Ryerson University, Toronto, Ontario, Canada.
  64. Nelson, J.W. (2010), "Composite materials for aircraft structures: A brief review of practical application", Ph.D. Research, Department of Mechanical and Industrial Engineering, Montana State University, Bozeman, MT, USA.
  65. Nichols, R.J. (1983), "Ford's CNG vehicle research", Energy Technol., 10, 1.
  66. Nicolici, S. and Bilegan, R. (2013), "Fluid structure interaction modeling of liquid sloshing phenomena in flexible tanks", Nucl. Eng. Des., 258, 51-56.
  67. Nikoomanesh, M.R., Moeini, M. and Goudarzi, M.A. (2019), "An innovative isolation system for improving the seismic behaviour of liquid storage tanks", Int. J. Press. Vessel. Pip., 173, 1-10. https://doi.org/10.1016/j.ijpvp.2019.04.012.
  68. Niwa, A. and Clough, R.W. (1982), "Buckling of cylindrical liquid- storage tanks under earthquake loading", Earthq. Eng. Struct. Dyn., 10(1), 107-122. https://doi.org/10.1002/eqe.4290100108.
  69. Ozdemir, Z., Souli, M. and Fahjan, Y. (2010), "Application of nonlinear fluid-structure interaction methods to seismic analysis of anchored and unanchored tanks", Eng. Struct., 32(2), 409-423. https://doi.org/10.1016/j.engstruct.2009.10.004.
  70. Ozdemir, Z., Souli, M. and Yasin, M.F. (2012), "Numerical evaluation of nonlinear response of broad cylindrical steel tanks under multidimensional earthquake motion", Earthq. Spectra, 28(1), 217-238. https://doi.org/10.1193/1.3672996.
  71. Ozkilic, Y.O. (2020), "A new replaceable fuse for moment resisting frames: Replaceable bolted reduced beam section connections", Steel Compos. Struct., 35(3), 353-370. https://doi.org/10.12989/scs.2020.35.3.353.
  72. Ozkilic, Y.O., Madenci, E. and Gemi, L. (2020), "Tensile and compressive behaviors of the pultruded GFRP lamina", Turk. J. Eng. (TUJE), 4(4), 169-175. https://doi.org/10.31127/tuje.631481.
  73. Pereira, M.F., De Nardin, S. and El Debs, A.L. (2020), "Partially encased composite columns using fiber reinforced concrete: Experimental study", Steel Compos. Struct., 34(6), 909-927. https://doi.org/10.12989/scs.2020.34.6.909.
  74. Phan Viet, N., Kitano, Y. and Matsumoto, Y. (2020), "Experimental investigations of the strengthening effects of CFRP for thin-walled storage tanks under dynamic loads", Appl. Sci., 10(7), 2521. https://doi.org/10.3390/app10072521.
  75. Phan Viet, N., Kitano, Y. and Matsumoto, Y. (2020), "Experimental investigations of the strengthening effects of CFRP for thin-walled storage tanks under dynamic loads", Appl. Sci., 10(7), 2521. https://doi.org/10.3390/app10072521.
  76. Phan, H.N., Paolacci, F. and Mongabure, P. (2017), "Nonlinear finite element analysis of unanchored steel liquid storage tanks subjected to seismic loadings", ASME 2017 Pressure Vessels and Piping Conference, Waikoloa, HI, USA, July.
  77. Qin, Y., Luo, K.R. and Yan, X. (2020), "Buckling analysis of steel plates in composite structures with novel shape function", Steel Compos. Struct., 35(3), 405-413. https://doi.org/10.12989/scs.2020.35.3.405.
  78. Rastgar, M. and Showkati, H. (2018), "Buckling behavior of cylindrical steel tanks with concavity of vertical weld line imperfection", J. Constr. Steel Res., 145, 289-299. https://doi.org/10.1016/j.jcsr.2018.02.028.
  79. Sadowski, A.J. and Rotter, J.M. (2013), "Buckling in eccentrically discharged silos and the assumed pressure distribution", J. Eng. Mech., 139(7), 858-867. https://doi.org/10.1061/(ASCE)EM.1943-7889.0000525.
  80. Shekari, M.R., Khaji, N. and Ahmadi, M.T. (2010), "On the seismic behavior of cylindrical base-isolated liquid storage tanks excited by long-period ground motions", Soil Dyn. Earthq. Eng., 30(10), 968-980. https://doi.org/10.1016/j.soildyn.2010.04.008.
