# Influence of Girder Flaring on Load Effect in Girders of Composite Steel Bridges
## 5 Parametric Study
### Shear in Girders Due to Live Load
#### 5.2.1 Effect of Girder Spacing  
The shear GDF expressions in the AASHTO Bridge Design Specifications [1] only include girder spacing in the determination of the shear load effect in girders. In this study, the same bridges used to examine the flexure effect are analyzed to determine the shear effect by positioning the truck(s) longitudinally on the bridge near the support at the wider girder spacing end in order to maximize the vertical reaction under the critical girder.  
Investigation of the effect of splayedness in the reference bridge B1 showed that an equivalent shear GDF based on the lever rule can be more effective in predicting the shear effect in splayed girders than using the AASHTO LRFD expressions. Therefore, the equivalent shear GDF was computed once based on the AASHTO LRFD expressions and once again based on the lever rule. Both values were then compared with the finite element model results for all fifteen bridges listed in Table 1.  
The effect of the splayedness ratio (S\({}_{2}\) - S\({}_{1}\))/L is examined for the shear GDF by studying bridges B1, B2, and B3. However, since the changes in this ratio at the wide end of the bridge (the longitudinal critical position for shear) are minimal, there is almost no change in the girder spacing between the three considered bridges. This leads to insignificant changes in the finite element results of the shear GDF. Likewise, the equivalent shear GDF based on the lever rule showed negligible change between the considered bridges, as the loaded region near the end support was relatively small in comparison with the entire surface area of the bridge.  
When comparing the interior girder shear GDF values computed by the three different methods, it became obvious that the AASHTO LRFD expressions yielded0 slightly lower values compared with the finite element results, while the lever rule produced almost the same outcome. For the exterior girders, the AASHTO LRFD shear GDF values were higher than the finite element results by as much as 19%, while the lever rule values were much closer to the finite element results, with a maximum difference on the conservative side equal to 7.8%.  
The girder spacing ratio S\({}_{1}\)/S\({}_{2}\) was also examined for the shear GDF by studying bridges B4, B1, and B5. The finite element results demonstrated that for interior girders,  
Figure 22: Comparison between the finite element and AASHTO flexural GDF: (**a**) interior girder; (**b**) exterior girder.  
increasing the S\({}_{1}\)/S\({}_{2}\) ratio by 14.3% resulted in a 10.54% increase in GDF value, while decreasing the S\({}_{1}\)/S\({}_{2}\) ratio by 20% led to a 12.88% reduction in GDF value. The same trend was observed for the exterior girders, where increasing the S\({}_{1}\)/S\({}_{2}\) ratio by 14.3% resulted in an increase in GDF value of 7.8%, while reducing the S\({}_{1}\)/S\({}_{2}\) ratio by 20% resulted in an 11.86% decrease in the GDF value. It can be observed that all splayed bridges acted like regular bridges with parallel girders, in which increasing girder spacing caused a linear increase in the values of the shear GDF.  
Figure 23a,b show the influence of the splayedness and girder spacing ratios on the shear GDF, respectively, for the interior and exterior girders. For bridges B1, B4, and B5, the GDF is computed based on finite element analysis, the AASHTO LRFD expressions, and the lever rule. Compared to the finite element results, the AASHTO expressions yielded slightly lower GDF values for the interior girders and up to 32.8% higher values for the exterior girders. On the other hand, using the lever rule led to reasonably close and conservative values in comparison with the refined analysis for both interior and exterior girders. Based on the outcome of the study concerning the variation in the girder spacing, the lever rule is recommended for determining the shear load effect in interior and exterior girders of splayed girder bridges in lieu of using a complex refined method.