# Influence of Girder Flaring on Load Effect in Girders of Composite Steel Bridges
## 5 Parametric Study
### Flexure in Girders Due to Live Load
#### 5.1.3 Effect of Cross-Bracing  
The AASHTO formulas used to calculate the GDF were developed based on bridge models not containing diaphragms or cross-bracings [30]. Therefore, the reference bridge in this study is assumed to have cross-bracing only at the ends of the bridge (40 m). However, two other bridges with different cross-bracing spacings are developed to address the cross-bracing effect on the structural behavior of splayed girder bridges. Bridge B8 has a  
Figure 16: Effect of deck slab thickness on flexural GDF: (**a**) cross-section of bridges B1, B6, and B7; (**b**) interior girder; (**c**) exterior girder.  
cross-bracing spacing equal to 5 m, while bridge B9 has a cross-bracing spacing equal to 10 m. Figure 17 shows the change in GDF due to the movement of two trucks in adjacent lanes in the transverse direction for two bridges--one in which the bracings are located at the supported ends only (reference bridge B1), and the other in which the bracings are located at 5 m intervals along the bridge (bridge B8). It is clear from the results that the fraction of flexural live load in the interior girder for the bridge without bracing is higher than in the corresponding bridge with bracing. In contrast, the presence of cross-bracing in bridge B8 resulted in higher GDF values in the exterior girders than those resulting from the same bridge without cross-bracing (bridge B1). Adding cross-bracing to a bridge results in more uniform deflection across all girders, thus increasing load distribution among the interior girders and leading to a lower GDF. However, increasing the rigidity of the cross-section with the addition of cross-bracing increases the effect of rigid body rotation on the exterior girder as a result of the eccentricity of the truck load in the transverse direction about the bridge centerline, which results in a higher GDF in the exterior girders.  
Finite element analysis showed that the presence of intermediate cross-bracing affects the GDF values, although the spacing of the cross-bracing is not a significant parameter. Adding cross-bracing to the reference bridge slightly increased the GDF of the exterior girder by up to 2% while reducing GDF of the interior girder by about 8%. Moreover, the analysis showed that rigid body rotation of splayed girder bridges is less pronounced compared to that in parallel girder bridges. This is because transverse eccentric truck positioning has a reduced effect due to the resistance of flared girders to superstructure twisting. Note that the AASHTO equivalent GDF expressions do not account for the presence or spacing of cross-bracing. Therefore, all three bridges--B1, B8, and B9--with different cross-bracing spacings have the same equivalent AASHTO GDF, as shown in Figure 18. Comparing this value for interior or exterior girders with the finite element outcome showed that the equivalent AASHTO GDF is a good predictor of the flexural live load distribution. Note that the rigid body rotation method for finding the equivalent GDF for the exterior girders resulted in a high value equal to 1.023, far exceeding the findings of the finite element analysis and the AASHTO approximate approach. Hence, such an approach is not recommended for splayed girder bridges since it results in an unreasonably higher load effect than the refined method.  
Figure 17: Finite element-based flexural GDF as a function of the distance from the parapet for bridges B1 and B8 under two side-by-side trucks.