• Structural Engineering and Mechanics
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• v.22 no.2
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• pp.197-222
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• 2006

In this paper, the non-linear time-dependent closed-form, discrete and combined solutions for the post-elastic response of a geometrically and physically non-linear suspended cable to a uniformly distributed load considering the creep effects, are presented. The time-dependent closed-form method for the particularly straightforward determination of a vertical uniformly distributed load applied over the entire span of a cable and the accompanying deflection at time t corresponding to the elastic limit and/or to the elastic region, post-elastic and failure range of a suspended cable is described. The actual stress-strain properties of steel cables as well as creep of cables and their rheological characteristics are considered. In this solution, applying the Irvine's theory, the direct use of experimental data, such as the actual stress-strain and strain-time properties of high-strength steel cables, is implemented. The results obtained by the closed-form solution, i.e., a load corresponding to the elastic limit, post-elastic and failure range at time t, enable the direct use in the discrete non-linear time-dependent post-elastic analysis of a suspended cable. This initial value of load is necessary for the non-linear time-dependent elastic and post-elastic discrete analysis, concerning incremental and iterative solution strategies with tangent modulus concept. At each time step, the suspended cable is analyzed under the applied load and imposed deformations originated due to creep. This combined time-dependent approach, based on the closed-form solution and on the FEM, allows a prediction of the required load that occurs in the post-elastic region. The application of the described methods and derived equations is illustrated by numerical examples.

• Structural Engineering and Mechanics
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• v.18 no.5
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• pp.565-589
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• 2004

The present paper concerns the macroscopic overall description of rheologic properties for steel wire and synthetic fibre cables under variable loading actions according to non-linear creep and/or relaxation theory. The general constitutive equations of non-linear creep and/or relaxation of tension elements - cables under one-step and the variable stress or strain inputs using the product and two types of additive approximations of the kernel functions are presented in the paper. The derived non-linear constitutive equations describe a non-linear rheologic behaviour of the cables for a variable stress or strain history using the kernel functions determined only by one-step - constant creep or relaxation tests. The developed constitutive equations enable to simulate and to predict in a general way non-linear rheologic behaviour of the cables under an arbitrary loading or straining history. The derived constitutive equations can be used for the various tension structural elements with the non-linear rheologic properties under uniaxial variable stressing or straining.

• Structural Engineering and Mechanics
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• v.18 no.5
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• pp.591-607
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• 2004

The substance of the use of the derived non-linear creep constitutive equations under variable stress levels (see first part of the paper, Kmet 2004) is explained and the strategy of their application is outlined using the results of one-step creep tests of the steel spiral strand rope as an example. In order to investigate the creep strain increments of cables an experimental set-up was originally designed and a series of tests were carried out. Attention is turned to the individual main steps in the production and application procedure, i.e., to the one-step creep tests, definition of loading history, determination of the kernel functions, selection and definition of constitutive equation and to the comparison of the resulting values considering the product and the additive forms of the approximation of the kernel functions. To this purpose, the parametrical study is performed and the results are presented. The constitutive equations of non-linear creep of cable under variable stress history offer a strong tool for the real simulation of stochastic variable load history and prediction of realistic time-dependent response (current deflection and stress configuration) of structures with cable elements. By means of suitable stress combination and its gradual repeating various loads and times effects can be modelled.