• Structural Engineering and Mechanics
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• 제38권2호
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• pp.157-169
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• 2011

In this paper the time-dependent closed-form static solution of the suspended pre-stressed biconcave and biconvex cable trusses with unmovable, movable and elastic or viscoelastic yielding supports subjected to various types of vertical load is presented. Irvine's forms of the deflections and the cable equations are modified because the effects of the rheological behaviour needed to be incorporated in them. The concrete cable equations in the form of the explicit relations are derived and presented. From a solution of a vertical equilibrium equation for a loaded cable truss with rheological properties, the additional vertical deflection as a time-function is determined. The time-dependent closed-form model serves to determine the time-dependent response, i.e., horizontal components of cable forces and deflection of the cable truss due to applied loading at the investigated time considering effects of elastic deformations, creep strains, temperature changes and elastic supports. Results obtained by the present closed-form solution are compared with those obtained by FEM. The derived time-dependent closed-form computational model is used for a time-dependent simulation-based reliability assessment of cable trusses as is described in the second part of this paper.

• 대한토목학회논문집
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• 제34권1호
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• pp.49-60
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• 2014

해협횡단 교량으로서 적용사례가 증가될 것으로 예상되는 다경간 현수교에 대한 거동을 간략하면서도 정확히 해석하기 위하여, 현수교에 대한 고유의 해석이론인 처짐이론 해석방법을 사용할 수 있다. 본 연구에서는 처짐이론 방법을 이용한 4경간 현수교의 구조해석을 수행하였다. 거더를 축인장력을 받는 단순보로 고려하였고, 연직방향 하중 및 지점부 모멘트에 의한 단순보의 수직변위를 산정하여, 이 변위가 케이블의 적합방정식을 만족할 때까지 반복해석을 수행하였다. 유한요소해석의 결과와 비교하여 모든 주탑의 휨강성을 고려하는 처짐이론 해석의 결과를 검증하고, 주케이블과 탑정부 간의 구속조건 변화에 따른 다양한 케이블 적합방정식을 이용하여, 4경간 현수교에서의 주탑 휨강성의 중요성을 확인하였다. 또한 중앙주탑 휨강성의 변화에 따른 간단한 변수해석을 수행하여 그에 따른 거동을 파악하였다.

• Structural Engineering and Mechanics
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• 제22권2호
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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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• 제18권5호
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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.