Numerical methods in bridge structure analysis - Computational Analysis and Design of Bridge Structures - page 81

For detailed analysis, most bridges should be modeled in 3D, not only for
better accuracy but also for simplification of component simulations. Even
a long-span bridge, such as a suspension bridge discussed in Chapter 12,
is preferable to be modeled in 3D rather than 2D because the stiffness of
components such as pylons and truss members of stiffening girder can be
easily computed and thus be simulated accurately in 3D. For certain analy-
sis purposes, such as extreme live loads analysis of floor beams in truss
bridges, 3D model becomes inevitable.
When dimensions in longitudinal and transverse axes are comparable,
such as middle- and short-span girder bridges, an intermediate model, or
the so-called grid model, is widely used. The element in a grid model is
retrograded from a 3D frame element by ignoring two translational dis-
placements on the grid plane and one rotational displacement along the
axis perpendicular to the grid plane. Thus, each node of an element has
only vertical displacements, bending rotation and torsional displacements.
Element internal forces contain bending and torsional moments plus shear,
accordingly. A grid model can easily analyze distributions in the longitudi-
nal direction of a girder and in the transverse direction among girders while
maintaining the same number of degrees of freedom. Therefore, the grid
model is very common in girder bridge analyses. Furthermore, the
grid model can be expanded to simulate a wide box girder, in which webs
are not connected directly by separate diaphragms, but by flanges (Hambly
1991). However, a true 3D model with shell elements is encouraged when
lateral distributions among webs of a box girder are of interest. Many
behaviors of a wide thin-walled box girder, such as warping when torsion
is restrained, distortion when insufficient diaphragm is used, and shear lag-
ging due to longitudinal shear deformations of flanges, cannot be repre-
sented in a grid model.
Most component design theories and code checking are based on inter-
nal forces over a cross section of a component. For example, when design-
ing rebar quantities of a frame member, bending moment, shear, and
axial forces should be known. When a bridge component is modeled as
truss or frame elements, internal forces output from FEM analyses can be
used directly for engineering design and code checks. When a component
is meshed into shell elements, such as a web in box girder as shown in
Figure 3.10a, results from FEM have to be translated into the perspec-
tive of a bridge component, or the original FEM results are not mean-
ingful and cannot be used in design or code checks. This is because the
stress results from FEM analysis are in each element's local coordinate
system, which may vary from one element to another. Stresses have to be
transformed to a unique axis that is meaningful to engineering, like the
longitudinal axis of a component. When in curve segments, elements have
to be unfolded along curves and stress results can then be plotted on flat
regions. As shown in Figure 3.10b, for example, the horizontal stresses