## 2 Structural Considerations of Steel Double-Beam Floor System
### Design Parameters of Steel Double-Beam Floor System with Concrete Panel  
This study aimed to develop the optimal design method for the steel double-beam floor system considering the rotational constraint of the concrete panel without the iterative analysis. To secure the rotational constraints equivalent to the rigid connection, the value of stiffness ratio should be less than 0.05 as shown in Figure 4. In previous work [7], the flexural behavior of the double-beam floor system was experimentally evaluated according to the presence of the concrete panel, and the stiffness ratio of the composite connection was determined to 0.032 (see [7] for the detailed information about the stiffness ratio). In addition, as the stiffness ratio is independent of the boundary conditions, in this study, the  
Figure 4: Relationship between rotational stiffness (stiffness ratio, \(\mu\)) and negative moment (end-fixity factor, \(r\)) in double-beam floor system with the connection type suggested by ANSI/ASC 360 (American National Standards Institute/American Institute of Steel Construction) [27]. stiffness ratio of the composite connection in the DBO system was fixed at 0.032 based on the previous work [7]. The stiffness ratio of the connection is defined as Equation (4). As shown in Figure 5, the connections between the double-beam and main beam were modeled as an idealized pinned connection without the rotational constraints; that is, the rotational stiffness of the connections (\(K_{R}\)) was generated by the flexural stiffness of the concrete panel (\(K_{P}\)), which is defined by Equation (5) according to the Kirchhoff-Love plate theory. \[\mu=\frac{K_{F}}{K_{R}}=\frac{(EI/L)}{K_{R}} \tag{4}\]  
where \(\mu\) is the stiffness ratio of the connection (0.032 for the DBO system), \(K_{F}\) is the flexural stiffness of the double-beam, \(K_{R}\) is the rotational stiffness of the connection, \(E\) is the elastic modulus of the double-beam (205,000 MPa), \(I\) is the moment of inertia of the double-beam (m\({}^{4}\)), and \(L\) is the length of the double-beam (m). Since \(K_{R}\) and \(K_{P}\) are equal, by substituting \(K_{P}\) in Equation (5) for \(K_{R}\) in Equation (4), the thickness of the concrete panel is calculated as Equation (6). The reinforcement of the concrete panel was designed to meet the minimum ratio of 0.0018, suggested by ACI 318-19 (American Concrete Institute) [28], for preventing cracks due to shrinkage and temperature. Since the reinforcement of the concrete panel has little effect on the flexural stiffness of the concrete panel, the flexural stiffness of the concrete panel was determined considering only the concrete material. The design parameter of the concrete panel considered in this study was the thickness of the concrete panel (\(T_{P}\)), and the design parameters of the double-beam affecting the thickness were the moment of inertia (\(I\)) and the length (\(L\)). Generally, the length of the beam elements is determined by the distance between columns according to the usage of buildings, so the remaining design parameters in the connection are the thickness of the concrete panel and the moment of inertia of the double-beam. These two design parameters have a dependency as summarized in Equation (6). The variation in the cross-section of the double-beam for quantity optimization leads to a change in the thickness of the concrete panel, and the changed thickness affects the rotational constraint of the connection. In other words, the dependency in the two design parameters of the connections causes the time-consuming iterative analysis in the quantity optimization process as the rotational constraint of the connection modified the moment demand of the double-beam related to the safety. To optimize the material quantity for the steel double-beam floor system in practice, a new optimal design method that can reflect the effect of rotational constraint without the iterative analysis is needed, and details are dealt with in Section 3.