## 3 Design of Experiments  
### Choice of Design Domain--Design Variables  
The motivation driving this work is to improve the understanding of the role played by the geometry of the twin-box deck in the aerodynamic and aeroelastic performance of cable-supported bridges. Several geometry-related design variables influence the wind-induced response of the twin-box deck; nevertheless, the consideration of a large number of design variables is usually cumbersome. The larger the number of considered design variables, the better the control is over the design of the twin-box deck; but it also introduces the difficulties associated with the management of a larger sample space, thereby increasing the process time and costs along with added complex interdependence between the design variables. Considering the expertise and the experience of the authors in this domain [23] and pondering the associated computational burden for the definition of the surrogate model, three geometric variables have been selected within the scope of the present study. The design variables chosen are the width of each deck, \(C\), the depth of each deck, \(D\), and the gap distance between the two decks, \(G\). A simple schematic sketch highlighting the different design variables is shown in Figure 2. Although the deck appendages, such as the deck barriers, do play a certain role in the bridge design and aerodynamics, these have not been considered in this study, as the main goal is to ascertain the effects caused by the fundamental geometrical features of the twin-box deck.  
In the present study, a twin-box deck design is always symmetric, thus, a change in one of the boxes is accompanied by a change in the symmetric box. Referring to Figure 2, the width of the deck can be varied by moving horizontally the corner point \(b\). The displacement range of point \(b\) is restricted to \(\pm 5\%\) of the reference single box width, \(C_{\text{ref}}\)  
Figure 2: Cross-sectional view of the twin-box deck showing the 3 selected design variables and the chosen limit bounds.  
This change in the left box is symmetrically replicated in the right box, thereby changing the total width of the twin-box deck. The depth of the deck can be modified by moving the points \(c\) and \(d\) simultaneously in the vertical direction. The lower limit is set as \(-10\%\), while the upper limit is set as \(+25\%\) of the reference depth \(D_{\text{ref}}\). The third variable considered herein is the gap distance between the two boxes. In [23], it was highlighted how the gap between the two boxes impacts the overall performance of the bridge. However, in those studies, the gap distance was restricted to relatively low values, setting the upper limit for \(G/D\) as 1.86. As this work focuses on larger gaps, the gap-to-depth ratio range considered in the present study is between 2.5 and 6, respectively. With the modifications in the positions of corner points \(b\), \(c\) and \(d\), there occurs a natural change in the side-corner angle, which remarkably influences the aerodynamic characteristics of the bridge. The total side-corner angle \(\theta_{\text{total}}\) is the sum of the upper \(\theta_{\text{upper}}\) and lower \(\theta_{\text{lower}}\) corner angles as depicted in Figure 2. For carrying out the experimental as well as numerical studies, a geometric scale ratio of 1:70 has been adopted in the present study. The geometrical design variables for the model at scale are listed in Table 1.