A generalized coordinate method for the analysis of 3D tall buildings

Abstract

A generalized coordinate method (GCM) is proposed for the reduction of unknowns in the 3D analysis of tall buildings when the displacement method is employed. The number of variables is reduced by the assumption of in-plane rigid floors and by use of a 2D polynomial approximation for the out-of-plane displacements of floors, and a 1D polynomial approximation of the displacements with the height of building. The overall stiffness equation is obtained in generalized coordinates. The transformations are performed at the member level so that calculations involving large matrices are avoided. The GCM might be considered as a reduction technique based on a combination of the FEM at member level and the Rayleigh-Ritz method at the structure level. The GCM has the advantages that (1) the number of unknowns is significantly reduced and is independent of the number of storeys: (2) the accuracy can be adjusted by selecting the number of terms of the displacement function. The storage needed, the required number of operations and the possibility of choosing hierarchical displacement functions to make the calculation adaptive are discussed. The method presented can easily be extended to nonlinear and dynamic analysis. However, the derivation in this paper is confined only to the linear elastic analysis of frame and frame-shear wall structures. Numerical examples are given to show the efficiency of the proposed method.