# Influence of Girder Flaring on Load Effect in Girders of Composite Steel Bridges
## 2 Background  
Many highway bridge design codes and standards, such as the AASHTO LRFD Highway Bridge Design Specifications [1], do not account for variable girder spacing in their simplified girder distribution factor (GDF) formulas. This leads to more conservative designs with high-cost implications for splayed girder bridges if the larger girder spacing is used to analyze the entire length of the bridge structure. The variable girder spacing along the bridge length can also have a significant effect on the deck slab structural design requirements along the bridge. The spacing of the girders has the most significant effect on the structural behavior of both the steel girders and the concrete deck in slab-on-girder bridges. [PERSON] et al. [2] tested different bridges with different girder spacing to examine the structural behavior of the deck slab and found out that there is a significant increase in deflections, compressive stresses, and tensile stresses in the deck slab due to the increase in girder spacing. A study by [PERSON] and [PERSON] [3] showed that the shear load effect in the interior girder is more sensitive than that in the exterior girder due to changes in the girder spacing. Since the AASHTO girder distribution factors cannot be used for irregular bridges with parallel girders that are unequally spaced, [PERSON] and [PERSON] [4] suggested an approximate method to calculate the GDF. The method proposed by the authors was based on analyzing transverse strips of the deck slab directly under the wheel loads as continuous beam on elastic spring supports that simulate the flexibility of the girders. The GDF values resulting from the approximate approach were close and slightly more conservative when compared with the corresponding finite element analysis for the cases of flexure and shear. Using an approach that utilizes a grillage analysis, [PERSON] et al. [5] examined a two-span continuous box-girder bridge with a maximum flare of 6.25% at one of the two bridge ends relative to the other. The results were compared with AASHTO GDF expressions when applied to a bridge having a constant girder spacing equal to the maximum girder spacing of the examined bridge at the wide end. The result showed high conservatism in the load effect in the girders, especially for the exterior ones. The NCHRP report 592 by [PERSON] et al. [6] suggest considering the largest girder spacing in a splayed girder bridge if it is analyzed using the lever rule. Utah's department of transportation bridge management manual recommends using a girder spacing at 2/3 of the span length on the wider bridge end to approximate a splayed girder bridge by a structure having uniform spacing [7]. Other state departments of transportation, such as Kansas [8], propose using AASHTOWare [9] to model a constant girder spacing bridge to represent the splayed girder bridge, but with the maximum girder spacing in order to analyze the interior girders. The Washington state department of transportation has a computer software (PGSuper) that can model a prestressed concrete bridge with different girder spacings at each end of the bridge [10]. Most of the recent research concerning the structural analysis of irregular highway bridges has focused on dynamic behavior under seismic loading [11; 12; 13]. The live load in highway bridges is primarily the weight of vehicular traffic moving on the bridge. It is critical because of its heavy weight, concentration at few points, and high uncertainty compared to dead loads. In the AASHTO LRFD Bridge Design Specifications [1], the design live load is specified as HL-93, which consists of either a design truck or a design tandem--whichever gives a larger effect--together with a design lane uniform load. In the AASHTO specifications, the fraction of the live load that is carried by an individual girder is often represented by formulas referred to as the girder distribution factor. This factor is different for flexure and shear, single-lane and multi-lane bridges, and interior and exterior girders.