Modelo nativo: InfoTren-N(atives)_spontaneous

Three-dimensional finite element models were created using Abaqus/Standard 6.11 (Dassault Systèmes 2010) and were used to model the elastic tension and compression behavior of prestressed concrete girder bridges. The Abaqus bridge superstructures were divided into five parts, including: neoprene bearing pads, traffic barriers, end or intermediate diaphragms, bridge deck, and girders. The geometry of each part was adequately subdivided using partitions for two reasons. First, prior to meshing, individual surfaces were defined to ensure that surface-to-surface constraints were easy to create and to ensure that applied loads could be placed at the correct locations. Second, subdividing each part allowed for use of hexahedral elements and the structured meshing technique in Abaqus, which was preferred because it was more efficient. The mesh for each part was constructed independently using automatic seeding and mesh generation in Abaqus. All parts for non-skewed bridges were meshed using element type C3D8R which is an eight node three-dimensional linear continuum element with reduced integration. Skewed bridge decks utilized a sweep meshing technique with hex-dominated elements. Generally, the majority of skewed bridge deck elements were hexahedral shaped, however select elements were six noded three-dimensional linear triangular prism wedge elements (element type C3D6) used to complete the meshing in areas of unusual geometry.

Characteristic element sizes were approximately 3 in. or smaller for bridge decks and approximately 2 in. or less for bridge girders, traffic barriers, and diaphragms. The mesh of each individual part was deemed satisfactory after verifying that no element had an aspect ratio greater than 2.5. Select elements on skewed bridge decks had aspect ratios larger than 2.5. However, less than two percent of the total elements in skewed bridge decks had an aspect ratio larger than 2.5. For these specific elements, an aspect ratio less than or equal to 4.0 was considered acceptable.

Each part was composed of solid, homogenous sections that included materials defined by their density, Young’s modulus, and Poisson’s ratio. The uniformly distributed density for all concrete components was assumed to equal 150 pcf (0.0868 lb/in.3) which was 5 pcf greater than the density of plain concrete (145 pcf) to account for the weight of the steel reinforcement as suggested by the AASHTO LRFD Bridge Design Specifications (2010). The Poisson’s ratio for all concrete components was assumed to be 0.2 as stated in

33

Section 5.4.2.5 of the AASHTO LRFD Specifications (2010). The Poisson’s ratio for neoprene bearing pad parts was assumed to be 0.49995 as discussed by Roeder et al. (1987) and the density was specified as 0.0813 lb /in.3.

Longitudinal rebar, transverse rebar, and prestressing strands were not discretely modeled. However, the effect of steel stiffness was accounted for in two ways: (1) prescribing transversely isotropic engineering constants (Young’s modulus and shear modulus) for girders, end diaphragms, and barriers, and (2) increasing the Young’s modulus of concrete parts using a steel and concrete volumetric ratio similar to those used for fiber-reinforced composite materials:

(3.2)

Traffic barriers and end diaphragms were assigned a longitudinal Young’s modulus calculated with Eqn. (3.2) based on the amount of longitudinal steel reinforcement. Additionally, the bridge girders were assigned two different materials, one for elements in the bottom flange (concrete plus the additional stiffness of prestressing steel) and one for elements in the remainder of the cross section (concrete only). The transverse Young’s modulus of these elements was set equal to the Young’s modulus of concrete for all elements in each respective part. In the bridge deck, it was assumed that the amount of longitudinal and transverse reinforcing steel was approximately equal. Therefore, the transversely isotropic elastic material properties were equal, with the Young’s modulus value accounting for the volumetric ratio of steel and concrete.

After meshing and assigning material properties, each part was assembled into a single composite structure using master-slave surface-to-surface tie constraints. Typically, the master surface was chosen in the following order: (1) bridge deck, (2) girder, (3) end diaphragm or traffic barrier, (4) bearing pad. The following surface-to-surface tie constraints were used with appropriate partitioning so that surface areas matched:

 Top of bridge deck to bottom of traffic barrier

 Bottom of bridge deck to top of haunch and top of end diaphragm

 Top of girder to bottom of haunch

              total only steel steel total only conc conc al longitudin V V E V V E E

34

 Girder web and top flange to end diaphragm (amount of connectivity dependent on desired fixity condition i.e., pinned, fixed, or free)

 Bottom of girder bottom flange to top of bearing pad

 End diaphragms in bays between adjacent girders were connected to each other behind the end of the girder web and top flange

Displacement/rotation boundary conditions were applied in the initial step, prior to any applied loads. The bottom surface of each bearing pad was restrained to have zero vertical displacement and a similar single bottom corner node on each bearing pad (e.g., only the southwest bottom node on each individual bearing pad) was restrained to have zero longitudinal and transverse displacement.