## 5 Determination of the Seismic Response of the Case Studied
### Incremental Dynamic Analysis  
IDA is an analysis that is carried out in the nonlinear range using a set of registers or synthetic accelerograms as dynamic excitation to obtain the performance of structures [41]. IDA is applied to the studied structure using a set of four records with a double component of the earthquake of 16 April 2016, obtained at different seismological stations in Ecuador [42]. Table 6 shows the main characteristics of these records, while Figures 11 and 12 show the seismic records and their response spectra, respectively. Note the different durations of the records, as well as the maximum acceleration values achieved [43]. IDA makes it possible to determine the seismic capacity of the structures considering the variability in the records used [44; 45; 46] and to objectively obtain the seismic performance factors of structural typologies [47]. Figure 11: _Cont_. Figure 10: Variation in the rotations of the centers of gravity of each floor with respect to the lateral displacement according to different pushover analyses: (**a**) conventional pushover analysis and (**b**) adaptive pushover analysis. Figure 11: Acceleration records from the four stations reported. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Earthquake** & **Date** & **Station ID** & **Location** & \begin{tabular}{c} **Epicentral** \\ **Distance [km]** \\ \end{tabular} & **Component** & \begin{tabular}{c} **Peak Ground** \\ **Acceleration [g]** \\ \end{tabular} \\ \hline Ecuador 7.8 & 16 April 2016 & \begin{tabular}{c} AES2 \\ \end{tabular} & \begin{tabular}{c} Esmeraldas \\ \end{tabular} & 76 & \begin{tabular}{c} E-W \\ N–S \\ \end{tabular} & \begin{tabular}{c} 0.1706 \\ 0.1122 \\ 1.3413 \\ \end{tabular} \\ Mw & 16 April 2016 & \begin{tabular}{c} APED \\ \end{tabular} & \begin{tabular}{c} Pedernales \\ \end{tabular} & 36 & \begin{tabular}{c} N–S \\ \end{tabular} & \begin{tabular}{c} 0.8258 \\ 0.348 \\ 0.4196 \\ \end{tabular} \\  & & \begin{tabular}{c} AMNT \\ \end{tabular} & \begin{tabular}{c} Manta \\ \end{tabular} & \begin{tabular}{c} \(171\) \\ \end{tabular} & \
\begin{tabular}{c} N–S \\ \end{tabular} &
\begin{tabular}{c} 0.5111 \\ \end{tabular} \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Information from the records used for IDA. Figure 12: Response, mean, and elastic design spectra corresponding to the accelerograms used for the IDA. reflected in the IDA curves in Figure 13, obtained by plotting the values of the maximum interstory drifts \((ID_{max})\) obtained in the centers of gravity of the floors of the building vs. the spectral acceleration \((S_{a})\) corresponding to the predominant period in the direction of analysis. Note that the average curve has a collapse threshold value lower than 0.2 g. The collapse threshold \(S_{CT}\) is defined on the average curve at the point where it undergoes a reduction in stiffness, such that the current stiffness is less than 20% of the initial stiffness of the curve. This criterion for capturing the collapse threshold, based on stiffness reduction, corresponds to the criterion originally formulated in [41]. By including the interstory drift as a damage measure \((DM)\) of the analysis, when an increase in the drift occurs, the reduction in the slope of the curve also occurs; therefore, the criterion adopted preserves a relationship with the overall damage of the structure. Finally, with the \(S_{CT}\) value resulting from the set of IDA curves and with the total deviation calculated from the data recommended in FEMA P-695 [47], the collapse fragility curve that gives the probability values of exceedance for a horizontal acceleration of the ground is obtained.