# Structural Analysis Model

The structural analysis is carried out using a nonlinear model. This allows for stress and load redistribution that can occur as the structure passes from an initial localized yielding in a member, to reaching the ultimate capacity of that member, and finally to a total bridge collapse. Moreover, the use of inelastic analysis allows to consider material nonlinearity, geometric nonlinearity and also boundary nonlinearity. In this study, the analysis was performed using ABAQUS, a commercially available finite element program. Material and other structural parameters are based on the collected information from the literature supplemented with engineering judgment.

For the purpose of finite element analysis, the geometry of bridge superstructure can be idealized in many different ways. For this study, a three-dimensional finite element method was applied to investigate the structural behavior of composite bridges. A concrete slab is modeled using isotropic, eight node solid elements, with three degrees of freedom at each node. The girder flanges and webs are modeled using three-dimensional, quadrilateral, four node shell elements with six degrees of freedom at each node. The reinforcement is represented by uniformly distributed layers of steel. The model assumes a complete connection between girders and concrete slab with no slip. Secondary elements were excluded from the analysis. The details of the model are given by Czarnecki and Nowak (2005a-c). An example of an FEM mesh for a bridge with four girders spaced at 3 m is shown in Figure 1.

 Figure 1 Deflected Shape, Finite Element Bridge Model

All investigated structures were designed as simply supported composite bridges in accordance with AASHTO LRFD (2004) Strength I limit state for flexure and shear. Span lengths ranging from 12 m to 42 m, with the intervals of 6 m, are considered. For each of the span lengths, three girder spacings are investigated: 1.8, 2.4, and 3 m. For all considered bridges, the longitudinal axis is assumed at right angle to the abutment. All bridges are designed as two-lane structures, and with deck slab thickness of 225 mm. Previous studies showed (Eamon and Nowak 2002 and 2004) that the effect of diaphragms on ultimate moment capacity is insignificant, therefore, the diaphragms are not considered in this study.

In the analysis, the load was applied in form of two side-by-side design trucks (AASHTO 2004). In the longitudinal direction, the trucks were positioned to generate the maximum bending moment. Different transverse positions were considered but the centerlines of the wheels of two adjacent trucks were placed no closer than 1.2 m.