# Influence of Girder Flaring on Load Effect in Girders of Composite Steel Bridges
## 5 Parametric Study
### Flexure in Girders Due to Live Load
#### 5.1.4 Effect of Other Parameters  
In this section, the number of girders, girder depth, and the span length of a splayed girder are considered to check the validity of using the AASHTO flexural GDF at the respective axle locations to determine the bending moment in the girders.  
By reducing the number of girders in reference bridge B1 from five to three and increasing them from five to seven, while keeping all parameters--including the girder spacing--constant, bridges B10 and B11 are generated, respectively. It is clear from the finite element results of Figure 19 that the number of girders in a splayed girder bridge affects the GDF of the exterior girders more than the interior girders (8.5% versus 2.5% maximum difference between the extreme values). Although the AASHTO GDF formulas do not consider the number of girders explicitly in a bridge, the specifications suggest using the lever rule if the number of girders is three, as is the case in bridge B10. However, for consistency, the equivalent GDF is used for all bridges in the study, which results in an equal equivalent GDF in all three bridges with different numbers of girders. The results show that the AASHTO GDF provides a good predictor of the flexural effect in the girders, especially when the number of girders is not excessively large. It should be noted that use of the lever rule to compute an equivalent GDF resulted in much higher values than the finite element outcome, where in the interior girders, the GDF value was equal to 1.14, and in exterior girders, it was equal to 1.045.  
In this study, the stiffness of the girder was adjusted by changing the depth of the steel girder web in the considered reference bridge. Bridges B12 and B13 were created by reducing the web depth of the 1700 mm girder in the reference bridge by 300 mm and increasing it by the same amount, respectively. Note that the girder level of rigidity in AASHTO is accounted for by the stiffness factor K\({}_{\text{g}}\), presented in this paper as Equation (3).  
Figure 19: Effect of number of girders on flexural GDF: (**a**) cross-section of bridges B1, B10, and B11; (**b**) interior girder; (**c**) exterior girder.  
Figure 18: Effect of cross-bracing spacing on flexural GDF: (**a**) plan of bridges B1, B8, and B9; (**b**) interior girder; (**c**) exterior girder.  
The finite element findings shown in Figure 20 confirm the increase in the GDF with increased girder depth, especially for the interior girders, though the increase in GDF is not very significant. The AASHTO equivalent GDF follows the same trend and provides a safe upper limit to the results of the refined analysis.  
B14 and B15 were generated by decreasing and increasing the 40 m simple span length of reference bridge B1 by 25%, respectively. Note that changing the bridges' span length affects the splayedness angle of the bridge and consequently the girder spacing at the truck axle critical locations for maximum flexural effect, albeit not by much. Figure 21 shows that an increase in the span length has a favorable influence on the interior girders' GDF, but not on that of the exterior girders. The AASHTO GDF expressions at the location of the axles are also capable of matching the finite element trend for the interior girders, but not the exterior girders, since the AASHTO exterior girder GDF is a result of a factor that is a function of the overhang width multiplied by the GDF of the interior girder. Nevertheless, the difference between the finite element and AASHTO results is insignificant.