Keywords: tension structures, cable trusses, time-dependent non-linear analysis, non-linear closed-form solution, creep of cables, geometrical non-linearity, system of cubic cable equations.

Cable trusses offer an economical and efficient alternative for many structural problems. Most of the recent methods of non-linear analysis of cable trusses are based on the discretisation of the equilibrium equations using the finite element method (FEM) and solving the resulting non-linear algebraic equations by numerical methods [1,2]. There have been only a few published analytical studies on non-linear solutions [3,4,5]. Rakowski [3] proposed a special non-linear closed-form solution for cable trusses: a non-linear task replaced by the linear one. For this purpose the equivalent loading parameters were derived and used. Because of the mathematical derivation difficulties that can arise in a non-linear analytical solution, numerical methods are by far the most popular. Irvine [5] investigates a static response of the cable trusses using the linearized engineering analytical theory of the suspended cable. He neglected all second-order terms that appear in the differential equations of equilibrium and in the cable equations. However, significant nonlinearities can occur in a response of the truss with different initial geometries and material properties of the carrying and stabilizing cables. That is why the authors focus on these problems, and elaborating them they start with the work of Irvine [5], which has been further complemented.

Ropes made from high strength synthetic fibres may soon be preferred for use in cable suspension bridges and roofs. They have many advantages over traditional materials and could be used to replace high tensile steel cables in many application areas of tension structures, particularly where low weight and corrosion resistance are of important concern. It is clear that in contrast to the classical tension steel rods and bars, which operate in the linear elastic range, steel cables and mainly fibre ropes have time-dependent non-linear viscoelastic properties. To predict the structural response and assess the structural reliability and serviceability of tension structures with suspended fibre cables during their entire service life, adequate closed-form and, or numerical analytical models for time-dependent analysis must be available. However, only a little attention is paid to the time-dependent analyses of cable trusses with rheological properties. Therefore the purpose of this paper is to derive and present time-dependent non-linear closed-form solution of a cable truss with viscolestic properties considering the creep effects of the synthetic fibre ropes. For the time-dependent analysis of a cable truss, the time domain is divided into a discrete number of time steps. The creep theory is adopted for rheological analysis.

In this paper the time-dependent non-linear closed-form static solution of the suspended biconvex and biconcave cable trusses with unmovable, movable or elastic yielding supports subjected to various vertical distributed loads is presented. Cable trusses with rheological properties are considered, when the ropes made from the high strength synthetic fibres are used. Irvine's linearized forms of the deflection and the cable equations are modified because the effects of the non-linear truss behaviour needed to be incorporated in them. The concrete forms of the system of two time-dependent non-linear cubic cable equations are derived and presented. From a solution of a non-linear vertical equilibrium equation for a loaded cable truss, the additional vertical deflection is determined. Transformation analytical model serves for determining the time-dependent response, i.e. horizontal components of cable forces and deflection of the geometrically non-linear truss due to the applied loading, considering effects of elastic deformations, creep strain increments, temperature changes and elastic supports. Verification of results (as the deflection of symmetric prestressed cable trusses has been compared with the non-linear FEM results) and illustrative examples are performed. The cable used in these examples is parallel lay aramid rope constructed from the basic 30 000 N Type G Parafil rope. The creep tests of these ropes were carried out by Guimarães and Burgoyne [6] and expressions for prediction of long-term creep were obtained. Finally, it is, perhaps, necessary to mention that, an area, included improvement of theoretical approaches (which unlike of the previous solutions, include geometrical nonlinearity and creep of cables) for predicting the time-dependent behaviour of prestressed cable trusses constructed of synthetic fibres, can be considered as distinct in this work.

1

A. Kassimali, H. Parsi-Feraidoonian, "Strength of cable trusses under combined loads". Journal of Structural Engineering, 113 (5), 907-924, 1987. doi:10.1061/(ASCE)0733-9445(1987)113:5(907)

2

H.A. Buchholdt, "Introduction to cable roof structures". 2nd Ed., Thomas Telford Ltd., London, 1999.

3

J. Rakowski, "Contribution on nonlinear solution of cable systems". Bauingenieur, 58 (2), 57-65, 1983, (in German).

4

S. Kmet, Z. Kokorudova, "Nonlinear analytical solution for cable truss". Journal of Engineering Mechanics, ASCE, 132 (1), 119-123, 2006. doi:10.1061/(ASCE)0733-9399(2006)132:1(119)

5

H.M. Irvine, "Cable Structures". The MIT Press, Cambridge, Mass. 1981.

6

G.B. Guimarães, C.J. Burgoyne, "Creep behaviour of a parallel-lay aramid rope". Journal of Materials Science, 27:2473-2489, 1992. doi:10.1007/BF01105061

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