Straight and curved steel I-girder bridges - Computational Analysis and Design of Bridge Structures - page 204

longitudinal and transverse axes). This method is most often used in
steel bridge design and analysis.
4. Plate and eccentric beam analysis methods. This method is an
advancement of a 2D grid/grillage analysis model. The deck is mod-
eled using plane shell elements, whereas the girders and cross frames
are modeled using beam elements offset from the plane shell elements
to represent the offset of the neutral axis of the girder or cross frame
from the neutral axis of the deck.
The offset length is typically equal to the distance between the cen-
troids of the girder and deck sections. This method is more refined than
the traditional 2D grid method. For this modeling approach, beam ele-
ment internal forces obtained from this method need to be eccentrically
transformed to obtain the composite girder internal forces (bending
moment and shear) used in the bridge design. More details and sketch
of the model are further discussed in the next point, 3D FEA methods.
5. 3D FEA methods . The 3D FEA method is meant to encompass any
analysis or design method that includes a computerized structural analysis
model where the superstructure is modeled fully in three dimensions:
modeling of girder flanges using line or beam elements or plate-, shell-,
or solid-type elements; modeling of girder webs using plate-, shell-, or
solid-type elements; modeling of cross frames or diaphragms using line
or beam, truss, or plate-, shell-, or solid-type elements (as appropriate);
and modeling of the deck using plate-, shell-, or solid-type elements.
This method is fairly time consuming and complicated and is argu-
ably deemed to be most appropriate for use for complicated bridges
(e.g., bridges with severe curvature or skew or both, unusual framing
plans, unusual support/substructure conditions, or other complicating
features). 3D analysis methods are useful for performing refined local
stress analysis of complex structural details (AASHTO/NSBA 2011).
However, there are some complications associated with 3D analy-
sis methods. For instance, in a 3D analysis, generally used girder
moments and shears are not directly calculated. Instead, the model
reports stresses in flanges, webs, and deck elements. If the designer
wishes to consider girder moments and shears, a postprocessor
with some kind of conversion or integration of the stresses over the
depth of the girder cross section will be required. A demonstration
of this kind of conversion is shown in Figure 7.9. In this figure force
results of a steel girder section are shown where top and bottom
flanges are modeled by beam elements (element numbers 30 and 90)
and web by two shell elements (element numbers 838 and 898).
Neutral axis is in the middle for a symmetric section. Resultants
for beam elements are shown in F x (axial force = 649.72 kip or
2890 kN), F y (transverse force = 9.95 kip or 44.3 kN for the top
flange), F z (vertical force = 0.28 kip or 1.2 kN for the top flange),