## 2 Methodology
### Analysis and Design of Archetypes  
Once the geometries of the archetypes were defined, a structural analysis was carried out. The material properties used for the analysis and subsequent design are presented in Table 1. The loads considered in the models were derived from Chilean standards NCh433 [55] and NCh1537 [56], which govern seismic and gravitational loads, respectively, for residential buildings. The gravitational loads were divided into dead and live loads, with dead loads including partition walls and topping slabs, and live loads defined based on the typical usage for residential occupancy. The values used are summarized in Table 2.  
The structural analysis was performed using a linear analytical model developed with the commercial software ETABS [57], in which the modeling included the following considerations:  
* Walls and slabs were modeled as four-node \"Shell\" elements. * Beams were modeled as two-node \"Frame\" elements. * Boundary conditions at the base were assumed to be simply supported. * The horizontal force-resisting system was explicitly modeled using the reinforced concrete slab, assuming a rigid diaphragm behavior. * Although the numerical models assumed fixed-base conditions for the buildings, aligned with common practice in FEMA-based evaluations, site classification was critical for defining the intensity and characteristics of ground motion input. Consequently, while soil-structure interaction (SSI) effects were not explicitly modeled in the structural simulations, the role of the soil was appropriately incorporated through ground motion selection, thereby ensuring consistency between the seismic hazard characterization and the structural performance evaluation framework. Although the numerical models used in this study assumed fixed-base conditions--an approach commonly adopted in FEMA P695-based evaluations--this simplification was considered reasonable given the site's classification as soil type C (with a Vs30 between 350 and 500 m/s), corresponding to relatively stiff deposits where soil-structure interaction (SSI) effects are typically less significant. However, it is acknowledged that in sloping terrain, especially where abrupt stiffness transitions or geotechnical variability exist, the \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Material** & **Grade** & **Modulus of** & **Characteristic\(f_{y}\)/\(f_{c}\)** & **Overstrength** & **Expected\(f_{y}\)/\(f_{c}\)** \\  & & **Elasticity (MPa)** & **(MPa)** & **Ratio** & **(MPa)** \\ \hline Concrete & G35 & 28,150 & 35 & 1.3 & 45.5 \\ Steel & A630-420H & 200,000 & 420 & 1.17 & 490 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Material characteristics and expected properties. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Load Type** & **Description** & **Load Value [KPa]** \\ \hline Live load & Departments Halls & 2 \\ \hline Dead load & Wall partitions and over-slabs & 1 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Gravitational loads considered in the structure. SSI could influence the fundamental periods, reduce the effective stiffness of the system, and affect the collapse margin ratio (CMR), potentially impacting structural safety margins. In this study, SSI effects were not incorporated because their inclusion would have required a reformulation of the structural models through more complex couplings, which fell beyond the methodological scope applied. In future work, SSIs could be considered using simplified models with calibrated equivalent springs, or through fully coupled numerical schemes incorporating three-dimensional soil modeling, particularly in contexts where the dynamic behavior of the ground may significantly influence the structural response. Regarding the stiffness of the mathematical model, the Chilean code does not prescribe the use of a stiffness modifier to consider cracking in the concrete, using gross section properties instead.