Dynamic Analysis of Multistory Buildings

Analysis and design of common types of buildings to resist earthquake forces is done by the method described in the Uniform Building Code. Approximate formulas for natural periods of fundamental mode of buildings are available and are used in the static method of aseismic design of Uniform Building Code. However, some building codes in the seismic regions require dynamic analysis of tall buildings and other important structures. The dynamic analysis of multistory structures is laborious and time consuming because of the many degrees of freedom involved. Modern electronic computers have made possible the dynamic analysis of multidegree freedom systems which was prohibitive by hand calculations. However, when the number of degrees of freedom is large, the dynamic analysis requires the use of digital computers of large capacities and the computer time used can be very expensive. In the modal method of dynamic analysis, the natural periods and mode shapes for various modes of vibrations are determined by computer analysis. The objective in this paper is to develop simplified methods for determining natural periods of vibrations of multistory buildings so that expensive computer time is kept to a minimum. Since the aseismic design by dynamic analysis require a few preliminary trials before final satisfactory design is achieved, the simplified methods can save laborious computer calculations in the preliminary design. The simplified methods discussed in this paper are developed using the concept of an elastic shear wave equation in solid uniform bars. A numerical example is presented to compare the simplified methods with the more rigorous analysis.