Reinforced concrete bridges - Computational Analysis and Design of Bridge Structures - page 112

4.4 pRIncIple and modelIng oF concRete
Beam-SlaB BRIdgeS
The selection of the most appropriate modeling scheme depends on the
nature of the information that is required. The first type of analysis could
be performed with a linear elastic model, and the second type could be con-
ducted with a more sophisticated RC model that is selected to represent the
key aspects of nonlinear behavior for a particular structure or structural
member.
4.4.1 linear elastic modeling
The simplest form of an RC bridge is the RC slab bridge of solid sections
or void sections. As described in Chapter 2, it can be simplified as a beam
or a grid. The solid section can be idealized as an isotropic plate with the
equivalent stiffness calculated from Equation 2.5. The voided section is
idealized as an orthotropic plate, that is, a continuous medium with dif-
fering stiffness in directions parallel and perpendicular to the voids. The
equivalent stiffness can be calculated from Equation 2.6 for rectangular
void block or from Equation 2.7 for circular block (Sen et al. 1994).
Analysis of slab bridge decks using FEM involves the modeling of a con-
tinuous bridge slab as a finite number of discrete segments of slab or elements
(Hambly, 1976). Generally all elements lie in one plane and are interconnected
at a finite number of points known as nodes. The most common types
of elements used are quadrilateral in shape, although triangular elements
are sometimes also necessary (O'Brien and Keogh 1999). Some types of
element, such as plate element, do not model in-plane distortion and con-
sequently the nodes have only three degrees of freedom, namely, out-of-
plane translation, and rotation about both in-plane axes (Timoshenko and
Woinowsky-Krieger 1959). No particular problem arises from using ele-
ments that allow in-plane deformation in addition to out-of-plane bending,
but the support arrangement chosen for the model must be such that the
model is restrained from free body motion in either of the in-plane direc-
tions or rotation in that plane. Such analyses are necessary only if they are
specifically required to model in-plane effects, such as axial prestress.
Finite element models, in which the elements are not at all located in
one plane, can be used to model bridge decks, which exhibit significant 3D
behaviors. The elements used for the modeling of slab bridge decks are flat
shell elements, which can model out-of-plane bending in combination with
in-plane distortion. The material properties of the elements are defined in
relation to the material properties of the bridge slab. In case of bridges
that are idealized as isotropic plates, only two elastic constants need to be
defined for the finite elements, E and ν. Geometrically orthotropic bridge
decks are frequently modeled using materially orthotropic finite elements.