Keywords: cable truss, transformation analytical model, creep of cable, yielding support,.

One of possible alternatives of simulation-based time dependent reliability assessment of double-chord cable structure, the Monte Carlo method, is applied in this paper. The influence of an excessive deflection of cable double-chords structure (caused by creep and rheologic changes) on its serviceability in required time is investigated [1]. Attention is turned to the individual main steps in the assessment procedure, i.e. to the definition and derivation of the transformation analytical model suitable for the Monte Carlo technique application, definition of the basic random variables and their statistic functions (four basic random variables, structural geometry, modulus of elasticity of the cables, pre-stressing forces of a bottom and top cable and loading are taken into account), determination of the response of the structure to the loading and affects, and to the definition of the limiting values considering serviceability of the structure.

The available literature on the behaviour and analytical transformation models of the cable double-chords structures is not so extensive [2], and mostly concerned with the engineering theory of flat cables with relatively low sag. In its linearized form this approximate theory provides explicit consistent methods for finding static response of perfectly flexible and elastic, hinge-suspended cable truss to applied loads. However, only a little attention is paid to the rheological analysis of cable truss suspended on the viscoelastic yielding supports. That is why the authors focuse on these points, and elaborating them they start with the works of H. Max Irvine [2] which has been further complemented.

Most of the recent methods of analysis of cable structures are based on the discretisation of the equilibrium equations and solving the resulting nonlinear algebraic equations by numerical methods [3,4]. With respect to the fact, that number of simulations (separate steps which differs from each other by applying random input variables) in dependence upon solved problem of structural reliability varies from a ten thousands to millions, the use of FEM in connection with solved problem of cable truss is at present too cumbersome. Proposed analytical model has in the comparison with the numerical model specific advantages.

The substance of a probabilistic structural simulation-based time dependent reliability assessment method is explained and the strategy of its application is outlined using serviceability assessment of the prestressed double-chord biconcave cable structure with elastic yielding support and rheological properties as an example. Special attention is given to the definition, development and description of the transformation analytical model serving for determining the response - horizontal components of cable forces and deflection of the structure to the several types of loading, considering effects of creep strain increments of cables and elastic yielding supports. The structural response to the loading and rheologic affects is obtained using the system of two linearized cable equations in the form of simple expressions for determining of the additional horizontal components of cable tension to applied load at the investigated time . From a linearized solution of a vertical equilibrium equation of a loaded cable truss the additional vertical deflection is determined. The structural response to the loading is compared using two different transformation models. First, the response is calculated using an obtained (developed) analytical model, next the response is calculated using FEM. Both results are of very good agreement. Considering the simulation-based time dependent reliability assessment concept, based on the Monte Carlo method, the analytical model seems to be in this particular case more convenient and practical compared to FEM model. The applied concept allows for determining the resulting probability of reliability considering interaction of several different random variables affecting the reliability (in the our case serviceability of cable structure), such as the effect of erection geometrical imperfections, physical and initial pretension imperfections and variable loading. This concept leads to a good understanding of the significance of individual random variables affecting the resulting probability of reliability. The serviceability of structure is obtained by comparing the calculated probability of reliability and the design probability contained in specifications. The designer is taking part on the calculation of the reliability. His/her involvement is not limited to interpretation of factors and equations contained in the specifications, as it is the case in the design according to the current reliability assessment method based on Partial Safety Factors.

1

Kmet,S., Holickova,L., "Creep of High Strength Steel Cables" Acta Mechanica Slovaca, Vol. 4, No. 3, 47-56, 2000.

2

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

3

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

4

Kmet,S., Tomko,M., "Time-dependent Analysis of the Suspended Cable Structures", Acta Mechanica Slovaca, Vol. 6, No. 3, 47-58, 2002.

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