## 1 Introduction
accelerograms must be selected and properly scaled in magnitude in order to match, on average, the target elastic spectrum at a 5% equivalent viscous damping ratio (with lower and upper tolerances of \(-10\%\) and \(+30\%\), respectively) in the range of periods relevant for the specific case study, which is the largest between \(0.15\div 2\) s and \(0.15\div 2\) T, where T is the fundamental elastic period of the structure in the direction where the accelerogram is applied. In case artificial accelerograms are used, they are generated to match, on average, the elastic response at 5% viscous damping, with lower tolerance of \(-10\%\) over the period range. The duration of the accelerograms is consistent with the magnitude and the other relevant features of the seismic event, but when site-specific data are not available, the pseudo-stationary part should be equal to 10 s and the total duration must not be less than 25 s. NLTHAs calculate the actual response of the system over the whole duration of the ground motion time-history and therefore permit to account for the actual dissipation capacity of the hysteretic dampers, overcoming the limitations on the maximum equivalent viscous damping ratio which affect NLSAs in the case of hysteretic dampers with high dissipation capability. However, in spite of the increasing spread of hysteretic dampers for both new and retrofitted buildings [17; 18; 19; 20; 21; 22; 23; 24; 25], the IBC [30; 31] does not provide specific recommendations for the analyses of structures provided with such devices but refers to the general provisions for buildings in seismic areas. The same consideration is valid also referring to the European design code [39]. In fact, the IBC [30; 31] and the European code [39] adopt similar provisions regarding non-linear static and dynamic analyses for structures subjected to seismic actions. This highlights that at the European level, there is also a lack of a clear guidance for practitioners who must tackle the design of damping systems for buildings, including instructions on the type of analyses to be performed. The present study aims at providing some guidance in this regard by comparing the results on NLSAs and NLTHAs of two archetype reinforced concrete (RC) frame buildings retrofitted with hysteretic steel braces in accordance with the requirements of the code [30; 31]. A parametric study is performed exploring various design solutions that consider hysteretic dampers with different ductility and stiffness, and two sites, with the goal of assessing the accuracy of NLSAs for buildings retrofitted with energy dissipation systems. To better highlight the limitations of the non-linear static procedure, the analyses are performed either considering limitation \(\eta\geq 0.55\) or using the actual \(\eta\) resulting from the equivalent viscous damping ratio of the retrofitted system. Additionally, since according to the code [30; 31] either natural or artificial accelerograms can be used in NLTHAs, a secondary goal of the study is to compare the results obtained using either time-histories. It is important to emphasize that within this article, reference is made exclusively to the IBC [30; 31]. Nevertheless, given the similarity between the Italian and European codes concerning the non-linear analysis methods, the relevance of this work should not be interpreted as solely limited to the Italian context.