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Two-dimensional rod theory for approximate analysis of building structures

  • Takabatake, Hideo (Department of Architecture, Kanazawa Institute of Technology, Institute of Disaster and Environmental Science)
  • Received : 2009.12.29
  • Accepted : 2010.02.06
  • Published : 2010.03.25

Abstract

It has been known that one-dimensional rod theory is very effective as a simplified analytical approach to large scale or complicated structures such as high-rise buildings, in preliminary design stages. It replaces an original structure by a one-dimensional rod which has an equivalent stiffness in terms of global properties. If the structure is composed of distinct constituents of different stiffness such as coupled walls with opening, structural behavior is significantly governed by the local variation of stiffness. This paper proposes an extended version of the rod theory which accounts for the two-dimensional local variation of structural stiffness; viz, variation in the transverse direction as well as longitudinal stiffness distribution. The governing equation for the two-dimensional rod theory is formulated from Hamilton's principle by making use of a displacement function which satisfies continuity conditions across the boundary between the distinct structural components in the transverse direction. Validity of the proposed theory is confirmed by comparison with numerical results of computational tools in the cases of static, free vibration and forced vibration problems for various structures.

Keywords

simplified analytical method;extended rod theory;two-dimensional stiffness of structures;preliminary design for buildings;dynamic analysis;shear wall with opening

References

  1. Buchholdt, H. (1997), Structural dynamics for engineers, Thomas Telford.
  2. Georgoussis, G.K. (2006), "A simple model for assessing periods of vibration and modal response quantities in symmetrical buildings", Struct. Des. Tall Spec. Build., 15(2), 139-151. https://doi.org/10.1002/tal.286
  3. Pubal, Z. (1988), Theory and calculation of frame structures with stiffening walls, Elsevier, Amsterdam.
  4. Rutenberg, A. (1975), "Approximate natural frequencies for coupled shear walls", Earthq. Eng. Struct. D., 4(1), 95-100. https://doi.org/10.1002/eqe.4290040107
  5. Smith, B.S. and Coull, A. (1991), Tall building structures: analysis and design, John Wily & Sons, New York.
  6. Scarlet, A.S. (1996), Approximate methods in structural seismic design, E&FN Spon.
  7. Takabatake, H. and Matsuoka, O. (1983), "The elastic theory of thin-walled open cross sections with local deformations", Int. J. Solids Struct., 19(12), 1065-1088. https://doi.org/10.1016/0020-7683(83)90080-X
  8. Takabatake, H., and Matsuoka, O. (1987), "Elastic analyses of circular cylindrical shells by rod theory including distortion of cross section", Int. J. Solids Struct., 23(6), 797-817. https://doi.org/10.1016/0020-7683(87)90080-1
  9. Takabatake, H., Mukai, H. and Hirano, T. (1993a), "Doubly symmetric tube structures: I: static analysis", J. Struct. Eng-ASCE, 119(7), 1981-2001. https://doi.org/10.1061/(ASCE)0733-9445(1993)119:7(1981)
  10. Takabatake, H., Mukai, H. and Hirano, T. (1993b), "Doubly symmetric tube structures: II: dynamic analysis", J. Struct. Eng-ASCE, 119(7), 2002-2016. https://doi.org/10.1061/(ASCE)0733-9445(1993)119:7(2002)
  11. Takabatake, H., Takesako, R. and Kobayashi, M. (1995), "A simplified analysis of doubly symmetric tube structures", Struct. Des. Tall Spec. Build., 4(2), 137-153. https://doi.org/10.1002/tal.4320040205
  12. Takabatake, H. (1996), "A simplified analysis of doubly symmetric tube structures by the finite difference method", Struct. Des. Tall Spec. Build., 5(2), 111-128. https://doi.org/10.1002/(SICI)1099-1794(199606)5:2<111::AID-TAL68>3.0.CO;2-F
  13. Takabatake, H. and Nonaka, T. (2001), "Numerical study of Ashiyahama residential building damage in the Kobe Earthquake", Earthq. Eng. Struct. D., 30(6) , 879-897. https://doi.org/10.1002/eqe.46
  14. Takabatake, H., Nonaka, T. and Tanaki, T. (2005), "Numerical study of fracture propagating through column and brace of Ashiyahama residential building in Kobe Earthquake", Struct. Des. Tall Spec. Build., 14(2), 91-105. https://doi.org/10.1002/tal.265
  15. Takabatake, H. and Satoh, T. (2006), "A simplified analysis and vibration control to super-high-rise buildings", Struct. Des. Tall Spec. Build., 15(4), 363-390. https://doi.org/10.1002/tal.276
  16. Tarjian, G. and Kollar, L.P. (2004), "Approximate analysis of building structures with identical stories subjected to earthquake", Int. J. Solids Struct., 41(5), 1411-1433. https://doi.org/10.1016/j.ijsolstr.2003.10.021

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