Analysis of free vibrations of tall buildings

An analysis of free vibrations of tall buildings, such as frame, shear- wall, and frame-shear-wall structures, is proposed and discussed in this paper. Frame buildings are treated as shear beams with varying cross sections, the solutions of mode shapes of such buildings are expressed in Bessel’s functions, and the parameter of determining the fundamental period can be found from a figure provided in the paper. Based on the fact that the shear deformation and bending deformation are all considered for shear wall and frame-shear-wall structures, the formulas for calculating free vibrations of such structures are presented. It is very simple and convenient to apply these formulas to dynamic analysis of tall buildings. The measurement results and statistical analysis of frame, shear-wall, and frame- shear-wall structures in sites, and three examples of determining free vibrations of structures are also given in this paper. The examples show that the effect of shear deformation on the first natural frequency is not significant, but the effect of that on higher natural frequencies may not be neglected © ASCE.