Proposal of a direct procedure for evaluating the damping ratio of structures equipped with non-linear viscous dampers

In this paper a direct procedure for evaluating the damping ratio of structures equipped with non-linear viscous dampers is described. The methods proposed in literature for determining the response of systems with viscous dampers are based in general on the estimate of equivalent damping ratio. Usually the supplemental damping ratio provided by dampers is expressed as the product of two terms. The first is a function of ductility demand and exponent of velocity, the latter is the damping ratio provided by dampers when structural behaviour is linear elastic. In case of non-linear viscous dampers, the expressions proposed for the damping ratio include a term related to the response, and consequently iterative procedures are required. Through the definition of a new dimensionless parameter, called damper index, it is possible to obtain directly the damping ratio related to the dampers. This parameter can be calculated once properties of structure and external force are known. The methodology has been validated through a numerical investigation regarding a group of RC frames equipped with dampers and subjected to earthquake motions. Finally, a procedure for obtaining the spectrum of damping ratio related to the damper index from design response spectra provided in seismic codes is proposed.