Keywords: suspended cable, closed-form model, time-dependent post-elastic analysis, post-elastic strain of cables, creep of cables, simulation-based reliability assessment, serviceability of suspended cables, Monte Carlo method.

The evaluation of the non-linear response of a suspended cable in the post-elastic region necessitates the development of accurate and computationally efficient analytical or numerical model. An important task in the post-elastic analysis of a suspended cable is a consideration of the creep strain of the cable corresponding to the stress level at the post-elastic region. Because the elastic limit is not clearly defined from the stress-strain diagram of cable, one of the important problems in the analysis and design of a suspended cable in the post-elastic (plastic) region is therefore to decide what cumulative inelastic extension due to inelastic strain and creep strain increments is reasonable for the whole suspended cable, according to its structural serviceability.

Serviceability criteria referring to deformations of a suspended high strength cable are the significant factors that influence the design in the post-elastic region. Limits to retain a suspended cable in the required behaviour interval are related to the maximum values of stresses lying in the post-elastic range for serviceability load conditions.

Only a few analytical closed-form studies on the behaviour and analysis of a suspended cable in the post-elastic region have been published. Because of the difficulties that can arise, numerical methods are by far most popular.

However, there is a lack of the non-linear post-elastic rheological analysis of a suspended cable considering creep of cables. So far, there is no analytical solution for the calculation of the deflection of a suspended cable depending on stress and time at the post-elastic conditions. That is why the authors focus on these problems, and when elaborating them start with the work of Irvine [1], which has been further complemented. A development of the analytical methods for a non-linear solution of cable structures is still an active area of the research, particularly for teh use of the probabilistic simulation-based reliability assessment of cable structures.

At present, stochastic approaches to the reliability assessment of structures are developed [2]. The general principles for a probabilistic design of bearing structures were published by the Joint Committee on Structural Safety [3].

The purpose of this paper is to present the non-linear time-dependent closed-form solution for the post-elastic response of a geometrically and physically non-linear suspended cable to uniformly distributed load considering the creep effects. For the time-dependent analysis of a suspended cable, the time domain is divided into a discrete number of time steps. At each time step, the cable is analysed under the corresponding stress-strain properties and the imposed deformations due to the applied load, due to creep, as well as due to geometric and material characteristics. In this paper, the time-dependent closed-form method for the particularly straightforward determination of the uniformly distributed load and accompanying deflection at time corresponding to the post-elastic region of a suspended cable considering the creep effects, is presented. In this solution, applying the Irvine theory, the direct use of experimental data, such as the actual stress-strain and strain-time properties of high-strength steel cables, is implemented. A suspended cable is analysed at the initial time and at time , when creep strain under the corresponding stress level is defined through the experimentally obtained constitutive equations [4].

One option for the fully probabilistic simulation-based reliability assessment concept, the Monte Carlo technique is described and applied in this paper. Considering the variation of post-elastic plastic strain and the variation in the geometry of a suspended cable reflecting the creep strain increments of the cable the time-dependent serviceability reliability assessment is presented. The application of the derived time-dependent analytical model and the probabilistic simulation-based reliability assessment approach is illustrated by numerical examples.

Many national and international specifications for the design of structures with steel cable components are based on the Partial Safety Factor Method. Factors of safety vary, but the working elastic stresses are usually used for a rope or strand in cable structures. In these cases the suspended cable will never enter the post-elastic region, nor should it. Therefore, design of the suspended cables in the elastic region is rather conservative. It is believed, that the presented solutions will lead to an improved analysis of the time-dependent response of suspended cables with rheological properties in the post-elastic region.

1

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

2

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

3

Vrouwenvelder, T., Faber, M., "Probabilistic model code Part 1 - Basis of design", Joint Commitee on Structural Safety, http://www.jcss.eth.ch, 2001.

4

Kmet, S., "Non-linear rheology of tension structural element under single and variable loading history Part I: Theoretical derivations", Structural Engineering and Mechanics An International Journal, 18(5), 565-589, 2004.

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