Keywords: suspended cable, closed-form model, discrete numerical model, FEM, synthetic fibre rope, creep of cable, random variables, reliability, serviceability, Monte Carlo method, simulation-based time-dependent reliability assessment.

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 nonlinear viscoelastic properties [1]. To predict the structural response and assess the structural reliability and serviceability of tension structures with suspended fibre or wire cables during their entire service life, adequate closed-form and numerical analytical models for time-dependent analysis and adequate methods for estimating the probability of failure must be available.

Various works have been published concerning closed-form and numerical methods for analysis of suspended cable structures considering geometrical and material nonlinearities [2,3,4]. These methods are restricted to the cases where only cables without rheological properties are analysed. In this paper, the solutions are proposed also for closed-form and numerical analysis of nonlinear suspended cables with viscolestic properties considering creep of the synthetic fibre ropes.

In this paper the nonlinear behaviour of suspended cable with rheological properties subjected to static loads is examined, taking into consideration the nonlinear effects of creep strain increments. The nonlinear creep theory is adopted for rheological analysis. Irvine's convenient form of the cable equation [2] is modified because the effects of a creep strain increments need to be incorporated to the cable equation. All the geometrical and force quantities of a suspended cable, geometrical-deformational equations considering large deflections, physical and constitutive creep equations as well as all the cable and deflection equations are expressed as the time and stress functions respecting nonlinear creep.

For the time-dependent discrete analysis of the suspended cable, a finite element method based on the displacement formulation is used, in which the resulting equilibrium equations are nonlinear. Several incremental and iterative solution strategies have been implemented to solve the geometrically and physically non-linear behaviour problem of suspended cable. A Total Lagrangian formulation is adopted to take into account large displacements of cable structure and a multi-linear stress-strain relationship is used for a cable material modelling. Modelling of the rheological cable properties is based on the nonlinear creep theory and experimentally obtained creep curves of tested cables under single and variable stress history. The resultin explicit time-dependent constitutive equations are able to describe creep strain increments of the cable under various stress levels. The time-dependent tangential stiffness matrix is defined as the sum of elastic linear stiffness matrix , geometrical stiffness matrix and the initial stress matrix .

The available methods for estimating the probability of failure can be roughly classified into two groups, which can be marked as gradient-based (FORM and SORM approaches) and simulation-based methods (Monte Carlo method) [5]. Simulation-based methods hinge upon the creation of a set of response samples on which the probability of failure can be estimated at time as where is the number of samples lying in the failure domain at time . The last from the described methods will be applied in the paper.

The intention of the paper is to illustrate the ability of the probabilistic time-dependent reliability assessment procedure applied to non-linear suspended cable structure with rheological properties, when a rope made from the high strength synthetic fibres is used in order to demonstrate the new qualitatively completely different concept. Attention is turned to the individual main steps in the assessment procedure, i.e. to the selection of an appropriate method of structural analysis and to derivation of an appropriate closed-form and discrete analytical models, analysis of random variables representing individual actions, evaluation of the structural response with respect to a history of the time-dependent action effects and to the definition of the limiting values considering serviceability of cable structure.

1

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

2

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

3

Buchholdt, H.A. "An introduction to cable roof structures", 2nd edition, Published by Thomas Telford Ltd., London, 1999.

4

Kwan, A.S.K., "Analysis of geometrically nonlinear cable structures", in Topping B.H.V., Editor, Progress in Civil and Structural Engineering Computing, Saxe-Coburg Publications, Stirling, UK, 149-170, 2003. doi:10.4203/csets.10.6

5

Melchers, R.E., "Structural reliability: Analysis and prediction", 2nd edition, Chichester: John Wiley & Sons, 1999.

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