A new Displacement-Based Design (DBD) procedure to proportion hysteretic damped braces (HYDBs) is proposed in order to take into account the effects of the seismic degradation of a structure that needs to be retrofitted. To this end, a hysteretic model based on plastic and damage mechanisms is adopted to describe the inelastic response of reinforced concrete (r.c.) frame members. Then, nonlinear seismic analysis of a single-degree-of-freedom system, equivalent to a multi-degree-of-freedom model of the structure, is used to generate the capacity boundary curve by means of the hysteretic model defined starting from the initial backbone curve. Two-, four- and eight-storey r.c. framed structures are designed for a medium-risk seismic zone of a former Italian code. These are then to be retrofitted by inserting HYDBs to attain performance levels imposed by current Italian code in a high-risk seismic zone. Different retrofitting solutions are compared, considering for each retrofitted structure: (i) variable damper ductility coupled with constant frame ductility; (ii) variable frame ductility coupled with constant damper ductility. The effects of different damage levels and different damage evolution laws are also investigated. Finally, pushover curves of the unbraced and damped braced structures are carried out, with and without considering degradation of the hysteretic response of r.c. frame members on the DBD procedure of the HYDBs.
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