Dynamics of Buildings with V‐Shaped Plan

Abstract

An analytical model is presented for the dynamic analysis of multistory buildings with flexible‐floor diaphragms. A long, narrow multistory building with a number of uniform stories and frames (or walls) is treated as a vertically oriented anisotropic plate. The resulting equations of motion and boundary conditions are solved to obtain the natural frequencies and mode shapes. The model is applied to buildings with V‐shaped plans. It is seen that for unequal stiffness of a wing in the transverse and longitudinal directions, all natural modes of vibration involve in‐plane floor deformations. However, if the two stiffnesses are equal, rigid‐floor as well as flexible‐floor modes exist, but the latter are not excited by spatially uniform ground acceleration. The floor flexibility, in general, does not substantially affect the natural periods, even though, depending upon the configuration, this may significantly affect the shear distribution among transverse frames. Floor flexibility tends to become more significant with increases in: (1) The difference between the transverse and the longitudinal stiffnesses; (2) the deviation of the angle between the wings from 90°; and (3) the length‐to‐width ratio, and with the decrease in height‐to‐length ratio.