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

This paper provides an overview concerning the continuous and discrete method of analysis for cable networks with different contour structures [1]. Usually the cable network of a saddle-shaped roof is formed inside a contour of two inclined plane arches which are supported by massive counterforts at lower ends. In the present paper the advantages of a hypar-network encircled by a spatial contour beam with an elliptical layout and without any external horizontal supports have been presented. Both the discrete and continuous calculation methods [2] can be used for the analysis of the stress-strain state of those networks.

An orthogonal hypar-network consists of concave carrying and convex stretching cables and may be described as a translatory surface:

In case of vertical loading, the condition of equilibrium may be written in form:

(2) Using also equations of deformation compatibility and Galyorkin [3] procedure, we obtain system of equations for relative deflections of the network and for the cable forces. An approximate analysis of a hypar-network brings us to a cubic equation for determination of the network's relative deflection:

In discrete analysis, generally a system of vector equations is to be solved [4,5]. In case of orthogonal cable network structures, the condition of equilibrium is to be formed for every node:

and equations of deformations compatibility for every cable:

For contour beam we can use any computational method, such as the finite element method, which give us deformations, depending of cable forces and . Solving the system of equations give us all node deformations, cable forces and internal forces in contour beam. Using this method we get more possibilities to use different load combinations, different contour beams and cable networks, but simultaneously we obtain a large non-linear equations system that is difficult to solve.

For the numerical example, a hypar-network with main parameters m, m, m and an analogical network surrounded by two inclined arches were chosen for detailed analysis [5]. Comparison of the behaviour of cable networks with different contour beams are presented in the paper.

1

H.A. Buchholdt, "An Introduction to Cable Roof Structures", Thomas Telford, London, 1999

2

I. Tärno, "Effects of contour ellipticity upon structural behaviour of hyparform suspended roofs", Publ. of Royal Institute of Technology, Stockholm, 1998.

3

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

4

V. Kulbach, "Statical analysis of girder- or cable-stiffened suspended structures", Proc. Estonian Acad. Sci., Eng., 1, 2-19, 1995.

5

V. Kulbach, J. Idnurm, I. Talvik, "Analysis of saddle-shaped cable networks with different contour structures", Proc. Estonian Acad. Sci., Eng., 2, 101-114, 2002

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