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Civil-Comp Proceedings
ISSN 1759-3433 CCP: 77
PROCEEDINGS OF THE NINTH INTERNATIONAL CONFERENCE ON CIVIL AND STRUCTURAL ENGINEERING COMPUTING Edited by: B.H.V. Topping
Paper 118
Simulation-Based Reliability Assessment of Tension Structures S. Kmet+, M. Tomko* and J. Brda*
+Department of Steel and Timber Structures
Full Bibliographic Reference for this paper
S. Kmet, M. Tomko, J. Brda, "Simulation-Based Reliability Assessment of Tension Structures", in B.H.V. Topping, (Editor), "Proceedings of the Ninth International Conference on Civil and Structural Engineering Computing", Civil-Comp Press, Stirlingshire, UK, Paper 118, 2003. doi:10.4203/ccp.77.118
Keywords: cable truss, transformation analytical model, creep of cable, yielding support,.
Summary
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 References
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