Cable-stayed bridges - Computational Analysis and Design of Bridge Structures - page 342

By using the matrix differential and considering Equations 11.7 and 11.5,
the following equation can be obtained:

A A S A D

T T

(11.9)

× =

After solving S from the linear equation group in Equation 11.9, the optimized
target values will be obtained from Equation 11.5 (Wang and Fu 2005).
The following procedures are commonly used in approaching the ideal
state in the complete stage * after the deck is superimposed:

1. Select all the cables to be tuned.

2. Perform static analysis under structural weight and superimposed
dead loads.

3. Select negative girder displacements at each anchor in step (2) as D .
This step varies in different situations.

4. Evaluate S as above.

5. Similar to jacking loads, reapply S on the structure and perform a
round of full analysis.

6. The sum of steps (2) and (5) is the ideal state at the complete stage.

11.2.4 anchor of pylons
Due to the weakness of cable supports as stated in Section 11.2.1, the
bending moments and vertical displacements under live loads can be sig-
nificant on the girder. This may become a control factor for the maximum
length a cable-stayed bridge can span. Figure 11.18 shows how the hori-
zontal stiffness of pylons influences the vertical stiffness of the girder. In
very long-span cable-stayed bridges, the anchor cables in the end spans
and end cables in the main span have smaller angles to the girder; the
vertical stiffness they provide to the girder becomes smaller. The upper
part of a middle pylon in multiple-span cable-stayed bridges lacks enough
horizontal anchor stiffness; hence, the vertical stiffness of the girder is
not sufficient.
Such behavior will lead to excessive displacement under live loads. Anchor-
age of pylons is a common issue in two-pylon bridges with a very long main
span or multiple-span cable-stayed bridges. As shown in Figure 11.18, it is
obvious that (1) adding secondary or auxiliary piers at side spans in very
long-span cable-stayed bridges, such as Pont de Normandie Bridge (shown
in Figure 11.3) and Sutong (illustrated example in Section 11.5) Bridge, and
(2) using cross cables to anchor a middle pylon to the deck where it has a
strong vertical stiffness (adjacent pylon area) are both effective geometry

* The complete stage of a cable-stayed bridge is defined as the stage when the erecting girder
is closed and the deck is superimposed.