Keywords: cable structure, differential equations, Galyorkin procedure, double-cabled suspension structure, suspension bridge, prestressed cable system, stretching cable.

The behaviour of prestressed suspension structures stiffened by girders or stretching cables is analysed in our paper. The common assumptions about the linear elastic strain-stress dependence of materials and absence of elongations of hangers are taken into account [1]. The cables are regarded as geometrically nonlinear rods without bending rigidity, and stiffening girder. The mutual action between the carrying cables and stiffening members are regarded as a continuous contact load for continuous analysis, or a nodal contact load for discrete analysis.

Continuous analysis of cable structures proceeds from non-linear conditions of equilibrium and equations of deformation compatibility. For a plane structure the conditions of equilibrium and the equations of deformation compatibility are presented as usual differential equations. Horizontal forces and deflection parameters of the cable are the main unknowns in the non-linear conditions of equilibrium and the equations of deformation compatibility. Using a trigonometric deflection function and the Galyorkin[2] procedure, a cubic equation for determination of relative displacement is obtained. In the case of inclined straight anchor cables of pylons, their deformation may be taken into consideration as linear functions of the cable's horizontal forces.

Discrete analysis[3] is based on the conditions of equilibrium, made for the nodal points of the cable. The cable is loaded by concentrated forces and it takes the form of a string polygon. The conditions of equilibrium are written for every node of a polygon and elongation of the cable is determined using the equations of deformation compatibility for every section of the cable. These conditions form a nonlinear system of equations, which gives displacements for all nodes and internal forces for cables and stiffening girder after solving.

For conclusions, the girder and cable stiffened suspension systems are similar in behavioral and calculation aspects. In the case of the continuous calculation method the deflection parameter for both the single cable and the compound structures may be found from a cubic equation. In the case of the discrete calculation method, the system of nonlinear equations, which consist of conditions of equilibrium for every cable node and equations of deformation compatibility, must be solved. Continual analysis may be preferred in the case of uniformly distributed loads applied on the whole or part of the structure. To describe cable's behavior under the action of great concentrated loads more exact analysis is needed. It requires application of the system of equations of the discrete calculation model. Therefore, it is possible to use these methods for an investigation of a different suspension structures.

1

Kulbach V., "Statical Analysis of Girder- or Cable-Stiffened Suspended Structures", Proc. Estonian Acad. Sci. Engin., 1 (1), 2-19, 1995.

2

Galyorkin B.G., "Collection of works", Publ. of the USSR Academy of Sciences (in Russian).

3

Kulbach V., Idnurm J., Idnurm S., "Discrete and Continuous Modeling of Suspension Bridge", Proceedings of the Estonian Academy of Sciences Engineering, 2, 121-133, 2002.

purchase the full-text of this paper (price £20)

go to the previous paper
go to the next paper
return to the table of contents
return to the book description
purchase this book (price £120 +P&P)