## 4 Parametric Study by Computational Analysis
### Influence of Single Parameters \(h\), \(t\), and \(a\)  
Indeed, the height of the U-rib (\(h\)) plays a crucial role in the design of the BUSP. Using a simple rectangular section beam as an example, its bending stiffness is directly proportional to the cube of its height. This example clearly illustrates that the distribution of material along the height direction significantly impacts the bending resistance of structures. To explore this further, this paper considers values of 70, 80, 90, 100, and 110 mm for \(h\). Figure 12 demonstrates that variations in \(h\) have a more pronounced effect on the bending stiffness of the U-rib compared to changes in \(t\) and \(a\). Increasing \(h\) effectively increases the bending stiffness of the BUSP. However, it is important to note that an increase in \(h\) does not necessarily result in smaller concrete stresses. Figure 13 provides information on the maximum stress and displacement of the concrete overlay in Structure 1, Structure 2, and the original structure for different values of \(h\) (70, 80, 90, 100, and 110 mm). Additionally, Figure 13c compares the stress of the steel crossbeams in Structure 1 and Structure 2 with that of the original structure. Figure 12: The bending stiffness of the U-rib varies with the change of \(h\), \(t\) and \(a\). Figure 13: The impact of changes in the \(h\) value on the bridge deck structure: (**a**) impact on stress of concrete overlay, (**b**) impact on displacement of concrete overlay, (**c**) impact on stress of crossbeam. These figures provide insights into how variations in \(h\) affect the internal stresses and displacements of the concrete overlay and the steel crossbeams. By analyzing these results, we can better understand the impact of parameter changes on the structural behavior and determine optimal design configurations for the BUSP. From the observation of Figure 13, it is evident that both Structure 1 and Structure 2 exhibit significant improvements in strength and stiffness when compared to the original structure. This improvement is primarily characterized by lower displacement and stress levels in the concrete overlay under the same load conditions, as well as enhanced stress in the steel crossbeam. Following the principle of a single variable, except for the height change of the U-rib, all other size parameters remain constant. By examining the graph in Figure 13, it can be seen that, except for the transition from 100 mm to 110 mm, the displacement, and stress of the concrete overlay increase as the height decreases under the five specified \(h\) values. Referring to Figure 10, it is noted that the total thickness of the concrete overlay, including the U-ribs, is 250 mm. Consequently, an increased \(h\) value leads to thinner sections without U-rib stiffeners in the concrete overlay, which could have an unfavorable impact on the stress distribution in those areas. In the range of \(h\) values between 70 mm and 100 mm, the reinforcement provided by the U-ribs mitigates this adverse effect to some extent. However, when the height of the U-ribs reaches 110 mm, this effect becomes more pronounced. Thus, for the BUSP, a larger \(h\) value does not necessarily translate to improved performance. Based on these findings, it is crucial to strike a balance between the height of the U-ribs and the overall design objectives of the BUSP. Simply increasing the height without considering the corresponding effects on stress distribution and performance might not yield the desired outcome. Therefore, careful consideration should be given to selecting an optimal \(h\) value during the design process. Based on the observation of Figure 12, increasing the value of \(t\) (thickness) is more advantageous in enhancing the stiffness of the BUSP compared to increasing the value of \(a\) (width). This is attributed to the fact that both \(t\) and \(h\) (height) are dimensions in the vertical direction, thus influencing the bending stiffness of the structure.