Equivalent viscous damping for displacement-based seismic design of hysteretic damped braces for retrofitting framed buildings

A displacement-based design (DBD) procedure aiming to proportion hysteretic damped braces (HYDBs) in order to attain, for a specific level of seismic intensity, a designated performance level of a structure is proposed for the retrofitting of framed buildings. A key step for the reliability of the DBD procedure is the selection of the equivalent viscous damping in order to account for the energy dissipated by the damped braced frame. In this paper, expressions of the equivalent damping are obtained considering the energy dissipated by the HYDBs and the framed structure. To this end, dynamic analyses of an equivalent single degree of freedom system, whose response is idealized by a trilinear model, are carried out considering real accelerograms matching, on the average, Eurocode 8 (EC8) response spectrum for a medium subsoil class. Then, a three-storey reinforced concrete (r.c.) framed structure of a school building, designed in a medium-risk seismic region according to the Italian code in force in 1975, is supposed as retrofitted as if in a high-risk seismic region of the current seismic code (NTC08) by the insertion of HYDBs. Nonlinear static analyses are carried out to evaluate the vulnerability of the primary structure, characterized by the lack of interior girders along the floor slab direction, and to select optimal properties of the HYDBs. The effectiveness of the retrofitting solutions is checked referring to nonlinear dynamic analyses, considering artificially generated accelerograms whose response spectra match those adopted by NTC08 for the earthquake design levels corresponding to the serviceability and ultimate limit states.