## 4 Performance-Based Design Process of Reinforced Concrete Column Members
### Example
When the damage index \(D_{k}\) and seismic intensity are constant, the stirrup ratio \(\rho_{\text{sw}}\) increased with the increase in earthquake duration \(t_{\text{d}}\), which indicates that the increase in earthquake duration \(t_{\text{d}}\) can aggravate the damage development of the construction member. When the earthquake duration \(t_{\text{d}}\) and damage index \(D_{k}\) are constant, the higher the seismic intensity, the greater the damage of the construction member. Similar phenomena can be seen in Figure 6b-f. Comparing Figure 6a-f, when the damage index \(D_{k}\), the earthquake \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline  & **Earthquakes** & \(T\) **(s)** & \(M\) **(kg)** & \(\mu\) & \(\begin{array}{c}A_{\text{PG}}\\ (\text{cm/s}^{2})\end{array}\) & \(V_{\text{PG}}\) & \(u_{\text{y}}\) & \(F_{\text{y}}\) \\ \hline \multirow{8}{*}{8 degrees (0.2 \(g\))} & Moderate earthquakes & & & & & & \\  & Major earthquakes & & & & & & & \\  & Moderate earthquakes & & & & & & & \\  & Major earthquakes & & & & & & & \\  & Moderate earthquakes & & & & & & & \\  & Moderate earthquakes & & & & & & & \\  & Major earthquakes & & & & & & & \\  & Major earthquakes & & & & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 2: _Cont._intensity, and the earthquake duration \(t_{\text{d}}\) are constant, the larger the fundamental period \(T\) is and the higher the stirrup ratio is, which indicates that the damage will be aggravated with an increase in the fundamental period \(T\). It can be seen from Figure 6 that when the seismic intensity and earthquake duration \(t_{\text{d}}\) are constant, a one-to-one correspondence between the damage index \(D_{k}\) and the stirrup ratio \(\rho_{\text{sv}}\) was established. Therefore, when the damage index (performance objective) is determined by the owner, the target stirrup ratio can be obtained according to Figure 6, that is, this design process can be used in the performance-based design. Comparison between the Design Method Based on Damage Index and the Design Method Based on Ductility Coefficient  
Based on the code for seismic design of buildings [27], when the ductility coefficient \(\mu\leq 1\), the construction member can be calculated according to linear elasticity, and there is no residual deformation after the earthquake. When the ductility coefficient \(1<\mu\leq 1.5\), the construction member is slightly damaged after the earthquake and can be used again after repair. When the ductility coefficient \(1.5<\mu\leq 2\), the construction member has medium damage after the earthquake and can be properly used after taking safety reinforcement measures. When the ductility coefficient \(2<\mu\leq 5\), the construction member is nearly severely damaged after the earthquake and can be used after major repair. When the ductility coefficient \(\mu>5\), the construction member is destroyed after the earthquake. Table 3 shows the performance index limit of the damage index-based design method and ductility coefficient-based design method [29]. In order to further study the difference between the design method based on the damage index versus the design method based on the ductility coefficient, according to the example (\(T=0.49\), \(8\) degrees), the \(D_{k}\)-\(\rho_{\text{sv}}\)-\(t_{\text{d}}\) relationship under different ductility coefficients is presented in Figure 7. The x-coordinate is the stirrup ratio \(\rho_{\text{sv}}\), and its range is \(0.1\%\) to \(3\%\). The y-coordinate is the earthquake duration \(t_{\text{d}}\), and its range is \(0\) to \(40\). The z-coordinate is the damage index \(D_{k}\), and its range is \(0\) to \(1\). When the limit value of ductility coefficient \(\mu\) is \(1.5\), it means that the construction member designed according to the design method based on the ductility coefficient can ensure mild damage after an earthquake.