## 4 Parametric Study by Computational Analysis
### Influence of Single Parameters \(h\), \(t\), and \(a\)
To assess the impact of variations in \(t\) on the performance of the BUSP, calculation models were created for the BUSP using different \(t\) values: 8 mm, 10 mm, 12 mm, 14 mm, and 16 mm. Figure 14 depicts the stress and displacement of the concrete overlay for the three structures under these specified \(t\) conditions. From the analysis of Figure 14, it is apparent that both the maximum stress and displacement of the concrete overlay decrease as the \(t\) value (thickness) increases. When \(t\) is increased from 8 mm to 16 mm, the range of variation in maximum stress within the concrete overlay is almost equivalent to the range observed when \(h\) (height) is increased from 70 mm to 110 mm. While increasing the \(t\) value can enhance the stiffness of the BUSP, it also leads to a significant increase in the amount of steel required. This implies that there would be a corresponding rise in construction costs and material consumption. From the analysis of Figure 15, it is evident that both for a single U-rib and for the BUSP, the increase in steel consumption caused by increasing the \(t\) value (thickness) is significantly greater than the effects of changes in \(h\) (height) and \(a\) (width) values. This suggests that increasing the height of the U-ribs in the BUSP is a more effective approach for managing tensile stress in the concrete overlay compared to thickening the BUSP. By focusing on increasing the height of the U-ribs, it is possible to improve the structural performance and control stresses without significantly escalating the steel consumption or construction costs associated with the thickening of the entire BUSP. This information highlights the importance of considering different design parameters and their respective effects on the performance and cost of the structure. Designers should prioritize the most effective and efficient strategies to achieve the desired objectives while optimizing resources and meeting project requirements. Figure 14: The impact of changes in the \(t\) 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. In addition, six different values of \(a\) (width), namely 650 mm, 670 mm, 690 mm, 710 mm, 730 mm, and 750 mm, were considered to study their influence on the stiffness of BUSP. Although Figure 12 indicated that varying width values could not effectively enhance the stiffness of the BUSP, changes directly affect the width of the U-shaped stiffeners at the bottom of the concrete overlay, thus increasing its bending stiffness. In Figure 16, it is evident that increasing the value of \(a\) leads to a significantly greater increase in the stiffness of the concrete components compared to the other two parameters (\(t\) and \(h\)). Additionally, as the value of \(h\) increases, the flexural stiffness of the concrete component decreases, which explains why the maximum tensile stress in the concrete increases when the \(h\) value is raised from 100 mm to 110 mm. The decrease in the stiffness of the concrete overlay with an increasing \(h\) value mainly results from the reduction in the thickness of the concrete overlay outside the U-ribs. These findings emphasize the importance of considering different design parameters and their respective effects on the stiffness and performance of the concrete components in BUSP structures. Designers should carefully evaluate the trade-offs between different parameters to optimize the overall structural design. Figure 16: The stiffness of the concrete varies with changes in \(h\), \(t\), and \(a\). Figure 15: U-rib and BUSP areas vary with changes in \(h\), \(t\), and \(a\). Figure 17 demonstrates that increasing the value of \(a\) (width) leads to a decrease in stress and displacement in the concrete overlay, as well as the stress in the steel crossbeam.