## 6 Results of Non-Linear Analyses
as 1.3 (Benevento)/1.6 (Tramutola) for the three-story building, and 2.0 (both Benevento and Tramutola) for the six-story building. Again, NLTHA,A provides better estimates, with maximum deviations of about 25% to 30% (three-story building in Tramutola and six-story building in Benevento). It is noteworthy that for both buildings equipped with the retrofitting system with \(\mu_{DB}\) = 3 in the sites of Tramutola (at both LLS and CLS) and Benevento (at LLS), all analyses yield consistent results. Figure 15: Comparison of _V/V\({}_{TH,N}\)_ for the case study structures; the curves refer to (a) results from NLSAs with actual \(\eta\); (b) results from NLSAs with \(\eta_{BC}\); (c) results from NLTHA,A. In terms of maximum shear force at base \(V\) (Figure 15), NLSA,\(\eta\) and NLSA,\(\eta_{IBC}\) show a fair performance, with \(V/V_{TH,N}\) ratios approaching unity: the maximum relative deviations from the benchmark are of the order of +10% (NLSA,\(\eta\))/+15% (NLSA,\(\eta_{IBC}\)) for the three-story building and \(-5\%\) (NLSA,\(\eta\))/0% (NLSA,\(\eta_{IBC}\)) for the six-story building. The influences of the seismic scenario and of the ductility of the damping system are negligible. On the other hand, NLTHA,A underestimates the shear force by 10% for the three-story building (Benevento and Tramutola), by 25-30% for the six-story building in Benevento and by less than 5% for the six-story building in Tramutola. Also, for NLTHA,A, virtually no influence of \(\mu_{DB}\) is shown. The main trends highlighted from the results shown in Figures 13-15 are summarized as follows:  
1. NLSAs provided accurate estimates of forces for both buildings (maximum deviation +15% in the study), and the accuracy was virtually unaffected by the ductility of the dampers. 2. NLSAs are not accurate when the structural performance is evaluated referring to displacements and deformations, e.g., maximum displacements between adjacent buildings or inter-story drifts. Only for low values (\(\mu_{DB}\) = 3) and in some cases even medium-low values (\(\mu_{DB}\) = 5) of ductility of the dissipative bracing system the estimates provided by NLSAs are fair, while the accuracy deteriorates as the damping capacity of the bracing systems increases. These estimates are always on the conservative side, but there is a potential concern of ending up with a design that is overly conservative. 3. Focusing on the outcomes in terms of maximum displacements at the top floor, the study is unable to provide conclusive results, as deviations from the benchmark range from \(-30\%\) to +200% depending on the building type, seismic scenario, and characteristics of the dissipative bracing system. However, as previously highlighted, the general trend shows that the accuracy of results deteriorates as \(\mu_{DB}\) increases. Moreover, in the six-story building, NLSAs with \(\eta_{IBC}=\max(0.55;\sqrt{10/\left(5+\xi_{eq}\right)})\) underestimate the displacement for low \(\mu_{DB}\)s (\(\leq\)5) and overestimate it for high \(\mu_{DB}\)s.
4. NLTHA,N generally underestimate the demand values in terms of forces and displacements, often by up to 30%. This underestimation occasionally shows a modest reduction with increasing \(\mu_{DB}\)s. In some cases, e.g., for \(\mu_{DB}\) = 3, there is even an overestimation of the maximum displacement and maximum inter-story drift. It is important to emphasize that in this study, the results of NLTHA,N are referred to as benchmark. However, both NLTHA,N and NLTHA,A are considered equivalent according to the IBC [30]. The study has some limitations, and its findings should not be considered as general until confirmed by further data. Firstly, the study focused only on two RC frames representative of low- to medium-rise structures with regular floor in plans and elevations; therefore, these results are representative of these categories of buildings.