Keywords: cable structure, differential equations, Galyorkin procedure, girder-stiffened structure, hanging roof, hypar-network, suspension bridge.

Our paper shows an overview of the continuous and discrete methods of analysis for different cable structures developed at Tallinn University of Technology [1,2]. In cases of distributed loads the non-linear conditions of equilibrium and equations of deformation compatibility are taken as initial equations [1]. To eliminate the horizontal displacements, the equations of deformation compatibility were used in an integrated form; corresponding integrals were replaced by respective displacements of the supporting structures subject to the action of cable forces. Determination of deflections and inner forces for certain cable structures under the action of distributed vertical loads may be carried out by means of exact analysis. A girder-stiffened structure has also an exact solution but in the form of complicated transcendental equations. A simpler, compact solution may be found with a proper approximation of the deflection function in the form of trigonometric dependences. Continuous analysis may be also applied to spatial cable structures in the form of hypar-networks with an elliptical contour beam. A suitable approximation of the deflection function with the use of Galyorkin [3] procedures brings us to values of the network's deflection and cable forces very close to exact ones.

The geometrically nonlinear equations for the analysis of different suspension systems presented in our paper enable adequate determination of deflections and inner forces for these structures. Comparison between results [4] also gives us the findings:

1. The displacements of bridge supports may bring a two- or threefold increase in the cable structure deflections in comparison with cases of immovable supports.
2. The deflection and inner forces of a network depend not only on the form and stiffness of the contour structure, but also on the network's parameters.
3. The dependence of the relative deflection upon the loading parameter for different cable structures may be characterized by a similar diagram.

1

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

2

J. Aare, V. Kulbach, "Accurate and Approximate Analysis of Statical Behaviour of Suspension Bridges", Journal of Struct. Mech., 17(3), 1-12, 1984.

3

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

4

V. Kulbach, "Cable Structures. Design and Static Analysis", Estonian Academy Publishers, Tallinn, 2007.

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