## 1 Introduction  
In downtown areas with a high density of buildings, the construction of new buildings with underground spaces is on the rise to efficiently use the limited areas. The top-down methods [1, 2] are widely used for structural systems of underground spaces, and steel floor systems have been preferred to increase in situ workability [3]. Since the underground spaces of buildings are used as parking lots or warehouses requiring a high gravity load, the material quantity with meeting design criteria increases. In particular, greenhouse gases (GHGs) generated from construction materials account for \(11\%\) of the total [4]; thus, reduction in the material quantity of structural members is essential to cope with global warming problems [5]. Recently, steel-concrete composite floor systems [6, 7, 8] have mainly been used to reduce the material quantity as the composite action of two materials can increase the flexural capacity in terms of stiffness and strength [9, 10, 11]. The initially developed steel-concrete composite floor systems [12, 13] were aimed at reducing the floor height and improve the constructability, so beam-column connections were pinned using bolts. However, these composite floor systems were ineffective in the reduction of material quantity when the moment demand generated at the center of the beam significantly increased due to a high load. The results of previous studies on the beam-column connections of the steel-concretecomposite floor systems showed that the connection reinforcement induced a negative moment at the ends of the composite beam, thereby decreasing the moment demand [14; 15; 16; 17; 18]. However, these composite floor systems have low constructability due to the complicated details for securing sufficient rotational constraints of the beam-column connections. To improve the constructability of the beam-column connection in the steel-concrete composite floor system, we proposed a steel double-beam floor system in previous works [7; 19] as shown in Figure 1. The steel double-beam floor system is a composite floor system composed of steel-reinforced concrete (SRC) columns, steel beams, and concrete panels. The steel double-beams are installed in the direction of the short side to distribute the gravity loads. In the steel double-beam floor system, it is possible to reduce the material quantity and improve the environmental performance even under the high gravity load, by introducing the rotational constraint from concrete panels installed at the ends of the double-beam. It is widely known that the constraint effect of concrete in steel-concrete composite joints greatly increases the structural performance of the connection against external loads [20; 21]. More reduction of the material quantity is possible if the optimal design is applied to the steel double-beam system. Generally, the optimal design requires iterative analysis taking a lot of time to minimize the objective functions such as cost [22], environmental impact [23], or a combination of both (i.e., multi-objectives) [24; 25], while the structural safety is satisfied. Moreover, when design parameters of different structural members have a dependency and they are reflected in the objective functions, the time-cost is increased by the iterative analysis. Since the design parameters of the steel double-beam and the concrete panel have a dependency, in practice, it is challenging to derive optimal design for the steel double-beam floor system using the time-consuming optimal design method with the iterative analysis. This study aims to develop an optimal design method for the steel double-beam floor system that can simply provide the design parameters without the iterative analysis. A new index, named the LM (Length-Moment) index, regarding the design parameter of steel beam is used to consider both material quantity and structural safety for the design conditions of the underground spaces used as a parking lot.