## 4 Parametric Study by Computational Analysis
### Influence of Spacing Parameters (\(e\) and \(w\))  
Distinguished from the size parameters of a single U-rib, the overall structural stiffness of the entire BUSP can be directly modified by adjusting the spacing parameters, thus enhancing its load-bearing performance. By reducing the spacing parameter \(e\), the number of U-ribs along the longitudinal direction of the BUSP increases, leading to an improvement in its longitudinal stiffness. Similarly, by decreasing the spacing parameter \(w\), the number of U-ribs along the transverse direction of the bridge increases, bolstering the bending stiffness in that direction. Figure 22: The variation of the maximum tensile stress in the concrete overlays with respect to \(A\). To investigate the effects of these spacing parameters, three distinct models with varying parameters were constructed, as depicted in Figure 23. Model 1 represents the original structure of the BUSP, while Model 2 reduces the value of \(w\) to half of the original structure. In Model 3, the value of \(e\) is halved compared to the original structure. Model 4 simultaneously reduces both \(e\) and \(w\) to half of their original values. The establishment of these models enables a comprehensive examination of the impact of spacing parameters on the overall stiffness of the BUSP. This investigation serves to inform engineers and designers seeking to optimize the structural performance and load-bearing capacity of the BUSP in different spatial orientations. Figure 24 presents a comprehensive comparison of the maximum tensile stress in the concrete overlay among four different models, each with varying spacing parameters for both Structure 1 and Structure 2. From the graph, it is evident that adjusting the spacing parameters \(e\) and \(w\) leads to a notable decrease in the maximum tensile stress within the concrete overlay. Additionally, this reduction proves to be significantly more effective compared to modifying the dimensions of a single U-rib. Notably, by reducing the values of \(e\) and \(w\), the stress levels near the transverse side span of the bridge are notably improved. This improvement becomes even more pronounced when increasing the number of transverse U-ribs (achieved by reducing the value of \(w\)). These findings emphasize the importance of optimizing the spacing parameters in enhancing the stress distribution and performance of the concrete overlay. Engineers and designers can utilize this information to create more resilient and robust structures, particularly in areas prone to high tensile stress concentrations near the transverse side span of the bridge. By analyzing Figure 24, it becomes apparent that adjusting the spacing parameters to alter the number of U-ribs in the concrete overlay leads to a corresponding shift in the location of the maximum tensile stress within the overlay. The specific positioning of this stress is showcased in Figure 25, which highlights the variations resulting from different spacing parameter configurations across both Structure 1 and Structure 2. Figure 23: The models with varying spacing parameters (unit: mm). Figure 24: Stress distribution inside the concrete overlay: (**a**) structure 1, (**b**) structure 2. Figure 25: The location of the maximum tensile stress in the concrete overlay. For a comprehensive examination, each structure includes four distinct spacing parameter setups for the BUSP. These configurations consist of the original BUSP structure, the BUSP structure with modified parameter \(w\), the BUSP structure with modified parameter \(e\), and the BUSP structure with simultaneous modifications to parameters \(w\) and \(e\). These visual representations offer valuable insights into the relationship between spacing parameters and the distribution of tensile stress within the concrete overlay. Engineers and researchers can utilize this knowledge to strategically optimize the design and placement of U-ribs to effectively manage stress concentrations in different regions of the BUSP.