Dynamics of a Class of Horizontal Setback Buildings

Abstract

Dynamics of a class of horizontal setback buildings with flexible floor diaphragms has been studied by developing a “separable model.” A rectangular plan building, with flexible floor diaphragms, is a particular case of the horizontal setback building. The mass and stiffness matrices have been written in terms of direct products of matrices. The separable buildings have two types of natural modes of vibration: (a) those which involve in-plane floor deformation, and (b) those in which the floors do not undergo in-plane deformation. Further, spatially uniform ground motion does not excite the modes involving in-plane floor deformation. Therefore, the problems associated with diaphragm flexibility, e.g., stress concentration at the re-entrant corners, are avoided in separable buildings. General conditions for a building to be separable have been obtained. In simplistic terms, these conditions imply that (a) all wings of the building should have identical value of lateral stiffness per unit plan area divided by mass per unit plan area in either of the principal directions of the wings, and (b) all of the floor diaphragms should have same ratio of lateral stiffness to mass. In other words, the building should be configured so that the fundamental period of vibration of each wing in either direction is the same, and that of all the floors for in-plane vibrations is the same.