## 3 Analyses Used in the Methodology
#### Ground Motions Used  
For this study, seismic records from the Chilean subduction zone were used. The set of acceleration records was obtained from the CESMD database [70]. The records were \begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameter** & **Dimensions** & **Value** \\ \hline Modulus of elasticity \(E\) & MPa & 200,000 \\ Yield strength \(F_{y}\) & MPa & 490 \\ Strain-hardening & - & 0.005 \\ parameter & - & 20 \\ Transition curve initial & - & 18.5 \\ shape parameter & - & 0.15 \\ Coefficient A2 & - & 0.15 \\ Coefficient A3 & - & 0 \\ Coefficient A4 & - & 1 \\ Fracture/buckling strain & - & 1 \\ Specific weight & kN/m\({}^{3}\) & 78 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Constitutive model parameters by [PERSON] for steel grade A630-420H. A1, A2, A3, and A4 correspond to transition curve shape calibrating coefficients. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameter** & **Dimensions** & **Value** \\ \hline Compression strength & MPa & 45.5 \\ Strength lower bound & MPa & 35 \\ Tension strength & MPa & 2.6 \\ Modulus of elasticity & MPa & 28,150 \\ Specific weight & kN/m\({}^{3}\) & 24 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Constitutive model parameters by [PERSON] et al. for concrete grade G35. applied using both horizontal components of the originating seismic events. The relevant characteristics of the original ground motions used are summarized in Table 7.  
In this study, a total of 14 pairs of ground motion records were used, obtained by rotating the horizontal components of seven original accelerograms. Although the FEMA P695 methodology recommends the use of a minimum of 22 pairs of records--particularly for studies aimed at evaluating seismic design factors for new structural systems or innovative materials--the objective of this research was to assess such factors for a well-established structural typology. However, this typology is subject to unique seismic demands dominated by subduction earthquakes, which are the primary seismogenic source in the study region. Moreover, the prevailing geotechnical conditions correspond to stiff soils, classified as site class C according to the Chilean seismic code. Consequently, the selection of ground motions was deliberately focused on strong subduction events recorded in Chile, ensuring that the seismic input was representative of the expected hazard scenario for this type of structure. At this stage, a variation of the standard FEMA P695 methodology was introduced. Instead of using the original ground motion records, the records were modified in order to match the elastic spectrum corresponding to the maximum considered earthquake (MCE). According to the Chilean code, this spectrum was derived from the elastic displacement spectrum, which was first amplified by 17% to obtain the design-level elastic displacement spectrum and then further amplified by an additional 30% to obtain the MCE displacement spectrum (see Figure 9). The spectrally matched ground motions corresponding to the MCE spectrum were used in the incremental dynamic analysis. Ground motion matching was performed using the software SeismoMatch [71]. The acceleration records were matched following the procedure described in the _Achisina Manual_[72], which defines the seismic hazard in Chile based on the elastic displacement spectrum derived from the Mw 8.8 earthquake that occurred on 27 February 2010. The software used requires the definition of the design spectrum in terms of the spectral acceleration \(S_{a}\). This spectrum can be obtained by applying the following conversion equation:  
\[S_{a}(T_{n})=1.17\Big{(}\omega^{2}\Big{)}S_{d}=1.17\Big{(}\frac{4\pi^{2}}{T_{n }^{2}}\Big{)}S_{d} \tag{2}\]