A consistent FEM-Vlasov model for hyperbolic cooling towers on layered soil under unsymmetrical wind load

  • Received : 2016.01.21
  • Accepted : 2016.04.09
  • Published : 2016.06.25


In this paper, the analysis of hyperbolic cooling tower on elastic subsoil exposed to unsymmetrical wind loading is presented. Modified Vlasov foundation model is used to determine the soil parameters as a function of vertical deformation profile within subsoil. The iterative parameter updating procedure involves the use of Open Application Programming Interface (OAPI) feature of SAP2000 to provide two way data flow during execution. A computing tool coded in MATLAB employing OAPI is used to perform the analysis of hyperbolic cooling tower with supporting columns over a hollow annular raft founded on elastic subsoil. The analysis of such complex soil-structure system is investigated under self-weight and unsymmetrical wind load. The response of the cooling tower on elastic subsoil is compared with that of a tower that its supporting raft foundation is treated as fixed at the base. The results show that the effect of subsoil on the behavior of cooling tower is considerable at the top and bottom of the wall as well as supporting columns and raft foundation. The application of a full-size cooling tower has demonstrated that the procedure is simple, fast and can easily be implemented in practice.


hyperbolic cooling tower;modified Vlasov model;unsymmetrical wind load;open application programming interface;finite element analysis


  1. Nasir, A.M., Thambiratnam, D.P., Butler, D. and Austin, P. (2002), "Dynamics of axisymmetric hyperbolic shell structures", Thin Wall Struct., 40(7-8), 665-690.
  2. Noorzaei, J., Naghshineh, A., Kadir, M.R.A., Thanoon, W.A. and Jaafar, M.S. (2006), "Nonlinear interactive analysis of cooling tower-foundation-soil interaction under unsymmetrical wind load", Thin Wall Struct., 44(9), 997-1005.
  3. Prasahanth, N. and Sulaiman, S. (2013), "To study the effect of seismic loads and wind load on hyperbolic cooling tower of varying dimensions and rcc shell thickness", Int. J. Emerging Trends in engineering and Development, 4, 260-269.
  4. Saygun, A. and Celik, M. (2003), "Analysis of circular plates on two-parameter elastic foundation", Struct. Eng. Mech., 15(2), 249-267.
  5. Tande, S.N. and Chougule, S.S. (2013), "Linear and nonlinear behavior of rc cooling tower under earthquake loading", Int. J. Latest Trends in Eng. Technol., 2(4), 370-379.
  6. Vallabhan, C.V.G., Straughan, W.T. and Das, Y.C. (1991), "Refined model for analysis of plates on elastic foundations", J. Eng. Mech. - ASCE, 117(12), 2830-2844.
  7. Viladkar, M.N., Bhargava, P. and Godbole, P.N. (2006), "Static soil-structure interaction response of hyperbolic cooling towers to symmetrical wind loads", Eng Struct., 28(9), 1236-1251.
  8. Viladkar, M.N., Godbole, P.N. and Krishna, P. (1998), "Finite element analysis of column supported hyperbolic cooling towers using semi-loof shell and beam elements", Eng Struct., 20(1-2), 75-85.
  9. Viladkar, M.N., Godbole, P.N. and Krishna, P. (2012), "Response of cooling towers to wind loads", ARPN J. Eng. Appl. Sci., 7114-120.
  10. Yang, Z.W. and Lu, W.D. (1992), "Static soil-structure interaction analysis by Fe-Be coupling method", Appl. Math. Model., 16(7), 384-389.
  11. ACI-318 (2011), Building code requirements for structural concrete and commentary.
  12. Asadzadeh, E., Rajan, A., Kulkarni, M.S. and Asadzadeh, S. (2012), "Finite element analysis for structural response of rcc cooling tower shell considering alternative supporting systems", Int. J. Civil Eng. Technol., 382-398.
  13. Bosak, G. and Flaga, A. (1996), "Probabilistic and deterministic aspects of combinations of wind, thermal and dead loads on cooling towers", J. Wind Eng. Ind. Aerod., 65(1-3), 107-120.
  14. C, A.A. (1977), Reinforced concrete cooling tower shells-practice and commentary, J ACI.
  15. Christian, L. (2011a), Earthquake behavior of natural draft cooling towers-Determination of behavior factors with special regard to different types of supporting column systems, Leuven, Belgium.
  16. Christian, L. (2011b), Free vibration and earthquake behavior of solar power plant chimneys, Corfu, Greece.
  17. Jia, X. (2013), "Revisiting the failure mode of a RC hyperbolic cooling tower, considering changes of material and geometric properties", Eng Struct., 47, 148-154.
  18. Lang, C., Meiswinkel, R. and Filippou, F.C. (2002), "Nonlinear analysis of shells of revolution with ring elements", Eng. Struct., 24(2), 163-177.

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