## 5 Conclusions  
In the steel double-beam floor system, the concrete panel should have an appropriate thickness to induce the rotational constraints required for a code-conforming rigid connection in the ends of the double-beam. However, the dependency of design parameters between the concrete panel and the double-beam caused time-consuming iterative analysis in the quantity optimization process. In this study, an optimal design method was developed to solve the iterative design problem of steel double-beam floor systems considering the beam-end constraints induced by the concrete panels. The LM index multiplied by the length and moment of structural members was employed as a design variable to consider both safety and material quantity. A series of structural analyses for the steel double-beam floor systems was performed to calculate the moment demand varying the live loads in consideration of the usage of underground space. The beam sections designed from the developed method were verified through comparison with the design results of the code-based design method requiring iterative analysis. In addition, the effect of rotational constraints caused by the concrete panels was quantitatively evaluated in terms of the environmental point of view. The conclusions that were obtained through this study are as follows:  
1. The LM index in terms of capacity (\(LM_{C}\)) was defined as the product of unbraced length (\(L_{b}\)) and nominal flexural strength (\(M_{n}\)) of the steel beam, and \(LM_{C}\) had an intrinsic characteristic of having a maximum value in the limiting unbraced length for inelastic lateral-torsional buckling (\(L_{r}\)). Since the value of \(LM_{C}\) is proportional to the material quantity, it was used as a design variable for quantity optimization instead of cross-sectional area;
2. The steel beam sections selected by the LM index satisfied the safety-related constraint conditions. As the LM index reflected the flexural strength considering the lateral torsional-buckling according to the \(L_{b}\), a cross-section with an LM index that minimizes the objective function automatically met the safety-related constraint conditions if the \(L_{r}\) and \(L_{b}\) were similar. For the steel double-beam floor system with the concrete panel (DBO system), the design results using the LM index showed that the range of the \(L_{r}\) (5.9-7.9 m) for the designed H-beam sections was similar to the range of the \(L_{b}\) (6.4-8.2 m) determined by the structural plan. Therefore, the developed design method could provide the optimal design proposals with securing structural safety for the DBO system;
3. Under the low gravity loads with a live load of 4 kN/m\({}^{2}\) or less, the design proposal derived by the developed method showed a higher material quantity of 2.0 ton compared to that of the code-based method. Since the \(M_{n}\) of the designed sections as the LM index tended to be larger than the Mu, the developed method evaluated the slightly higher material quantity than that of the code-based method under the low gravity load. On the other hand, for the high gravity load with a live load of 6.0 kN/m\({}^{2}\) or more, the material quantities derived by the developed and code-based methods were equal. At the high gravity loads, as the \(M_{u}\) increased, the difference in \(M_{n}\) of the designed section using the LM index decreased, so the developed method suggested the same optimal design proposal as the code-based method. Therefore, the developed design method provided a more optimal design option under the high gravity loads;
4. The steel double-beam floor system without concrete panel (DBX system) had a higher global warming potential (GWP) than the general beam-girder system (GBG system) at high gravity loads where the live loads exceeded 6.0 kN/m\({}^{2}\).