# Influence of Girder Flaring on Load Effect in Girders of Composite Steel Bridges
## 5 Parametric Study
### Flexure in Girders Due to Live Load
#### 5.1.1 Effect of Girder Spacing  
As mentioned before, the influence of the girder spacing on the structural behavior was examined using two distinct approaches--first, by examining the splayedness ratio (S\({}_{2}-\)S\({}_{1}\))/L effect, and second, by exploring the girder spacing ratio S\({}_{1}\)/S\({}_{2}\) effect--in order to gain a better insight into the effect of the change in the girder spacing along the bridge span. Bridges B2 and B3 in Table 1 were developed based on the reference bridge B1 to observe the effect of the splayedness ratio (S\({}_{2}-\)S\({}_{1}\))/L on the structural behavior. Figure 13a provides a plan view showing bridge B1 in black, B2 in blue, and B3 in green. Starting with the reference bridge B1, the girder spacing at the wide end was kept constant, while the spacing at the narrow end was adjusted to vary the splayedness ratio--increasing it by 33% to form bridge B2 and decreasing it by 33% form bridge B3. It should be noted that increasing the splayedness ratio leads to a reduction in girder spacing along the span, while decreasing the ratio leads to increased girder spacing. The finite element results in Figure 13b show that increasing the splayedness ratio by 33% leads to a 7.254% reduction in the flexure GDF for interior girders, while decreasing it by 33% leads to an almost equal increase in the GDF. For exterior girders, increasing the splayedness ratio by 33% results in an 8.12% reduction in the flexure GDF value, while decreasing it by 33% causes the flexure GDF to increase by 6.93%, as shown in Figure 13c. The bridges were also analyzed using the AASHTO-based equivalent GDF approach outlined earlier, allowing us to find the flexure GDF values with a simple approach and compare them to the finite element outcome. Figure 13b,c show that for the interior and exterior girders, the equivalent AASHTO flexure GDF values for the three bridges are very close to the finite element values, with reasonable conservatism, amounting to a maximum percentage difference of less than 5% for all the considered bridges. Bridges B4 and B5 were developed by modifying reference bridge B1 with the aim of assessing the effect of the girder spacing ratio S\({}_{1}\)/S\({}_{2}\) on the structural response. To effectively examine this ratio without interference from the splayedness ratio, the (S\({}_{2}-\)S\({}_{1}\))/L ratio for all three bridges was set to be constant--equal to 0.05625. Figure 14a shows a plan view for bridges B1, B4, and B5. By decreasing the girder spacing of the reference bridge at any section along the span by 750 mm and increasing it by 750 mm, the S\({}_{1}\)/S\({}_{2}\) ratios for bridges B1, B4, and B5 become 0.5, 0.4, and 0.571, respectively. The finite element results for the interior girders, shown in Figure 14b,c, indicate that increasing the S\({}_{1}\)/S\({}_{2}\) ratio by 14.3% leads to a 15.05% increase in the GDF, while decreasing the S\({}_{1}\)/S\({}_{2}\) ratio  
Figure 13: Effect of girder splayedness ratio on flexural GDF: (**a**) plan of bridges B1, B2, and B3; (**b**) onterior girder; (**c**) exterior girder. by 20% leads to a 16.39% reduction in the GDF. For the exterior girders, increasing the S\({}_{1}\)/S\({}_{2}\) ratio by 14.3% leads to a 15.17% growth in the GDF, while decreasing the S\({}_{1}\)/S\({}_{2}\) ratio by 20% leads to a 17.41% reduction in the GDF. Note that although the S\({}_{1}\)/S\({}_{2}\) ratio increased by 14.3% and then decreased by 20%, these changes resulted in almost equal absolute percentage changes in the GDF for interior and exterior girders, as they caused the same changes--increasing or decreasing--in girder spacing value at any particular section along the bridge length. However, the small difference between the percentage growth and reduction in the GDF--whether in the interior or exterior girder--is due to minor changes in the truck(s)' longitudinal location between bridges B1, B4, and B5 in order to maximize the GDF for flexure.