Dynamics of Buildings with Y-Shaped Plan and Flexible Floor Diaphragms

A long, narrow multistory building with Y-shaped plan having a number of identical frames and floors placed uniformly is modeled including in-plane floor flexibility and analyzed using the equivalent vertically oriented anisotropic plate concept. It is observed 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 motion. A Y-shaped building could therefore be configured so as to have some total lateral stiffness in the two directions for each wing. This will ensure that stress concentration at reentrant corners, caused by the floor-diaphragm flexibility, does not take place. The method is illustrated with a numerical example. In general, the in-plane floor flexibility does not substantially alter the natural periods, even though this may significantly affect the shear distribution among transverse frames, depending upon the configuration.