## 4 Application to Steel Buildings in Downtown Area
### Verification of Proposed Optimal Design Method  
Based on the results of frame analysis in Section 4.1, the design proposal derived by the code-based method and the proposed method for the DBO system, subjected to 8 kN/m\({}^{2}\) of live load, is summarized in Table 2. The cross-sections of all members designed by the two methods were equal, and the thickness of the concrete panel by them also equal due to the dependency of design parameters between the double-beam and concrete panel. Thus, the proposed optimal design method using the LM index can optimize the material quantity while avoiding the iterative process. To further investigate the feasibility of the proposed optimal design method in the quantity-optimization, the cross-sections designed by the two methods were compared for the five levels of live load. Figure 10 shows the comparison of the total material quantity of steel members designed by the code-based method and the proposed method according to the level of live load considered for the DBO system. Overall, the material quantities derived by \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Live Load** **(kN/m\({}^{2}\))**} & \multirow{2}{*}{**Model**} & \multicolumn{3}{c}{\(M_{u}\) (kNm)} & \multicolumn{3}{c}{\(LM_{D}\) (kNm\({}^{2}\))} \\ \cline{3-8}  & & \
\begin{tabular}{c} **Main Beam or** \\ **Double-Beam** \\ \end{tabular} & **Gider** & **Sub Beam** &
\begin{tabular}{c} **Main Beam or** \\ **Double-Beam** \\ \end{tabular} & **Gider** & **Sub-Beam** \\ \hline \multirow{3}{*}{2.5} & GBG & 489.5 & 386.2 & 584.7 & 2055.9 & 3939.2 & 5963.9 \\  & DBX & 482.5 & 614.3 & 372.0 & 2026.5 & 5037.3 & 3050.4 \\  & DBO & 181.2 & 230.2 & 372.0 & 579.8 & 1887.6 & 3050.4 \\ \hline \multirow{3}{*}{4} & GBG & 600.5 & 474.3 & 719.7 & 2522.1 & 4837.9 & 7340.9 \\  & DBX & 594.3 & 755.5 & 457.5 & 2496.1 & 6195.1 & 3751.5 \\  & DBO & 222.8 & 283.2 & 457.5 & 713.0 & 2322.2 & 3751.5 \\ \hline \multirow{3}{*}{6} & GBG & 747.8 & 595.1 & 897.3 & 3140.8 & 6070.0 & 9152.5 \\  & DBX & 740.7 & 950.9 & 571.9 & 3110.9 & 7797.4 & 4689.6 \\  & DBO & 278.6 & 347.1 & 571.9 & 891.5 & 2846.2 & 4689.6 \\ \hline \multirow{3}{*}{8} & GBG & 896.5 & 714.1 & 1077.2 & 3765.3 & 7283.8 & 10987.4 \\  & DBX & 891.3 & 1135.1 & 688.8 & 3743.5 & 9307.8 & 5648.2 \\ \cline{1-1}  & DBO & 336.2 & 433.8 & 688.8 & 1075.8 & 3557.2 & 5648.2 \\ \hline \multirow{3}{*}{12} & GBG & 1196.4 & 951.7 & 1433.3 & 5024.9 & 9707.3 & 14619.7 \\ \cline{1-1}  & DBX & 1188.7 & 1516.2 & 917.8 & 4992.5 & 12432.8 & 7526.0 \\ \cline{1-1}  & DBO & 447.0 & 539.6 & 917.8 & 1430.4 & 4424.7 & 7526.0 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Results of moment demands and LM index in terms of demand from frame analysis. Figure 9: Bending moment diagram in the beam elements according to the structural system. the two design methods were similar. In particular, when the live load was lower than 4.0 kN/m\({}^{2}\), the design proposal derived by the proposed method showed higher material quantity than that of the code-based method. At relatively low live loads, since the \(M_{n}\) of the H-beam optimized by the LM index tended to be slightly larger than \(M_{u}\), the design proposal by the proposed optimal design method was analyzed to evaluate the material quantity somewhat higher than the code-based method. This is because the \(L_{r}\) of the optimized section at low live loads was shorter than that of the \(L_{b}\), so that the section, satisfying the safety-related constraint conditions of the code-based method, did not satisfy the safety-related constraint conditions of the proposed method. For live loads of 6, 8, and 12.0 kN/m\({}^{2}\), the material quantities derived by the two design methods were equal to 80.0, 90.0, and 105.5 ton, respectively. Therefore, the proposed design method yielded a quantity-optimized design proposal similar to the code-based method while avoiding a time-consuming iterative process.