  81. Sunitha, K. and Jacob, B. (2015), "Dynamic buckling of steel water tank under seismic loading", Int. J. Civil Eng. (IJCE), 4(6), 81-90. https://doi.org/10.1002/stco.201900003.
  82. Tarakcioglu, N., Gemi, L. and Yapici, A. (2005), "Fatigue failure behavior of glass/epoxy±55 filament wound pipes under internal pressure", Compos. Sci. Technol., 65(3-4), 703-708. https://doi.org/10.1016/j.compstruct.2009.07.027.
  83. Torayca (2020), High-Performance Carbon Fiber Torayca, Torayca Cloth, Toray Industries, Inc, Tokyo, Japan.
  84. Van Cao, V. and Ronagh, H.R. (2014), "Reducing the seismic damage of reinforced concrete frames using FRP confinement", Compos. Struct., 118, 403-415. https://doi.org/10.1016/j.compstruct.2014.07.038.
  85. Vasiliev, V.V. and Morozov, E.V. (2013), Advanced Mechanics of Composite Materials and Structural Elements, Newnes, Sebastopol, CA, USA.
  86. Virella, J., Godoy, L. and Suarez, L. (2003), "Influence of the roof on the natural periods of empty steel tanks", Eng. Struct., 25(7), 877-887. https://doi.org/10.1016/S0141-0296(03)00022-1.
  87. Virella, J., Godoy, L. and Suarez, L. (2006a), "Dynamic buckling of anchored steel tanks subjected to horizontal earthquake excitation", J. Constr. Steel Res., 62(6), 521-531. https://doi.org/10.1016/j.jcsr.2005.10.001.
  88. Virella, J.C., Godoy, L.A. and Suarez, L.E. (2006), "Dynamic buckling of anchored steel tanks subjected to horizontal earthquake excitation", J. Constr. Steel Res., 62(6), 521-531. https://doi.org/10.1016/j.jcsr.2005.10.001.
  89. Virella, J.C., Godoy, L.A. and Suarez, L.E. (2006b), "Fundamental modes of tank-liquid systems under horizontal motions", Eng. Struct., 28(10), 1450-1461. https://doi.org/10.1016/j.engstruct.2005.12.016.
  90. Wikipedia (2020), Finite Element Method. https://en.wikipedia.org/wiki/Finite_element_method
  91. Xu, G., Ding, Y., Xu, J., Chen, Y. and Wu, B. (2020), "A shaking table substructure testing method for the structural seismic evaluation considering soil-structure interactions", Adv. Struct. Eng., 23(14), 3024-3036. https://doi.org/10.1177/1369433220927267.
  92. Yan, K., Zhang, Y., Cai, H. and Tahouneh, V. (2020), "Vibrational characteristic of FG porous conical shells using Donnell's shell theory", Steel Compos. Struct., 35(2), 249-260. https://doi.org/10.12989/scs.2020.35.2.249.
  93. Yazdanian, M., Razavi, V. and Mashal, M. (2016), "Study on the dynamic behavior of cylindrical steel liquid storage tanks using finite element method", J. Theoret. Appl. Vib. Acoust., 2(2), 145-166. https://doi.org/10.22064/TAVA.2016.21833.
  94. Zeybek, O., Celik, A. and Ozkilic, Y. (2023), "Buckling of axially loaded shell structures made of stainless steel", Steel Compos. Struct., 48(6), 681. https://doi.org/10.12989/scs.2023.48.6.681.
  95. Zeybek, O., CELIK, A. and Ozkilic, Y. (2023), "Buckling of axially loaded shell structures made of stainless steel", Steel Compos. Struct., 48(6), 681. https://doi.org/10.12989/scs.2023.48.6.681.
  96. Zeybek, O., Topkaya, C. and Rotter, J.M. (2019), "Stress resultants for wind girders in open-top cylindrical steel tanks", Eng. Struct., 196, 109347. https://doi.org/10.1016/j.engstruct.2019.109347.
  97. Zhang, H., El Ansary, A.M. and Zhou, W. (2022), "Prediction of buckling capacity of liquid-filled steel conical tanks considering field-measured imperfections", Eng. Struct., 262, 114351. https://doi.org/10.1016/j.engstruct.2022.114351.