In this paper, a new method is presented for designing nonlinear viscous dampers to improve the seismic response of multi-storey frames with braces. In this regard, a 2/3-scale three-storey steel structure is used as a benchmark case. Considering the cylindrical friction damper equipment on the bracings, the optimum slip loads are calculated for cylindrical friction damper of all stories under selected earthquakes records. For three earthquakes in optimised slip loads, the force versus the difference between velocities of two ends of cylindrical friction dampers for all stories is combined and plotted according to the velocity range for all earthquakes. Finally, the velocity–force curve is fitted and used for finding the design parameter of nonlinear viscous dampers. Similarly, the aforementioned steps are applied for El-Centro with three scales (of 50, 100 and 200% El Centro). According to the analysis results, the viscous dampers which are designed by using this approach present better performance than that of cylindrical friction dampers and considerably reduce the structural response. The values of displacement, acceleration and base shear are reduced between 63–96%, 44–85% and 14–78%, respectively. Moreover, the results of viscous dampers designed using three and one earthquakes are very similar.
