Cable-stayed bridges - Computational Analysis and Design of Bridge Structures - page 344

By removing superimposed dead loads and disassembling girder segments
and cables stage by stage, the bridge state * of each erection can be obtained,
which will be used to control girder displacements and cables stressing dur-
ing forward erection. It should be noted that it is impossible for an actual
forward stage to reach precisely the state obtained by backward analysis.
This can be understood from the fact that the closure segment stress will
not reach zero after the superimposed dead loads are removed in backward
analysis, whereas in reality it is zero after closure.
Unlike backward analysis, forward analysis based on the actual state
of any construction stage can predict the state when the bridge closes in
the middle span. This prediction is very important for cable tunings at
any stage. Because retuning every pair of cables will increase on-site labor
dramatically and hence slow the construction pace, usually only the newly
installed pairs of cables are jacked according to the analysis results back-
ward to that stage. If, however, tuning one pair of cables cannot keep the
state of the bridge in control, retuning of multiple cables will be required.
The retuning is required at least in the complete stage.
To exactly simulate removal and installation of some components, a
dedicated analysis program is required. The backward analysis can be per-
formed as follows:
1. Apply negative nodal forces of the removed components in the previ-
ous stage
2. The sum of step (1) and the state before removal equals the state after
removal
The forward analysis can be performed as follows:
1. Analyze the new stage with the application of the installed compo-
nents' weight.
2. Analyze jacking loads, if applicable.
3. The sum of steps (1) and (2) and the state before the installation equals
the state after erection.
11.2.6 geometric nonlinearity—P-delta effect
The girder of a cable-stayed bridge works as a continuous girder with a
spring support at each anchorage of the cable. However, as the girder is
under compression, its bending stiffness will be reduced due to the P-Delta
effect. Similar to the girder, the pylons are under compression. Its bending
behavior would also be affected by the P-Delta effect.
* A bridge state is defined as the bridge's geometry configuration, internal forces, and struc-
tural displacements.