## 2 Structural Considerations of Steel Double-Beam Floor System
### Reduction of Moment Demand in the Double-Beams  
The main beam or double-beam can be idealized according to the boundary conditions and load conditions. As shown in Figure 3a, the main beam of the GBG system can be idealized as a beam that receives a concentrated load in the center with a fixed end condition because the connection of the GBG is designed as an idealized rigid connection. Since the connection of the DBX system is a bolted connection with ideally no rotational constraints at the ends of the double-beam, the double-beam in the DBX system can be thought of as a simply supported beam receiving a uniformly distributed load and a concentrated load, as shown in Figure 3b. The boundary condition at the ends of the double-beam in the DBO system can be idealized as a fixed-end condition if the rotational constraint of the beam-ends is secured large enough. While the load conditions of the double-beam in the DBO and DBX systems are identical, the rotational constraints from the concrete panel can significantly reduce the positive moment demand of the double-beam in the DBO system by generating the negative moment at both ends and shortening the effective length, as shown in Figure 3c. In other words, the addition of concrete panels to the double-beam can realize an economic design of the steel double-beam floor system.  
To quantitatively analyze the reduction in the moment demand induced by the rotational constraint, the moment demands by the floor loads were compared between the GBG, DBX, and DBO systems. The moment demand in the main beam of the GBG system for an arbitrary floor load of \(w\) (kN/m\({}^{2}\)) is calculated by Equation (1). The moment demands in the double-beam of DBX and DBO systems are determined using Equations (2) and (3), respectively.  
\[M_{1}=\frac{P_{1}L_{1}}{8}=\frac{L_{1}}{8}(A_{1}w) \tag{1}\]  
\[M_{2}=\frac{P_{2}L_{1}}{4}+\frac{W_{1}L_{1}{}^{2}}{8}=\frac{L_{1}}{4}(A_{2}w) +\frac{L_{1}{}^{2}}{8}(D_{c}w) \tag{2}\]  
\[M_{2}=\frac{P_{2}L_{2}}{8}+\frac{W_{1}L_{2}{}^{2}}{12}=\frac{L_{2}}{8}(A_{2}w )+\frac{L_{2}{}^{2}}{12}(D_{c}w) \tag{3}\]  
where \(M_{1}\) is the moment demand (kNm) of the main beam in the GBG system, \(P_{1}\) is the concentrated load (kN) acting as the center of the main beam, \(L_{1}\) is the length of the main beam and double-beam (8.4 m), \(A_{1}\) is the tributary area of the main beam, which is (10.2 m \(\times\) (8.4 m/2))/2 \(\times\) 2 EA = 42.84 m\({}^{2}\), \(w\) is the arbitrary floor load (kN/m\({}^{2}\)), \(M_{2}\) is the moment demand (kNm) of the double-beam in the DBX system, \(P_{2}\) is the concentrated load (kN) acting as the center of double-beam, \(W_{1}\) is the uniformly distributed load (kN/m) from the slab, \(A_{2}\) is the tributary area of the double-beam, which is (8.2 m \(\times\) (8.4 m/2))/2 \(\times\) 1 EA = 17.22 m\({}^{2}\), \(D_{c}\) is the half-width of the concrete panel, which is 1.0 m, \(M_{3}\) is the  
Figure 3: Idealized moment diagram induced by one-way gravity load: (**a**) Main beam in GBG system, (**b**) steel double-beam in double-beam floor system without a concrete panel (DBX) system, and (**c**) steel double-beam in DBO system.  
moment demand (kNm) of the double-beam in the DBO system, and \(L_{2}\) is the effective length of double-beam in DBO system (6.4 m).  
The maximum moment in the main beam and double beam of GBG, DBX, and DBO systems was calculated as 45.0, 45.0, and 17.2 \(w\) using Equations (1)-(3). Therefore, the rotational constraint from the concrete panel in ideal conditions can reduce the moment demand of the double-beam in the DBO system to a maximum of about 38.2% compared to the moment demand of the main beam in the GBG system.