A direct procedure for the seismic design of frame structures with added viscous dampers

A direct procedure for the seismic design of building structures with added viscous dampers is described in this paper. The procedure is applicable to regular multi-storey frame structures, which are characterized by a period of vibration lower than 1.5 s. 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. Typically, the design philosophy is to limit the structural damages under severe earthquakes. In more detail, the procedure may be summarized as follows. 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. At this stage of the research, the procedure is suitable for the preliminary design phase, since correction factors for the higher modes contributions are necessary to improve its accuracy, especially for high-rise buildings. 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.