# Influence of Girder Flaring on Load Effect in Girders of Composite Steel Bridges
## 1 Introduction  
The complexity of transportation networks has been increasing with time to accommodate growing volumes of traffic due to population growth and societal needs. Often, this issue requires the use of irregular bridge layouts to account for different traffic levels, highway separations, grades, and curvatures. In some cases, special geometries of bridges are needed to provide for the gradual change in the number of traffic lanes. Such a situation may demand widening or narrowing of the bridge along the span length, which often results in a bridge with linearly varying superstructure width. A bridge at a highway partial separation (on-off ramp) is one example of such bridges. To satisfy the variation in a bridge's width, flared girders are often used in slab-on-girder bridges, which significantly impact the load distribution within the primary members. In general, splayed, flared, or non-parallel girders are essentially beams with varying spacing between them along the span of the bridge. In this study, the minimum girder spacing at the narrow end and maximum girder spacing at the wide end of the bridge are denoted by \(\mathrm{S_{1}}\) and \(\mathrm{S_{2}}\), respectively, as shown in Figure 1 for a typical simply supported splayed girder bridge. A comprehensive literature search on the subject revealed that this type of bridges is not adequately covered in previously published research studies addressing the structural analysis of highway bridges. Bridge design codes and specifications do not allow the load effect in the structural members of irregular bridges to be determined by the simplified deck slab analysis approaches and formulas for the girder distribution factors. The current methodology for analyzing a flared girder bridge requires the development of a three-dimensional (3D) model using a refined method, such as the finite element procedure. Fully detailed 3D modeling of such an irregular bridge is somewhat complex, error-prone, and time-consuming, yields results that are hard to interpret, and is not always the first preferred choice for bridge engineers. Hence, there is a need to develop an approach that does not require the use of a refined method for analyzing a flared girder bridge, while allowing for the determination of the effect of girder splayedness on the distribution of gravity loads within the structure with reasonable accuracy. This study aims to quantify the effect of a gradual linear change in the girder spacing along the span length on the live and dead load distribution in exterior and interior girders of composite steel girder bridges. The objectives of this study are as follows: (1) investigate the effect of splayed girders on dead and live load distribution represented in interior and exterior girder distribution factors for composite steel girder bridges; (2) study the influence of different bridge parameters on the girder distribution factors for both flexure and shear in splayed girder bridges; and (3) recommend a simple approximate approach to determine the girder distribution factor for flexure and shear in splayed girder bridges. The concrete slab-on-steel girder bridges are very popular around the world due to the versatility of their application, simplicity of their structural system, uncomplicated design requirements, economy, and ease of construction. Therefore, only this type of bridge is addressed in this study. Simply supported short- and medium-length bridges up to 50 m are considered, and all the considered bridges are flared symmetrically on either side of the bridge's centerline. In all cases, linearly variable deck widths with the corresponding girder splayedness ratio are addressed.