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CivilComp Proceedings
ISSN 17593433 CCP: 83
PROCEEDINGS OF THE EIGHTH INTERNATIONAL CONFERENCE ON COMPUTATIONAL STRUCTURES TECHNOLOGY Edited by: B.H.V. Topping, G. Montero and R. Montenegro
Paper 94
TimeDependent NonLinear ClosedForm Solution of Cable Trusses S. Kmet and Z. Kokorudova
Faculty of Civil Engineering, Technical University of Kosice, Slovak Republic S. Kmet, Z. Kokorudova, "TimeDependent NonLinear ClosedForm Solution of Cable Trusses", in B.H.V. Topping, G. Montero, R. Montenegro, (Editors), "Proceedings of the Eighth International Conference on Computational Structures Technology", CivilComp Press, Stirlingshire, UK, Paper 94, 2006. doi:10.4203/ccp.83.94
Keywords: tension structures, cable trusses, timedependent nonlinear analysis, nonlinear closedform solution, creep of cables, geometrical nonlinearity, system of cubic cable equations.
Summary
Cable trusses offer an economical and efficient alternative for many structural
problems. Most of the recent methods of nonlinear analysis of cable trusses are
based on the discretisation of the equilibrium equations using the finite element method (FEM) and solving the
resulting nonlinear algebraic equations by numerical methods [1,2]. There have
been only a few published analytical studies on nonlinear solutions [3,4,5].
Rakowski [3] proposed a special nonlinear closedform solution for cable
trusses: a nonlinear task replaced by the linear one. For this purpose the equivalent
loading parameters were derived and used. Because of the mathematical derivation
difficulties that can arise in a nonlinear analytical solution, numerical methods are
by far the most popular. Irvine [5] investigates a static response of the cable trusses
using the linearized engineering analytical theory of the suspended cable. He
neglected all secondorder terms that appear in the differential equations of
equilibrium and in the cable equations. However, significant nonlinearities can occur
in a response of the truss with different initial geometries and material properties of
the carrying and stabilizing cables. That is why the authors focus on these problems,
and elaborating them they start with the work of Irvine [5], which has been further
complemented.
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. 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 timedependent nonlinear 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 closedform and, or numerical analytical models for timedependent analysis must be available. However, only a little attention is paid to the timedependent analyses of cable trusses with rheological properties. Therefore the purpose of this paper is to derive and present timedependent nonlinear closedform solution of a cable truss with viscolestic properties considering the creep effects of the synthetic fibre ropes. For the timedependent analysis of a cable truss, the time domain is divided into a discrete number of time steps. The creep theory is adopted for rheological analysis. In this paper the timedependent nonlinear closedform static solution of the suspended biconvex and biconcave cable trusses with unmovable, movable or elastic yielding supports subjected to various vertical distributed loads is presented. Cable trusses with rheological properties are considered, when the ropes made from the high strength synthetic fibres are used. Irvine's linearized forms of the deflection and the cable equations are modified because the effects of the nonlinear truss behaviour needed to be incorporated in them. The concrete forms of the system of two timedependent nonlinear cubic cable equations are derived and presented. From a solution of a nonlinear vertical equilibrium equation for a loaded cable truss, the additional vertical deflection is determined. Transformation analytical model serves for determining the timedependent response, i.e. horizontal components of cable forces and deflection of the geometrically nonlinear truss due to the applied loading, considering effects of elastic deformations, creep strain increments, temperature changes and elastic supports. Verification of results (as the deflection of symmetric prestressed cable trusses has been compared with the nonlinear FEM results) and illustrative examples are performed. The cable used in these examples is parallel lay aramid rope constructed from the basic 30 000 N Type G Parafil rope. The creep tests of these ropes were carried out by Guimarães and Burgoyne [6] and expressions for prediction of longterm creep were obtained. Finally, it is, perhaps, necessary to mention that, an area, included improvement of theoretical approaches (which unlike of the previous solutions, include geometrical nonlinearity and creep of cables) for predicting the timedependent behaviour of prestressed cable trusses constructed of synthetic fibres, can be considered as distinct in this work. References
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