## 3 Nonlinear Dynamic Analysis
### Results of the Dynamic Response and Discussion  
Exemplary maximum horizontal forces (base shear) calculated using the THA method for the analysis model after a nonlinear analysis are shown in Figures 8 and 9 for Model No. 1 and Figures 10 and 11 for Model No. 2, calculated using the most intense earthquake. The calculated resultant displacements due to excitation from station No. 3134 are observed to be higher than those for the load from station No. 2703 in model No. 1 and model No. 2. This difference is because the values of PGA and PGV obtained from the records at station No. 3134 are higher than the values obtained at station No. 2703 (comp. Figures 1 and 2 and Table 3). A comparison of the obtained base shear values in the analyzed models for all excitations is presented in Figure 12. \begin{table}
\begin{tabular}{c c c} \hline \hline \multirow{2}{*}{**Mode Shape**} & **Measured Values of Frequency [Hz]** & **Calculated Values of Frequency [Hz]** \\ \hline Flexural in ’y’ direction & 1.89 & 1.84 \\ Flexural in ’x’ direction & 2.62 & 2.65 \\ Torsional & (2.5–3.5) & 3.35 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Natural frequencies of the model based on dynamic measurements. Figure 7: Histogram of measured and calculated natural frequencies of the building. Figure 8: Maximum horizontal force (Base Shear) for stations No. 2703 and No. 3134 for model No. 1—masonry and RC walls. Figure 10: Maximum horizontal force (Base Shear) for stations No. 2703 and No. 3134 for model No. 2—RC walls. Figure 9: Maximum horizontal force (Base Shear) for Aquila, El-Centro, and Sitka for model No. 1—masonry and RC walls. The results from Table 3 indicate that the highest base shear force can be observed in the L'Aquila earthquake and El Centro earthquake in model No. 1 and model No. 2, respectively. Despite the significantly shorter duration time of the intense phase for the L'Aquila earthquake, the base shear force is highest in model No. 1. The base shear force from event 3134 is higher than that from event 2703; the reason for this is that the horizontal vibration components had significantly higher PGA and PGV values. The results from Table 3 also indicate that the base shear force from Model No. 2 is higher than that of Model No. 1 (comp. Figure 12). The exemplary resultant maximum horizontal displacement for the analysis model using  
(Figure 13b) were found to be higher than those from station No. 2703 (Figure 13a). The reason for this is that the horizontal vibration components had significantly higher PGA and PGV values. The values of the resultant displacements were calculated using the following formula:  
\[\text{D}=\sqrt{\text{X}^{2}+\text{Y}^{2}} \tag{1}\]  
The calculated values for the analyzed earthquakes are shown in Table 4.  
The resultant displacements in the X-Y directions for the whole building, mm. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Selected Results**} & \multicolumn{5}{c}{**Excitations from the Station**} \\ \cline{2-6}  & **Station** & **Station** & **No. 2703** & **Station** & **Sitka** & **El Centro** & **L’Aquila** \\ \hline Maximum relative displacement between the roof & & & & & \\ and 6 th floor in Model No. 1 & 20.22 & 32.00 & 20.67 & 57.60 & 21.49 \\ \hline Maximum relative displacement between 6 th floor & & & & & \\ and foundation in Model No. 1 & 16.68 & 31.74 & 8.26 & 60.02 & 36.72 \\ \hline Resultant maximum displacement in Model No. 1 & 26.15 & 54.03 & 26.40 & 96.14 & 49.52 \\ \hline Maximum relative displacement between roof and & & & & & \\ 6 th floor in Model No. 2 & & & & & \\ \hline Maximum relative displacement between 6 th floor & & & & & \\ and foundation in Model No. 2 & & & & & \\ \hline Resultant maximum displacement in Model No. 2 & 33.33 & 44.38 & 23.06 & 62.41 & 28.04 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: The resultant displacements in the X-Y directions for the whole building, mm. Figure 14: Calculated resultant displacements for excitation from station: (**a**) No. 2703 and (**b**) No. 3134 for model No.