# Influence of Girder Flaring on Load Effect in Girders of Composite Steel Bridges
## 4 Detailed Analysis of Reference Bridge B1
Therefore, to ensure that the results of this study are applicable to different in-plan splayedness orientations, two bridges similar to the reference bridge are modeled, but with a different splayedness orientation, as shown in Figure 11. For the first bridge (B1\(-\)a), the girder that is perpendicular to the line of supports is the exterior girder. In the second bridge (B1\(-\)b), the first interior girder is the one perpendicular to the line of supports. Finite element models are developed for each of the two alternative splayed girder bridges, B1\(-\)a and B1\(-\)b, and the same loading procedure followed in the reference bridge for maximizing flexural effect is applied for these two bridges, with consideration of the same longitudinal truck(s)' position. Results from the 3D finite element analysis showed the most critical GDF values, whether in the exterior or in the first interior girders, negligibly changed (by less than 1%) in the two alternative bridges B1\(-\)a and B1\(-\)b compared to the reference bridge B1. Based on the above, it can be concluded that lack of symmetry of the girder splayedness is not an important factor in the analysis of splayed girder bridges. After presenting the finite element results for the reference bridge, an approximate procedure is proposed and demonstrated for computing the GDF for both flexure and shear in interior and exterior girders. This method avoids the need for a refined method of analysis as it utilizes a one-dimensional beam analysis. The procedure is based on the AASHTO LRFD formulas used to calculate the GDF for flexure and shear in slab-on-parallel-girder bridges. The objective of this procedure is to find out if such a simple method can be reasonably used to determine the load effect in the girders of such irregular bridges without the use of three-dimensional finite element analysis. Figure 10: Shear GDF of reference bridge B1 due to one, two and three loaded lanes: (**a**) Case 1, truck lines of wheels placed parallel to parapet; (**b**) Case 2, truck axes placed perpendicular to girder under consideration. The general concept of the approximate approach is to compute the GDF for interior or exterior girders considering the actual girder spacing at each truck axle position along the bridge using the AASHTO LRFD formulas [1]. Each of the three GDF values at the front, middle, and rear axles is then multiplied by the corresponding axle load, and structural analysis of a single composite girder is carried out to determine the live load flexural effect on the interior girders from Equations (1) and (2) or the shear effect on the interior girders from Equations (4) and (5) at the critical location. For the live load effect on the exterior girders, Equations (7) and (8) can be used to determine the GDF for cases of flexure and shear, respectively. The same single composite girder is loaded again with the full AASHTO truck load, without multiplying it by the GDF, and structural analysis is used again to obtain the critical flexural or shear effect in the girder at the critical location. Finally, the equivalent GDF is obtained as the ratio of the maximum live load effect due to multiplying the load by the GDF corresponding to the live load effect under the full truck load without any factors. The outlined approach consolidates the three hand-calculated GDF values at the three different axle locations into one quantity at the critical location for flexure or shear. Such an approach makes it convenient to compare the AASHTO results with the finite element findings obtained with the help of Equations (8) or (9). To test the proposed approximate method, the equivalent GDF values for the reference bridge B1 are calculated and compared with the finite element outcome. Figure 12a shows the flexural results of the equivalent GDF by the AASHTO formulas (referred to as \"Equ AASHTO\") with the finite element outcome (referred to as \"FEM\").