On the design of viscous dampers to be inserted in high-rise Moment-resisting frame structures

The object of this paper is to investigate the applicability of simplified methods for the design of viscous dampers to be inserted in high-rise moment-resisting frame structures. The simplified methods of analysis allow to easily estimate the response of an elastic structure with fluid viscous dampers by performing a modal analysis and estimating an additional damping ratio for each vibration mode of the structure. The corresponding design formulas provide a simple and fast tool for determining the damper properties corresponding to the desired values of supplemental damping ratio. Traditionally, simplified analysis formulas are derived neglecting the vertical relative displacement between the ends of the damper, but this could lead in general to overestimate the damper energy dissipation and to underestimate the required damping coefficients. This effect could become significant for medium-rise to high-rise frame structures, where the vertical relative displacement between the ends of the dampers could be comparable with the horizontal one. Therefore, modified design formulas have been proposed in literature to account for the vertical displacement of the frame nodes. The aim of this study was then to investigate the above-mentioned effect on the effectiveness of viscous dampers and to evaluate the accuracy of simplified design formulas in different conditions. In particular, a widespread simplified design method was considered together with its extension for considering the vertical displacement of the frame nodes. Thus, two distinct design criteria were identified which were examined by comparing the effects of their application both in terms of design outcomes and in terms of seismic response. An extensive numerical analysis was carried out to evaluate the accuracy of these criteria for two steel moment-resisting frames, one medium-rise and the other high-rise, equipped with damping systems designed assuming four different values of the added damping ratio and two different distributions of damper properties along the height. The analyses were performed by applying a set of seven spectrum-compatible ground motions. The response of the models with dampers was compared with the target response of a corresponding ideal structure in which the damping system was modelled with Rayleigh damping.