Centres of rigidity in multi-storey asymmetric diaphragm systems for eigenmodal vibrations

Abstract

In this paper a general methodology is proposed for calculating the centres of rigidity of multi-storey asymmetric buildings subjected to eigenmodal vibrations with possible modal damping. The methodology is applicable to any building with horizontal diaphragms, even to those with complex topology, possible coupling of diaphragms and existence of additional masses out of diaphragms, assuming linearly elastic behaviour. The methodology is presented in a simple formulation, using only the stiffness resisting diaphragm forces during these vibrations. The methodology uses the results of two eigenmodes obtained by eigenmodal analysis, which can be carried out by a variety of standard programs for dynamic analysis of structures, along with a small post-processing effort that can be easily programmed in a worksheet. A numerical example presents the individual steps of the proposed methodology, while two additional numerical examples demonstrate it's simplicity and efficiency. It is shown that the centres of rigidity lie on a fixed position in each diaphragm for each proper pair of eigenmodal vibrations, irrespective of the existence of modal damping, and therefore they can be included in the basic dynamic characteristics of the building.