Nonlinear seismic analysis of unsymmetric-plan structures retrofitted by hysteretic damped braces

A displacement-based design procedure using hysteretic damped braces (HYDBs) is proposed for the seismic retrofitting of unsymmetric-plan structures. An expression of the viscous damping equivalent to the hysteretic energy dissipated by the damped braced frame is proposed under bidirectional seismic loads, where corrective factors are assumed as a function of design parameters of the HYDBs. To this end, the nonlinear dynamic analysis of an equivalent two degree of freedom system is firstly carried out on seven pairs of real ground motions whose displacement response spectra match, on average, the design spectrum proposed by the Italian seismic code for a high-risk seismic zone and a medium subsoil class. Then, the extended N2 method considered by the European seismic code, which combines the nonlinear static analysis along the in-plan principal directions of the structure with elastic modal analysis, is adopted to evaluate the higher mode torsional effects. The town hall of Spilinga (Italy), a reinforced concrete (r.c.) framed building with an L-shaped plan, is supposed to be retrofitted with HYDBs. Six structural solutions are compared considering two alternative in-plan distributions of the HYDBs, to eliminate (elastic) torsional effects, and three design values of the frame ductility combined with a constant design value of the damper ductility. To check the effectiveness and reliability of the DBD procedure, the nonlinear static analysis of the test structures is carried out, by evaluating the vulnerability index of r.c. frame members and the ductility demand of HYDBs for different in-plan directions of the seismic loads.