Nonlinear seismic analysis of r.c. framed buildings with setbacks retrofitted by damped braces

Current seismic codes allow the use of damped braces (DBs) for the seismic retrofitting of reinforced concrete (r.c.) framed buildings, but simplified design procedures need to be developed in the case of structures with in-elevation irregularities due to setbacks. In this work, an improved Displacement-Based Design (DBD) procedure of hysteretic damped braces (HYDBs) is proposed to take into account the higher vibration mode effects along the elevation. In line with the extended N2 method, this iterative procedure combines the usual nonlinear static analysis with an elastic modal analysis. Two in-elevation irregular six-storey r.c. framed buildings, characterized by one setback (at the third-storey) and two setbacks (at the second- and fourth-storey), are to be retrofitted by inserting of HYDBs to attain performance levels imposed by the Italian code (NTC08) in a high-risk zone. Local and global displacement-based demand parameters are considered to compare the nonlinear dynamic response of the original and retrofitted structures, considering sets of ground motions whose response spectra match those adopted by NTC08 at serviceability and ultimate limit states. R.c. frame members are idealized by a two-component model, assuming a bilinear moment-curvature law whose ultimate bending moment depends on axial load, while the response of the HYDBs is idealized by a bilinear force-displacement law to prevent yielding and buckling of steel braces.