## 8 NLTH Analyses  
In this section, the proposed \"Method-B1\" is assessed through comparison with the results of nonlinear time-history analyses (NLTHs). These included seven bidirectional independent ground motion records compatible, in average terms, with the ULS design spectrum (see Section 4). The numerical model of the MDOF braced frame (see Figure 13a) was developed in Midas-Gen 2023 v1.1 [51]. The Rayleigh formulation, with both stiffness and damping matrices updated at each time step, was enrolled to account for the structural damping of the frame. The cyclic response of the RC column elements was simulated through concentrated elastic perfectly-plastic hinges with a kinematic hardening rule. Indeed, this is the only option provided by the software to account for the influence of the axial load on the two flexural strengths associated to the cross-section (i.e., the N-M-M domain). Possible shear failures were accounted for by means of elasto-fragile \"shear hinges\" located at both end nodes of the column elements and featuring a peak strength of 180 kN (see Section 4). Nonlinear \"FEMA infill strut type\" elements (see [51] for detailed info) with an associated \"Takeda hysteretic rule\" were employed to simulate the equivalent struts of the masonry infills with parameters calibrated according to the Decanini model (see Table 1). To model the dampers, the Midas elements \"_Seismic Control Device_--_Type 2\"_ with an associated \"_Degrading Bilinear Model_\" were adopted. However, both the \"_plastic hardening_\" and \"_stiffness degrading_\" options were de-activated by setting \(\alpha_{1}=10^{-4}\) and \(\beta=0\) for all dissipative elements (see [51] for detailed info), while other dampers' design parameters were set according to Table 5. In this regard, Figure 13b proves that the dampers' hysteretic loops calculated for one of the seven NLTH analyses are compliant with the design force-displacement response for all three typologies of device (two in the X direction and one in the Y direction). In particular, it can be noted that the dampers installed along the transversal (Y) direction (blue plot) experience the highest axial deformation; (about 21 mm). On the contrary, in the other direction the lateral displacement demand is split among the dampers installed at the first (L1) and second (L2) levels; (about 8 mm and 11 mm, respectively). \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Iteration No.**} & \multicolumn{8}{c}{**Dampers’ Design Parameters**} & \multicolumn{8}{c}{**Max Inter-Storey Displacement**} \\ \cline{2-11}  & \(t_{k,L1}^{(a)}\) & \(t_{k,L2}^{(a)}\) & \(t_{k,L1}^{(a)}\) & \(t_{k,L2}^{(a)}\) & \(k_{el,DB,L1}^{(a)}\) & \(k_{el,DB,L2}^{(a)}\) & \(F_{y,DB,L1}^{(a)}\) & \(F_{y,DB,L2}^{(a)}\) & \(d_{max,L1}\) & \(d_{max,L2}\) \\  & **(-)** & **(-)** & **(-)** & **(-)** & **(-)** & **(kN/mm)** & **(kN)** & **(kN)** & **(mm)** & **(mm)** \\ \hline j = 1 & 1.78 & 1.78 & 0.45 & 0.45 & 193.6 & 30.1 & 85.3 & 64.1 & 5.7 & 12.8 \\ \hline j = 2 & 0.72 & 1.78 & 0.18 & 0.45 & 78.4 & 30.1 & 34.2 & 64.1 & 12.5 & 12.6 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Iterative adjustment of the design parameters of the dampers for the longitudinal (X) frame. Moreover, Figure 13c shows the relevant time histories of the accumulated energies. At the end of the ground motion, the dampers dissipate about 50% of the total input energy of the earthquake. To assess the suitability of the refined \"Method-B1\" for defining a damper's layout tailored to the presence of masonry infills and glazed curtain walls, the peak inter-storey displacements (\(d_{max,L1}\) and \(d_{max,L2}\)) are compared with the relevant performance targets (\(d_{PP,L1}\) and \(d_{PP,L2}\)).