Analytical models for low‐rise buildings with flexible floor diaphragms

Abstract

AbstractThe observed behaviour of buildings during earthquakes indicates clearly the importance of the flexibility of floor and roof diaphragms in the response of many structures. This paper presents a new analytical method for the dynamic analysis of some one‐ and two‐storey buildings whose floors may have significant in‐plane flexibility. The method begins by treating the floors as bending beams and the walls as shear beams. The equations of motion and the boundary conditions for the floors and the walls are then formulated in one coordinate system and solved exactly to obtain the characteristic equation for the system, which can be solved numerically to obtain the natural frequencies. These, in turn, can be used to determine the mode shapes of the system and the participation factors for earthquake response. Solutions are given for one‐ and two‐storey buildings that resist lateral loads in the transverse direction by two end walls. Perturbation techniques are also applied to simplify further the determination of the fundamental frequency of such single‐storey structures. To illustrate the method, a two‐storey structure, the Arvin (California) High School Administration Building, damaged in the Kern County earthquake of 1952, has been analysed in its transverse direction. It is seen that the first two modes, dominated by the floor and the roof vibrations, make the largest contributions to the total base shear in the structure.