Time-dependent analysis and simulation-based reliability assessment of suspended cables with rheological properties

Abstract

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 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 (four basic random variables, such as structural geometry, cable’s modulus of elasticity and creep strain increments and loading, are considered), evaluation of the structural response with respect to the interaction of the random variables considering a history of the time-dependent action effects and to the definition of the limiting values considering serviceability of cable structure. The potential of the method using direct Monte Carlo technique as one of the possible alternatives for simulation-based time-dependent reliability assessment as a powerful tool is emphasized. The influence of an excessive deflection of suspended cable (caused by creep of cable and rheologic changes) on its serviceability in required time is investigated and illustrative examples are performed.

Introduction

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 [1]. 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 numerical analytical models for time-dependent analysis and adequate methods for estimating the probability of failure must be available.

Various papers and books have been published concerning closed-form [2], [3], [4], [5] and numerical [6], [7], [8], [9], [10], [11], [12], [13], [14] methods for analysis of suspended cable structures considering geometrical and material non-linearities. Most of the recent methods of non-linear analysis of cable structures are based on the discretisation of the equilibrium equations using FEM and solving the resulting non-linear algebraic equations by numerical methods. The non-linear material model of cable structural element was proposed by Jonatowski and Birnstiel [6]. The complementary energy principle for a cable modelled as one-dimensional continuum has been presented for large deflection analysis by Cannarozzi [15]. Kanno et al. [16] derived a special method for friction or friction-less analysis of non-linear elastic cable structures based on second-order cone programming. Lefik and Schrefler [17] present an example of the use of an artificial neural network for parameter identifications of a theoretical elasto-plastic model of the behaviour of a superconducting cable under cyclic loading. Iványi and Topping [18] presented a new graph representation for cable-membrane structures modelled using both one- and two-dimensional elements. Al-Quassab and Nair [19] applied the wavelet-Galerkin method to study the free vibrations of a suspended cable.

The common approach to these investigations is to study the cable structure as a geometrically non-linear system. However, only a little attention is paid to the time-dependent analyses of suspended cable with rheological properties. Therefore the purpose of this paper is to derive and present non-linear time-dependent closed-form and discrete static solutions of a suspended cable with viscoelastic properties considering the creep effects of the synthetic fibre ropes. For the time-dependent analysis of a suspended cable, the time domain is divided into a discrete number of time steps. The creep theory is adopted for rheological analysis. In the case of closed-form analysis the Irvine’s convenient form of the cable equation [2] is modified because the effects of a creep strain need to be incorporated to the cable and deflection equation. For the time-dependent discrete non-linear analysis of the suspended cable, a finite element method based on the displacement formulation is used. A time-dependent tangential stiffness matrix of the cable element is defined. Incremental and iterative solution strategies have been implemented to solve the geometrically and physically non-linear behaviour problem.

Structural reliability theory has received considerable attention in the literature [20], [21], [22], [23]. The general principles for a probabilistic design of bearing structures were published by the Joint Committee on Structural Safety and can be found in [24].

The available methods for estimating the probability of failure P_f(t) 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). The progress in the use for bearing structures and elements reached the Monte Carlo simulation method and its modifications [25], [26], [27]. Simulation-based methods hinge upon the creation of a set of N(t) response samples on which the probability of failure can be estimated at time t as P_f(t) = N_f(t)/N(t), where N_f(t) is the number of samples lying in the failure domain at time t. 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 different concept. Attention is turned to the individual main steps in the assessment procedure, i.e. to the selection of an appropriate method of the time-dependent 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 the interaction of the random variables considering a history of the time-dependent action effects and to the definition of the limiting values considering serviceability of cable structure.

Finally, it is, perhaps, necessary mentioning that although the engineering theory of a suspended cable was well developed, despite numerous examples in the literature, no other closed-form model has as yet been proposed which can predict the creep and associated deflections in suspended cables composed of synthetic fibres. An area, included improvement of theoretical approaches (which unlike of the previous solutions, include creep) for predicting the time-dependent behaviour of suspended cable composed of synthetic fibres, can be considered as distinct in this work.