Determination of initial cable forces in prestressed concrete cable-stayed bridges for given design deck profiles using the force equilibrium method

doi:10.1016/S0045-7949(98)00315-0

Computers & Structures

Volume 74, Issue 1, January 2000, Pages 1-9

https://doi.org/10.1016/S0045-7949(98)00315-0 Get rights and content

Abstract

The determination of initial cable forces in a prestressed concrete cable-stayed bridge for a given vertical profile of deck under its dead load is an important but difficult task that affects the overall design of the bridge. A new method utilizing the idea of force equilibrium is presented in this paper for their determination. The method can easily account for the effect of prestressing and the additional bending moments due to the vertical profile of the bridge deck. It is much more rational and simple than the traditional “zero displacement” method, and it is able to achieve bending moments in the bridge deck approaching those in a continuous beam over rigid simple supports.

Introduction

The cable-stayed bridge is a modern form of bridge which is both economical and aesthetic. It has been extensively employed in the construction of long-span bridges in the past few decades. However this kind of structure is highly statically indeterminate, and therefore many schemes of initial cable forces are possible. In the particular case of prestressed concrete cable-stayed bridges, it is especially important to choose an appropriate scheme of initial cable forces while the bridge is under dead load only. Owing to shrinkage and creep, the deflections will change with the passage of time and the internal forces may also redistribute. Should an inappropriate scheme of initial cable forces be chosen, an unfavourable pattern of internal forces may be locked in subsequently, for which there may be no simple solution.

Theoretically it is possible to search for a “stable” scheme of initial cable forces under which there is the minimum redistribution of internal forces and time-dependent displacements. However it is usually very difficult in view of the many factors affecting the subsequent time-dependent deformations. For example, many cable-stayed bridges are constructed using cast in situ segmental cantilever construction, which gives rise to complex effects of shrinkage and creep because of the different ages of concrete. The presence of longitudinal prestressing also complicates the problem further. Inevitably some simplifying assumptions have to be made.

Section snippets

Review of existing methods

The scheme of initial cable forces giving rise to bending moments in the bridge deck approaching those of an equivalent continuous beam with all the supports from cables and towers considered as rigid simple supports is generally acknowledged to be both rational and practical, as the long-term behaviour of the bridge is reasonably “stable”. The problem hinges upon how to achieve this scheme of initial cable forces. There are two main categories of methods in achieving an appropriate scheme of

The force equilibrium method

In the force equilibrium method, the cable-stayed bridge is modelled as a planar structure. The method works on an evolving substructure eventually comprising the bridge deck and towers, and searches for a set of cable forces which will give rise to desirable bending moments at selected locations of the substructure. As the method works only on the equilibrium of forces rather than deformation, there is no need to deal with non-linearity caused by cable sag and other effects. The method is

Numerical examples

Two numerical examples are presented to demonstrate that the present method is both rational and reliable. Both are taken from existing prestressed concrete cable-stayed bridges in China, but some minor simplifying modifications are made.

Conclusions

A new method utilizing the idea of force equilibrium is presented for the determination of an optimum scheme of initial cable forces in a prestressed concrete cable-stayed bridge for a given vertical profile of deck under its dead load as well as prestress. In the proposed method, the stiffnesses of the cables do not enter into the calculations, and it therefore obviates the need for introducing non-linearity into the algorithm. The bending moments, rather than the displacements, of the deck

Acknowledgements

The financial support of the block grant from the University Research Committee, The University of Hong Kong is acknowledged.

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