The “direct five-step procedure” for the design of added viscous dampers to be inserted into existing buildings: formulation and case study

This paper introduces an updated formulation of a five-step procedure dealing with the design of fluid viscous dampers for the seismic retrofitting of existing frame buildings. The original design procedure is known as the “direct five-step procedure,” and is articulated into 5 consecutive steps guiding the designer from the identification of the expected seismic performances, to the sizing of the added viscous dampers up to the final verification of the seismic behavior through non-linear dynamic time history analyses. The procedure leads to the full definition of the mechanical characteristics of the commercial non-linear viscous dampers and allows to estimate the maximum dissipative forces acting in the dampers and the internal forces in the frame members. The objective of the design procedure, when applied to a new building, is to size the dampers in order to keep the structural elements within the linear elastic range considering a “rare” earthquake design level. However, when dealing with an existing building, especially if originally designed considering vertical loads only, the insertion of viscous dampers could be not sufficient to keep the structural elements in the elastic range. Thus, it might be necessary to accept local plastic excursion of the structural elements, by taking into account the ductility capacity (albeit probably limited) of the structural members (hysteretic dissipation associated with damage in beams and columns). This latter aspect is explicitly considered in the updated formulation of the “direct five-step procedure” presented here through the introduction of an overall response reduction factor accounting for both the ductility capacity of the structural members and the viscous damping provided by the added dampers. The design procedure is then applied to a 11-storey frame structure case study, which is representative of reinforced concrete buildings designed for vertical loads only. Three different retrofitting design strategies are considered, based on different exploitation of viscous energy dissipation provided by the dampers and hysteretic energy dissipation due to the excursion of the structural members into the inelastic regime.