Peak velocities estimation for a direct five-step design procedure of inter-storey viscous dampers

In the last decades, the use of added viscous dampers for the mitigation of the effects due to the seismic action upon the structural elements has been worldwide spread. In this respect, several design methods aimed at sizing the viscous dampers to be inserted in building structures have been proposed. Among others, some of the authors proposed a five-step procedure which guides the practical design from the choice of a target reduction in the seismic response of the structural system (with respect to the response of a structure without any additional damping device), to the identification of the corresponding damping ratio and the mechanical characteristics (i.e. the damping coefficient values for chosen damping exponent, the oil stiffnes, the maximum damper forces) of the commercially available viscous dampers. The procedure requires the development of numerical simulations for the evaluation of the peak inter-storey velocity profiles, necessary for the evaluation of the damper forces. In the present paper a comprehensive study on the interstorey velocity profiles developed in shear-type building structures under seismic excitation is conducted with the purpose of deriving analytical formulae for their estimation. The analytical estimations of the peak inter-storey velocities are then used to simplify the original five-step procedure leading to a direct (i.e. fully analytical) procedure. The direct procedure is suitable for the preliminary design of the added viscous dampers, in particular for practitioners not dealing everyday with the design of added viscous dampers.