Seismic Modal Contribution Factors

Over the years, the belief that the first mode of vibration governs the seismic response of shear-type frame structures has been widely accepted and proved to be effective for preliminary structural design. Indeed, most of the actual seismic design procedures are based on drift profiles which are typically an approximation of the shape of the fundamental mode of vibration. In this paper, an analytical study on the dynamic properties of multi-storey shear-type frames is carried out with the purpose of precisely identifying the contribution of the modes of vibration to the seismic response of such structures, both in terms of maximum inter-storey displacement profiles (which govern the beams and columns maximum actions) and maximum inter-storey velocity profiles (which govern the viscous dampers maximum forces, of fundamental importance for building structures equipped with additional viscous dampers). A new parameter, referred to as Seismic Modal Contribution Factor, which represents the contribution of the generic mode to the seismic response of the structure, is introduced. With respect to the well-known Modal Contribution Factor, grounded on the concept of modal static response, the Seismic Modal Contribution Factor explicitly takes into account also the dynamic nature of the response due to earthquake excitation. The Seismic Modal Contribution Factor could be a meaningful parameter to be implemented in a professional structural design software and used in conjunction with the common modal participating mass ratios to identify the number of modes to be included in the analyses.