## 4 Results and Discussion
### Total System Uncertainty  
The total system uncertainty was determined using the following expression:  
\[\beta_{TOT}=\sqrt{{\beta_{TRT}}^{2}+{\beta_{DR}}^{2}+{\beta_{TD}}^{2}+{\beta_ {MDL}}^{2}} \tag{10}\]  
where  
\(\beta_{TOT}\): the total system uncertainty (bounded between 0.275 and 0.950); \begin{table}
\begin{tabular}{c c c c c c c c c} \hline  & & \multicolumn{3}{c}{**x**} & \multicolumn{3}{c}{**y**} \\ \hline
**Archetype** & \(\hat{S}_{CT}\) & \(S_{MT}\) & \(CMR\) & \(SSF\) & \(\hat{S}_{CT}\) & \(S_{MT}\) & \(CMR\) & \(SSF\) \\ \hline \(0^{\circ}\) & 2.910 & 1.439 & 2.022 & 1.110 & 3.266 & 1.638 & 1.994 & 1.130 \\ \(15^{\circ}\) & 3.720 & 1.550 & 2.401 & 1.090 & 4.546 & 1.552 & 2.628 & 1.110 \\ \(30^{\circ}\) & 2.880 & 1.670 & 1.725 & 1.090 & 3.658 & 1.392 & 2.628 & 1.120 \\ \(45^{\circ}\) & 3.460 & 1.525 & 2.268 & 1.140 & 4.819 & 1.037 & 4.647 & 1.140 \\ \hline \end{tabular}
\end{table} 
Table 10: A summary of the values extracted from the IDA curves and calculated collapse margin ratios (CMRs). Figure 16: Spectral shape factor for different displacement-based ductility values. \(\beta_{TRT}\): the record-to-record uncertainty (0.20-0.40) (calculated value = 0.4); \(\beta_{DR}\): the design requirements uncertainty (0.10-0.50) (assumed value = 0.2); \(\beta_{TD}\): the test data uncertainty (0.10-0.50) (assumed value = 0.2); \(\beta_{MDL}\): the modeling uncertainty (0.10-0.50) (assumed value = 0.2). FEMA P695 explicitly links uncertainty parameters to the quality of design provisions, experimental data, and nonlinear modeling. These are categorized as superior (\(\beta\) = 0.10), good (\(\beta\) = 0.20), fair (\(\beta\) = 0.35), and poor (\(\beta\) = 0.50). When combined with record-to-record (RTR) uncertainty--dependent on the period-based ductility--this approach yields a total system collapse uncertainty ranging from \(\beta_{TOT}\) = 0.275 for high-certainty systems to \(\beta_{TOT}\) = 0.950 for low-certainty systems. The values used in this study fell within that range and reflected both the structural typology considered and the quality of the available data and modeling tools. The record-to-record uncertainty reached its maximum value for all the analyzed archetypes, as the period-based ductility exceeded a value of 3 in every case (see the results in Figure 14). Based on the values used, the total uncertainty was calculated as \(\beta_{TOT}\) = 0.53. This value was used to determine the adjusted acceptable collapse margin values for target collapse probabilities of 10% and 20%. These values were obtained by interpolating the reference data provided in FEMA P695, according to the procedure used in [78]. Using the obtained values of \(\hat{S}_{CT}\) and the associated record-to-record uncertainty, fragility curves were developed for the studied archetypes. The resulting fragility curves are shown in Figure 17, where paired curves for each analysis direction can be observed. It is important to note that the fragility curves for all archetypes exhibit higher values of \(\hat{S}_{CT}\) in the y-direction than in the x-direction, indicating that the archetypes are less likely to collapse under a given seismic demand, expressed as the spectral acceleration \(S_{a}\) in the y-direction compared with the x-direction. Figure 17: Fragility curves obtained for the archetypes with slope inclinations of (**a**) 0\({}^{\circ}\), (**b**) 15\({}^{\circ}\), (**c**) 30\({}^{\circ}\), and (**d**) 45\({}^{\circ}\). In these figures, the red and blue lines represent the fragility curves in the x and y directions, respectively. Using the values of S\({}_{\rm MT}\), interpolation was performed on the fragility curves to obtain the probability of collapse in each analysis direction under the seismic demand corresponding to the maximum considered earthquake (\(MCE\)). The resulting values are presented in Table 11, detailing the probability of collapse (%) for \(MCE\)-level demand.