A Direct Procedure for The Seismic Design of Frame Structures with Added Viscous Dampers

A direct procedure for the seismic design of regular multi-storey frame structures with added viscous dampers is described in this paper. It aims at providing practical tools for a direct identification of the mechanical characteristics of the manufactured viscous dampers which allow to achieve target levels of performances. First, a target damping reduction factor is selected to achieve a desired reduction in the peak structural response under earthquake excitation. Second, linear damping coefficients are calculated taking advantage of the properties of the modal damping ratios of classically damped systems. Then, analytical formulas allow the estimation of peak velocities and forces in the dissipative devices, and an energy criterion is used to identify the non-linear mechanical characteristics of the actual manufactured viscous dampers. Finally, the internal actions in the structural elements are estimated through the envelope of two equivalent static analyses (ESA), namely: ESA1 in which the naked structure is subjected to a given set of equivalent lateral forces, and ESA2 in which the structure, with rigid diagonal braces substituting the added viscous dampers, is subjected to a top floor lateral force. A numerical verification of the final behaviour of the system by means of non-linear time-history analyses is recommended. An applicative example is finally provided to highlight the simplicity of the proposed procedure.