## 3 Numerical Example
### Ground Motion Selection  
The TBEC 2018 earthquake ground motion selection and scaling process was used in this study [9]. Eleven ground motion records, which were selected from the PEER Ground Motion Database, were used for the time history analyses [55].  
According to TBEC 2018, firstly, the elastic design spectrum was obtained according to the location of sample models. The location of the sample model is at 40.783267\({}^{\circ}\) latitude and 29.959924\({}^{\circ}\) longitude coordinates in Kocaeli province with high earthquake effects. The soil class is ZC class, which is suitable for very dense sand, gravel, and hard clay layers. The earthquake ground motion level was selected as DD1, which is a very rare earthquake ground motion where the probability of exceeding the spectral magnitudes in 50 years is 2% and the corresponding recurrence period is 2475 years. In TBEC 2018, design spectral acceleration coefficients are determined as 1.0 s and a short period similar to the \(SM_{s}\), \(SM_{1}\) of FEMA-P-1051 [56]. Design spectral acceleration coefficients for the sample  
Figure 4: Models views and axes (1–5, A–E): plan (**a**) and 3D view (**b**) of the isolated model.  
model location, soil type, and earthquake ground motion level were determined for the short period (\(SD_{s}\)) and 1.0 s period (\(SD_{1}\)), as presented in Table 2.  
The elastic design spectrum created using the spectral coefficients in Table 2 was utilized to obtain the acceleration time series that would be utilized in the time history analysis. According to TBEC 2018, the 11 selected earthquake acceleration records should match 1.3 times the calculated design for the elastic design spectrum. The effects of energy components on the optimization process were investigated by selecting ground motions with different magnitudes, PGA, PGV, and PGD. Each record's horizontal components were scaled using the 5% elastic damping ratio elastic acceleration spectrum specified in TBEC-2018. The procedure was scaled using spectral matching, which is the most recommended method for selecting earthquake records for seismic codes [53]. Spectral matching was carried out for period values ranging from 0.5 to 1.25 times the fundamental vibration period (\(T_{M}\)) of the base-isolated example model. Since the fundamental vibration period limit values (\(T_{0}\)) for the base-isolated sample structures were taken as 2 and 4 s in the study, the lower limit value was calculated as 1s and the upper limit value as 5 s. As a result, the selected earthquake acceleration records were matched for 1 s and 5 s sections according to the elastic design acceleration spectra. The design elastic acceleration spectrum and the matched selected earthquake ground motion spectra are presented in Figure 5. Furthermore, because the optimization procedure required numerous iterations, the ground motions chosen for time history analysis, whose parameters are listed in Table 3, were shortened. The shortening process was performed to cover the arias intensity of the ground motions between 5% and 95%. This method, defined as significant durations, was used in this study because it is one of the main methods used in shortening ground motions in structural analyses [57]. The significant durations of ground motions were calculated with the help of the SeismoSignal v2024 [58]. In addition, seismic loading and structural analyses were performed in a single direction and results were obtained.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Spectral Parameters** & **Coefficient** \\ \hline \(S_{s}\) & 1.588 \\ \(S_{1}\) & 0.433 \\ Short period (\(SD_{s}\)) & 1.9056 \\
1.0 s period (\(SD_{1}\)) & 0.6495 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Spectral coefficients of soil class (ZC) and design earthquake level (DD-1) for building location [9].  
Figure 5: The spectra of the scaled records for 5% damping [9; 55].