Cable-stayed bridges - Computational Analysis and Design of Bridge Structures - page 345

The P-Delta effect can be categorized as the initial stress problem in
mechanics, which is that the existing stress condition of a component will
affect its behavior when new loads are acting on it. Hence, the superpo-
sition principle will be no longer valid. The change of component stress
under new loads will further affect its behavior. The iteration process is
inevitable. The P-Delta phenomenon is common in bridge structures. It can
be ignored in many situations during preliminary analyses. However, in
cable-stayed bridges, it has to be considered as the initial stresses accumu-
lated in the girders and pylons are significant.
By using nonlinear iteration process, the P-Delta effect is fairly easy to
be accounted for in dead load analysis. As the positions and magnitudes
of dead loads are known and do not vary, loads can be scheduled into
several different steps. For each step, the analysis can be linear and the
stresses obtained will be considered when evaluating the stiffness of the
next step.
However, it could be extremely complicated to reach the theoretical solu-
tion for live load analyses as the positions, magnitudes, and/or load pat-
terns vary. For most live load standards, seeking theoretical solutions is
impractical. In general, the following steps are used as a practical way to
consider P-Delta effects in live load analyses:
1. Include the effects of axial forces in the girder and pylons after sec-
ondary dead loads are imposed when evaluating influence values.
2. Use regular methods to obtain extreme live load positions and
magnitudes.
3. Apply the earlier extreme live loads as a dead load case on the
bridge and conduct a nonlinear analysis so as to adjust the extreme
results.
Some researchers even suggest moving all axle positions obtained in step (2)
equally from left to right and step by step to further search for the true
extreme positions. This method assumes the linear results are very close
to reality. However, as a general rule to bridge modeling and structural
analyses, this method lacks theoretical support and should be studied case
by case.
As there will be many points of interest in a cable-stayed bridge that need
to perform the earlier tedious live load analyses, a finite element analysis
(FEA) and live load analysis package specifically developed for cable-stayed
bridges is essential.
11.2.7 geometric nonlinearity—Cable sag effect
Due to its own weight, a cable between two anchors will sag downward
and will not remain straight. Taking a horizontal cable as an example,