## 4 Performance-Based Design Process of Reinforced Concrete Column Members
### Example  
The performance-based design process is presented by using a single degree-of-freedom structure. When the seismic intensity was set to 7 degrees (0.1 \(g\)), the peak acceleration of ground \(A_{\rm PG}\) under moderate earthquakes was 98 cm/s\({}^{2}\), and the peak  
Figure 4: The performance-based design process. acceleration of ground \(A_{\rm PC}\) under major earthquakes was 220 cm/s\({}^{2}\). When the seismic intensity was set to 8 degrees (0.2 \(g\)), the peak acceleration of ground \(A_{\rm PG}\) under moderate earthquakes was 196 cm/s\({}^{2}\), and the peak acceleration of ground \(A_{\rm PG}\) under major earthquakes was 400 cm/s\({}^{2}\)[27]. The ratio of the peak velocity of ground \(V_{\rm PG}\) to the peak acceleration of ground \(A_{\rm PG}\) was 0.15 s [28]. In the example, the fundamental period \(T\) was changed by changing the floor load; the floor loads 40 kN/m\({}^{2}\), 60 kN/m\({}^{2}\), 80 kN/m\({}^{2}\), 100 kN/m\({}^{2}\), 120 kN/m\({}^{2}\), and 150 kN/m\({}^{2}\) were applied. The earthquake durations were set as 5 s, 10 s, 20 s, and 30 s [28]. Figure 5 shows the single degree-of-freedom structure. Table 1 is the design information for the structure. Table 2 contains the calculation results of the design parameters. \begin{table}
\begin{tabular}{c c c c c c c} \hline
**Member** & **Section Size \(b\times h\)** & **Height of Column H/ Length of Beam \(L\)** & **Strength Grade of Concrete** & **Longitudinal Reinforcement Type** & **Stirrup Type** \\
**Type** & **(mm \(\times\) mm)** & **(mm)** & **(mm)** & & **(mm)** & **(mm)** & **(kN)** \\ \hline Column & 400 \(\times\) 400 & 3000 & & & & \\ Beam & 200 \(\times\) 350 & 3000 & & & & \\ \hline \end{tabular}
\end{table} 
Table 1: The design information for the structure. Figure 5: The single degree-of-freedom structure. \begin{table}
\begin{tabular}{c c c c c c c c} \hline
**Earthquakes** & **\(T\) (s)** & **\(M\) (kg)** & \(\mu\) & \(\begin{array}{c}A_{\rm PG}\\ (\text{cm/s}^{2})\end{array}\) & \(\begin{array}{c}V_{\rm PG}\\ (\text{cm/s})\end{array}\) & \(\begin{array}{c}u_{\rm y}\\ (\text{mm})\end{array}\) & \(\begin{array}{c}F_{\rm y}\\ (\text{km})\end{array}\) \\ \hline Moderate earthquakes & & & & & 98 & 14.7 & & \\ Major earthquakes & & & & 220 & 33 & & 21.33 \\ Moderate earthquakes & & & & 98 & 14.7 & & \\ Major earthquakes & & & & 220 & 33 & & 6 & 42.67 \\ Moderate earthquakes & & & & 98 & 14.7 & & & \\ Major earthquakes & & & & 220 & 33 & & 6 & 42.67 \\ Moderate earthquakes & & & & 98 & 14.7 & & & \\ Major earthquakes & & & & 220 & 33 & & 6 & 42.67 \\ Moderate earthquakes & & & & 98 & 14.7 & & & \\ Major earthquakes & & & & 220 & 33 & & 6 & 42.67 \\ Moderate earthquakes & & & & 98 & 14.7 & & & \\ Major earthquakes & & & & 220 & 33 & & 6 & 42.67 \\ Moderate earthquakes & & & & 98 & 14.7 & & & \\ Major earthquakes & & & & 220 & 33 & & 6 & 42.67 \\ Moderate earthquakes & & & & & 98 & 14.7 & & & \\ Major earthquakes & & & & 220 & 33 & & 6 & 42.67 \\ Moderate earthquakes & & & & & 98 & 14.7 & & & \\ Major earthquakes & & & & 220 & 33 & & 6 & 42.67 \\ Moderate earthquakes & & & & & 98 & 14.7 & & & \\ Major earthquakes & & & & 220 & 33 & & 6 & 42.67 \\ \hline \end{tabular}
\end{table} 
Table 2: The calculation results of the design parameters. It can be found from Reference [22] that when the damage index is greater than 0.8, the column member is in the collapse state. When the damage index is less than 0.3, the column member is in the nondamaged state. Therefore, the change of the stirrup ratio is discussed when the damage index is 0.4, 0.5, 0.6, and 0.7. Since the design information of the column members are the same, this study only introduces the reinforcement results of column 1. The calculation results of the stirrup ratio are shown in Figure 6.  
As shown in Figure 6a, when the earthquake duration \(t_{\text{d}}\) and earthquake intensity are constant, the increase in the stirrup ratio \(\rho_{\text{sw}}\) can slow down the damage.