Numerical methods in bridge structure analysis - Computational Analysis and Design of Bridge Structures - page 82

851

−220

−220

−220

−220

(a) 315 315

−3974 −3974

(b) 10090 −10550

(c) 10221 −3258

Figure 3.10 Interpretation of stresses as engineering perspectives. (a) Shell elements of
a web in a box girder and vertical shear stresses. (b) Stresses along horizon-
tal direction after unfolded. (c) Major principal stresses.

along web curves are transformed from two axial stresses and one shear
stress of all involved shell elements. What is shown in Figure 3.10b can
be defined as axial stress perpendicular to a cross section, which is one of
the dominating stresses and is what a bridge engineer looks for. Further,
the major/minor principal stresses, * which are transformed from stress
components at any point, are needed more often and more meaningful
than their original stress components in each element's local coordinate
system. Figure 3.10c shows the major principal stress of the same web as
in Figure 3.10a and b.
When a bridge is modeled as shell elements, or further as 3D block ele-
ments, engineers often want to compare the stress distribution obtained
from shell elements to that from a simple model as frame elements so that
the differences from the beam theory can be better understood. Special
functions in postprocessing in this regard are particularly important to
bridge analysis, or 3D detailed modeling will be greatly limited in bridge
analysis and design. For example, Figure 3.11 shows a special function in
a postprocessing package that can first transform stress components to
axial stress perpendicular to any predefined cross section and then inte-
grate this stress over the cross section to obtain equivalent sum forces
over the section. The equivalent forces, which are shown at the bottom
of Figure 3.11, can then be used to compute axial stress distribution by
beam-bending theory. The stress comparison, as shown in both top and
bottom flanges, can help engineers to understand effects such as warping,
distorting, and shear lags.

* The two or three result stresses at any point on plane or in spatial that are transformed
from its three or six stress components as shown in Figure 3.1