# Seismic Response of a Three-Dimensional Asymmetric Multi-Storey Reinforced Concrete Structure
## 5 Nonlinear Seismic Response of the SMART 2013 RC Structure  
After the seismic simulation to the low-intensity ground motion, the inelastic seismic response of the asymmetric three-storey RC structure subjected to high-intensity ground motions was investigated. Such a nonlinear analysis was part of the SMART 2013 international benchmark. The analysis case consisted of several simulations for three different seismic sequences: the design signal (Run 9), the Northridge earthquake main shocks (Run 11, Run 13, Run 17, and Run 19), and the Northridge aftershock (Run 21 and Run 23). The \"Runs\" are different regarding the strength of the ground motions. The PGA of each ground motion is presented in Table 8. The ground motion of Run 19 is the unscaled Northridge earthquake with PGAs of 1.1 g and 1.0 g in the \(x\) and \(y\) directions, respectively. Figure 22 shows the time history of the input ground motion used for the nonlinear seismic analysis. First, the ground displacement of Run 9 was applied to the structure at the actuator locations of the shaking table. Figure 23 shows the experimental and numerical responses of the structure in the \(x\) direction sampled at point A of the third floor. The numerical response agreed well with the experimental result. The absolute maximum values of displacement and acceleration obtained from the shaking table test were 2.02 mm and 4100 mm/s\({}^{2}\), respectively. They are about twice as high as the responses to the low-intensity ground motion in Section 4.2, where the earthquake signal is scaled by 50%. Figure 23: Numerical and experimental responses in the \(x\) direction due to the ground motion of Run 9; responses sampled at point A on the third floor. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Run** & **PGA X (g)** & **PGA Y (g)** & **Percentage of Nominal Signal (Cs)** & **Type** \\ \hline
9 & 0.22 & 0.23 & 100 & Design earthquake signal–nominal \\
11 & 0.21 & 0.16 & 11 & Scaled Northridge earthquake–step 1 \\
13 & 0.40 & 0.21 & 22 & Scaled Northridge earthquake–step 2 \\
17 & 0.60 & 0.40 & 44 & Scaled Northridge earthquake–step 3 \\
19 & 1.10 & 1.00 & 100 & Real Northridge earthquake–nominal \\
21 & 0.14 & 0.14 & 33 & Scaled Northridge aftershock–step 1 \\
23 & 0.70 & 0.40 & 100 & Real Northridge aftershock–nominal \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Nominal input ground motions for a nonlinear seismic analysis. Figure 22: High-intensity ground motions for a nonlinear seismic analysis of the SMART 2013 structure. Following Run 9, the Northridge earthquake's main shocks (Run 11, Run 13, Run 17, and Run 19) with successively increasing PGA were applied to the structure at the actuator locations of the shaking table. Figures 24-27 show the displacement and acceleration at point A of the third floor. Overall, the numerical responses agreed well with experimental results, even during the high-intensity ground motions. The response was largest in the case of Run 19, where the absolute maximum displacement and acceleration were 36.73 mm and 22,420 mm/s\({}^{2}\) (2.28 g), respectively. These values are about 13.4 and 5.8 times higher than the calculated responses from Run 9, respectively. In Run 13, the numerical response does not reflect the high-frequency experimental response well after about 5 s. This difference in response may be due to a gradual error in predicting structural stiffness during numerical analysis [34; 35]. Despite the partial difference between the numerical and experimental results, the computed displacement and acceleration appear to capture the general trend of the experimental seismic behavior of the structure. After Run 13, the first three natural frequencies of the structure decreased by 26.66%, 19.98%, and 17.72%, respectively. These results implied that the stiffness of the SMART 2013 RC structure decreased after Run 13 compared to its initial stiffness. In the shaking table test corresponding to Run 13, significant cracks began to develop at the lower part of concrete walls and the column.