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


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.


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


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