# Influence of Girder Flaring on Load Effect in Girders of Composite Steel Bridges
## 4 Detailed Analysis of Reference Bridge B1  
In this section, the method outlined earlier for determining the girder distribution factor is illustrated in detail for the reference splayed girder bridge B1. The 40 m simply supported bridge is composed of five girders that are spaced at 4.5 m at the wide end and 2.25 m at the narrow end, with the overhang width being one-third of the girder spacing. The bridge has a 220 mm thick concrete slab and contains diaphragms in the shape of cross-bracing only at the supports. The structural layout, cross-section dimensions, and finite element model are shown in Figure 7.  
Each splayed highway bridge modeled in this study was loaded for maximum flexure and shear effect by moving one, two, and three trucks within their lanes in the transverse direction to maximize the live load effect in the girders. Moving the side-by-side trucks incrementally from one parapet to the opposite side leads to changes in the flexural and shear GDF values among the bridge girders. Figure 8 shows the load effect in the reference bridge due to two side-by-side trucks longitudinally positioned near the midspan, considering the longitudinal normal stresses in the bottom flanges and vertical shear stresses in the webs of the girders. Figure 7: Details of reference bridge B1: (a) plan; (b) cross-section; (c) finite element mesh. For the reference bridge under consideration, Figure 9 shows the flexural GDF values plotted against the distance of the truck from the parquet in cases of one, two, and three trucks with consideration of the appropriate multiple presence factors. The results indicate that critical flexure in the first interior girder G2 led to the highest GDF (equal to 0.808) when compared with the central interior girder G3. Furthermore, the exterior girder G1 had the highest GDF among all the girders--equal to 0.871. For flexure, the overall GDF value was governed by two-lane loading for the exterior girder, and by three-lane loading for the interior girders. Note that the girder designation (G1, G2, and G3) has been presented earlier in Figure 5b. For the case of shear load effect in the girders, two cases of in-plan truck orientation were checked because maximization of the GDF for the interior girders required a different truck placement to that for the exterior girders. One of the two truck placements consisted of the trucks' lines of wheels being parallel to the parquet (Case 1), while the second consisted of the trucks' axes being perpendicular to girder under consideration (Case 2). The results, shown in Figure 10 as a function of the lateral distance from the parquet, show that the maximum shear GDF for the exterior girder is governed by one-lane loading, while for the interior girder, it is governed by two-lane loading. This finding is not in agreement with the flexural effect, where three-lane loading governs the GDF for the interior girders. Similar to the flexure case, shear GDF in first interior girder governs the central interior  
Figure 8: Load effect in reference bridge B1 by finite element analysis: (**a**) entire bridge; (**b**) normal stresses in bottom flanges; (**c**) shear stresses in webs. Figure 9: Flexural analysis of reference bridge B1: (**a**) transverse truck positioning; (**b**) GDF due to one, two and three loaded lanes. girder. Compared to the flexural GDF, the shear GDF is larger in magnitude, which is an expected result since there is little differential vertical deflection among the girders near the support, leading to little load sharing. The critical shear GDF is 1.036 for the exterior girder and 1.313 for the interior girder, resulting in a 26.7% difference between the two values. All bridges considered in this study and shown in Table 1 are symmetrical in plan around the centerline of the bridge, which results in the central girder(s) being the shortest and the exterior girders being the longest in length.