Nonlinear Static Analysis of Cable Roof Structures with Unified Kinematic Description

  • LEE, Sang Jin (ADOPT Research Group, Department of Architectural Engineering, Gyeongsang National University)
  • Received : 2015.07.20
  • Accepted : 2016.01.25
  • Published : 2016.03.30


A finite element analysis technology applicable to the prediction of the static nonlinear response of cable roof structure is presented. The unified kinematic description is employed to formulate the present cable element and different strain definitions such as Green-Lagrange strain, Biot strain and Hencky strain can be adopted. The Newton-Raphson method is used to trace the nonlinear load-displacement path. In the iteration process, the compressive stress of a cable element is not allowed. For the verification of the present cable element, four numerical examples are tackled. Finally, numerical results obtained by using the present cable element are provided as new benchmark test results for cable structures under static loads.


  1. Argyris, J. and Scharpf, D. (1972) Large deflection analysis of prestressed networks, Journal of the Structural Division 98 (3), pp.633-654.
  2. Baron, F. and Venkatesan, M. S. (1971) Nonlinear analysis of cable and truss structures. Journal of the Structural Division, Proceedings of the American Society of Civil Engineers, ASCE, Vol. 97, no. ST2, pp. 679-710.
  3. Broughton, P. and Ndumbaro, P. (1994) The Analysis of Cable and Catenary Structures. London, England: Thomas Telford Services Ltd.
  4. Desai, Y. M., Popplewell, N., Shah, A. H. and Buragohain, D. N. (1988) Geometric nonlinear static analysis of cable supported structures, Computers and Structures, vol. 29, no. 6, pp. 1001-1009.
  5. Gambhir ML, de Batchelor BV. (1977) A finite element for 3-D prestressed cablenets. International Journal of Numerical Methods in Engineering, 11, pp.1699-1718.
  6. Jayaraman, H. B. and Knudson, W. C. (1981) A curved element for the analysis of cable structures. Computers & Structures, Vol. 14, No. 3/4, pp. 325-333.
  7. Kollr, L. (2003) Covering grandstand by cable structures, Periodica Polytechnica Ser. Civ. Eng. Vol. 47, No. 1, pp.43-48
  8. Kwan, A.S.K. (1998) A new approach to geometric nonlinearity of cable structures, Computers and Structures, 67, pp. 243-252
  9. Lewis, W.J. (1989) The efficiency of numerical methods for the analysis of prestressed nets and pin-joined frame structure, Computer & Structures, Vol 33. No. 3 pp. 791-800.
  10. Lewis, W.J. (2003) Tension structures: Form and behaviour, Thomas Telford.
  11. Meek, J.L. (1991) Computer methods in structural analysis. E. & F.N. Spon.
  12. Michalos, J. and Birnstiel, C. (1960) Movements of a cable due to change in loading. Journal of the Structural Division, ASCE, Vol. 86, No. ST12, pp. 23-38.
  13. Mitsugi, J. (1994) Static analysis of cable networks and their supporting structures. Computers & Structures, 51(1), pp. 47-56.
  14. Salehi Ahmad Abad, M., Shooshtari, M. Esmaeili, Alireza Naghavi Riabi, V. (2013) Nonlinear analysis of cable structures under general loadings. Finite Elements in Analysis and Design, 73, pp. 11-19
  15. O'Brien, W. T. and Francis, A. J. (1964) Cable movements under two-dimensional loads. Journal of the Structural Division, ASCE, Vol. 90, No. ST3, pp. 89-123.
  16. Peyrot, A. H. and Goulois, A. M. (1978) Analysis of flexible transmission lines. Journal of the Structural Division, ASCE, Vol. 104, No. ST5, pp. 763-779.
  17. Peyrot, A. H. and Goulois, A. M. (1979) Analysis of cable structures. Computers & Structures, Vol. 10, No. 5, pp. 805-813.
  18. Poskitt, F. (1967) Numerical solution of nonlinear structures. Journal of Structural Division, ASCE, ST3, 93, 69-94
  19. Saafan, S. A. (1970) Theoretical analysis of suspension roofs. Journal of the Structural Division, ASCE Vol. 96, No. ST2, pp. 393-404.
  20. Such, M., Jimenez-Octavio, J.R., Carnicero, A. and Lopez-Garcia, O. (2009) An approach based on the catenary equation to deal with static analysis of three dimensional cable structures, Engineering Structures, Vol. 31, pp. 2162-2170.
  21. Thai, H.-T. and Kim, S.-E. (2011) Nonlinear static and dynamic analysis of cable structures. Finite Elements in Analysis and Design, 47, pp. 237-246
  22. Tibert, G. (1999) Numerical analyses of cable roof structures. MScThesis, Royal Institute of Technology.
  23. Webster, R. L. (1975) Nonlinear static and dynamic response of underwater cable structures using the finite element method. Offshore Technology Conference, Paper No. OTC2322, Dallas, Texas, pp. 753-764.
  24. West, H. H., and Kar, A. K. (1973) Dicretized initial-value analysis of cable nets. International Journal of Solids and Structures, Vol. 9, pp.1403-1420.