## 5 Optimum Design for the Selected Earthquake Ground Motion Set  
In order to consider the uncertainty of the ground motion, the effectiveness of the developed optimization method was assessed by the selected ground motion group. As described above, the selected set of real earthquake records can be considered a representation of the seismic design spectrum complying with a severe earthquake intensity of CSBDC [4]. Figure 7 compares the longitudinal reinforcement of a single column for each floor of the code-designed structure,  
Figure 6: \(TR\), IDA curves, and longitudinal reinforcement comparison of CSDBC-designed structure and optimized structure: (**a**) \(TR\) of each floor, (**b**) longitudinal reinforcement of single column for each floor, (**c**) IDA curves for each floor. the optimization results obtained by the selected earthquakes, and the average value of the optimization designs. As assumed in the optimization procedure, the longitudinal reinforcement is assumed to be a continuous optimization variable. Steel bars available in commerce (shown as the red line with stars in Figure 7) were selected after obtaining the average value of the optimized longitudinal reinforcement for the columns. Though the diameter of the steel bars is discrete, in fact, the real reinforcement listed in Table 3 has a negligible bias with the average calculation results. Compared with the initial designed structure, for the optimization result, the reinforcement dimension of the third story experiences a slight decrease by 11%, the dimensions of the fourth and fifth floors significantly reduce by 27.6% and 33.2%, and the increase of longitudinal reinforcement for the first and second floors are 30.9% and 33.1%. Because the steel bars located at the corner of the column can not only achieve a maximum moment of inertia but also avoid concrete cracking due to stress concentration, CSDBC [4] restricts that the diameter of the corner steel bar should be bigger than the diameter of the middle bar. Similarly, the diameters of steel bars located at the same position of the column are suggested to be as similar as possible on successive floors for convenient construction. To consider the above factors, here are some suggestions about the reinforcement based on the average of the optimization solutions:  
1. Try to make the corner steel bars have the same diameter with the code-designed structure;
2. Try to use the corner steel bars with a bigger diameter than the middle bars;
3. Try to use steel bars with the same diameter at the same position of the column on successive floors. The _TR_ distributions along the height of the code-based structure and optimized structure (reinforced using the steel bars in commerce) under the ground motion intensity relating to the collapse damage of the code-based structure subjected to the selected 11 ground motions are compared in Figure 8. As for the optimal design structure, the _TR_ values of all the stories are larger than 20%. This means the optimized structure does not collapse at the collapse intensity of the initial structure; and it leads to a more uniform distribution of the _TR_ along the height of the building. This phenomenon implies that the potential of the materials has been optimally exploited using the optimization design. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Story** & **Code-Designed** & **Optimized** \\ \hline
1 & 12\(\Phi\)22 & 12\(\Phi\)25 \\
2 & 12\(\Phi\)22 & 12\(\Phi\)25 \\
3 & 12\(\Phi\)22 & 4\(\Phi\)22 + 8\(\Phi\)20 \\
4 & 12\(\Phi\)20 & 4\(\Phi\)22 + 4\(\Phi\)20 \\
5 & 12\(\Phi\)20 & 4\(\Phi\)22 + 4\(\Phi\)18 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Longitudinal reinforcement of columns for code-designed and optimized structures. Figure 7: Longitudinal reinforcement of single column for each floor comparisons of CSDBC-designed structure and optimized structure. The IDA curves and collapse points of the initial structure and the optimal structure under the selected 11 earthquake records are illustrated in Figure 9a,b, respectively.