# Seismic Response of a Three-Dimensional Asymmetric Multi-Storey Reinforced Concrete Structure
## 5 Nonlinear Seismic Response of the SMART 2013 RC Structure
Figure 24: Numerical and experimental responses in the \(x\) direction due to the scaled Northridge earthquake of Run 11; responses sampled at point A on the third floor. Figure 25: Numerical and experimental responses in the \(x\) direction due to the scaled Northridge earthquake of Run 13; responses sampled at point A on the third floor. Figures 28 and 29 show the numerical and experimental responses of the SMART 2013 RC structure for the Northridge aftershock (Run 21 and Run 23). Overall, the numerical results reflected the experimental results, although there was a slight phase difference in the result of Run 23. The difference could be because the numerical model did not accurately reflect the stiffness degradation after severe damage to the structure. The cumulative error of numerical solutions of earlier seismic sequences might have also influenced the response difference. Tables 9 and 10 present the absolute maximum displacement and acceleration, respectively, that were calculated from each simulation stage. The displacement error was less than 10% for Run 19, wherein the ground motion was the strongest, whereas the error was around 20-30% for other runs. Table 11 shows the absolute maximum seismic responses at sampling points A to D in both the \(x\) and \(y\) directions for the case of Run 19. Although the peak values were somewhat different from the experimental values, the time histories in Figures 23-29 show that the numerical solution had a similar tendency to the response obtained from the experiment. Figure 30 shows the concrete walls after the shaking table test corresponding to Runs 13-19. Severe cracks and spalling of concrete occurred at the lower part of the concrete walls and the column connected to the foundation. Figures 31 and 32 show the Fourier frequency spectrum of displacement in the \(x\) and \(y\) directions, respectively, for Runs 17, 19, and 21. Overall, the spectra show a good agreement with those obtained from the experiment, particularly in the frequency range up to about 3 Hz. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Seismic Simulation**} & \multicolumn{3}{c}{**Absolute Maximum Acceleration, \(a_{x}\)**} \\ \cline{2-3}  & **Analysis (m/s\({}^{2}\))** & **Experiment (m/s\({}^{2}\))** & **Error (\%)** \\ \hline Run 9 & 3.88 (0.40 g) & 4.10 (0.42 g) & 5.37 \\ Run 11 & 2.46 (0.25 g) & 3.39 (0.34 g) & 27.43 \\ Run 13 & 5.67 (0.58 g) & 9.73 (0.99 g) & 41.73 \\ Run 17 & 10.50 (1.07 g) & 10.83 (1.10 g) & 3.05 \\ Run 19 & 22.42 (2.28 g) & 16.11 (1.64 g) & 39.17 \\ Run 21 & 4.42 (0.45 g) & 3.23 (0.33 g) & 36.84 \\ Run 23 & 13.15 (1.34 g) & 9.28 (0.95 g) & 41.70 \\ \hline \hline \end{tabular}
\end{table} 
Table 10: Absolute maximum acceleration at point A on the third floor. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Seismic Simulation**} & \multicolumn{3}{c}{**Absolute Maximum Displacement, \(a_{x}\)**} \\ \cline{2-3}  & **Analysis (m/s\({}^{2}\))** & **Experiment (m/s\({}^{2}\))** & **Error (\%)** \\ \hline Run 9 & 3.88 (0.40 g) & 4.10 (0.42 g) & 5.37 \\ Run 11 & 2.46 (0.25 g) & 3.39 (0.34 g) & 27.43 \\ Run 13 & 5.67 (0.58 g) & 9.73 (0.99 g) & 41.73 \\ Run 17 & 10.50 (1.07 g) & 10.83 (1.10 g) & 3.05 \\ Run 19 & 22.42 (2.28 g) & 16.11 (1.64 g) & 39.17 \\ Run 21 & 4.42 (0.45 g) & 3.23 (0.33 g) & 36.84 \\ Run 23 & 13.15 (1.34 g) & 9.28 (0.95 g) & 41.70 \\ \hline \hline \end{tabular}
\end{table} 
Table 10: Absolute maximum acceleration at point A on the third floor. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Seismic Simulation**} & \multicolumn{3}{c}{**Absolute Maximum Displacement, \(a_{x}\)**} \\ \cline{2-3}  & **Analysis (m/s\({}^{2}\))** & **Experiment (m/s\({}^{2}\))** & **Error (\%)** \\ \hline Run 9 & 2.47 & 2.02 & 22.28 \\ Run 11 & 4.83 & 5.57 & 13.29 \\ Run 13 & 9.51 & 12.92 & 26.39 \\ Run 17 & 15.23 & 22.02 & 30.84 \\ Run 19 & 33.09 & 36.73 & 9.91 \\ Run 21 & 1.5