• Journal of the Computational Structural Engineering Institute of Korea
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• v.20 no.1
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• pp.1-7
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• 2007

This study introduces an elastic parabolic cable element for initial shaping analysis of cable-stayed bridges. First, an elastic catenary cable theory is shortly summarized by deriving the compatibility condition and the tangent stiffness matrices of the elastic catenary cable element. Next, the force-deformation relations and the tangent stiffness matrices of the elastic parabolic cable elements are derived from the assumption that sag configuration under self-weights is small. In addition the equivalent cable tension is defined in the chord-wise direction. Finally, to confirm the accuracy of this element, initial shaping analysis of cable-stayed bridges under dead loads is executed using TCUD in which stay cables are modeled by an elastic parabolic cable and an elastic catenary cable element, respectively. Resultantly it turns that unstrained lengths of stay cables, the equivalent cable tensions, and maximum tensions by the parabolic cable element are nearly the same as those by the catenary cable elements.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.31 no.5A
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• pp.361-367
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• 2011

This study introduces an elastic parabolic cable element for initial shaping analysis of cable-supported structures. First, an elastic catenary cable theory is shortly summarized by deriving the compatibility condition and the tangent stiffness matrices of the elastic catenary cable element. Next, the force-deformation relations and the tangent stiffness matrices of the elastic parabolic cable elements are derived and discussed under the assumption that sag configuration under self-weights is small. In addition the equivalent cable tension is defined in the chord-wise direction. Finally, to demonstrate the accuracy of the elastic parabolic cable element, nonlinear relationships of nominal cable tension-chord length and nominal cable tension-tangential stiffness for a single element are presented and compared with results using an elastic catenary cable theory as the slope is varied.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2000.10a
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• pp.331-338
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• 2000

In this paper, a non-linear finite element formulation for the spatial cable-net structures is simulated and using this formulation, the characteristics of structural behaviors for the elastic catenary cable are examined In the simulating procedure for the elastic catenary cable, nodal forces and tangential stiffness matrices are derived using catenary parameters of the exact solutions by a governing differential equation of catenary cable, cable self-weights and unstressed cable length. Dynamic Relaxation Method that considers kinetic damping is used for the structure analysis and Newton Raphson Method is used to verify the accuracy of solutions. In the analysis of two dimensional cable, the results obtain from the elastic catenary elements are shown more accurate than does of truss elements and in the case of spatial cable-net structures, Dynamic Relaxation Method is more stable to be converged than Newton Raphson Method.

• Computational Structural Engineering
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• v.11 no.1
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• pp.179-190
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• 1998

A geometrically nonlinear finite element formulation of spatial cable networks is presented using two cable elements. Firstly, derivation procedures of tangent stiffness and mass matrices for the space truss element and the elastic catenary cable element are summarized. The load incremental method based on Newton-Raphson iteration method and the dynamic relaxation method are presented in order to determine the initial static state of cable nets subjected to self-weights and support motions. Furthermore, static non-linear analysis of cable structures under additional live loads are performed based on the initial configuration. Challenging example problems are presented and discussed in order to demonstrate the feasibility of the present finite element method and investigate static nonlinear behaviors of cable nets.

• Journal of the Earthquake Engineering Society of Korea
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• v.2 no.2
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• pp.95-104
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• 1998

The dynamic behavior of the marine cable is essentially nonlinear and dominated by geometric nonlinearity. Furthermore, fluid drag force makes the problem more complex and difficult. Therefore, it has certain limitations to obtain the dynamic behavior of the marine cable by analytical method. The purpose of this paper is to apply the elastic catenary cable element to the problem of under water cable including the hydrodynamic effects of fluids. The static and dynamic formulations for the three-dimensional elastic catenary coble under water effects are derived and the finite element analysis procedures are presented. In the analysis, the hydrodynamic forces are modeled by modified Morison equation. A comparison of the results obtained using present method with previously published results showed the validity of present method. The dynamic behavior of the marine cable subjected to current is investigated using present method and it can be illustrated that the dynamic behavior of the marine cable subjected to current varies with the incident angle of the current and inclined angle of the cable.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2005.04a
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• pp.481-488
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• 2005

This study presents a elastic parabolic cable element for initial shaping analysis of cable structures. First, the compatibility condition and the tangent stiffness matrices of the elastic catenary cable element are shortly summarized. Next the force-deformation relations and the tangent stiffness matrices of the elastic parabolic cable elements are derived from the assumption that sag configuration under self-weights is small. To confirm the accuracy of this element, initial shaping analysis of cable-stayed bridges under dead loads is executed. Finally, the accuracy and the validity of the analysis-results are compared and analyzed through numerical examples.

• Structural Engineering and Mechanics
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• v.62 no.1
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• pp.85-95
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• 2017

This paper presents an explicit analytical iteration method for form-finding analysis of suspension bridges. By extending the conventional analytical form-finding method predicated on the elastic catenary theory, two nonlinear governing equations are derived for calculating the accurate unstrained lengths of the entire cable systems both the main cable and the hangers. And for the gradient-based iteration method, the derivation of explicit calculation for the Jacobian matrix while solving the nonlinear governing equation enhances the computational efficiency. The results from sensitivity analysis show well performance of the explicit Jacobian matrix compared with the traditional finite difference method. According to two numerical examples of long span suspension bridges studied, the proposed method is also compared with those reported approaches or the fundamental criterions in suspension bridge structural analysis, which eventually confirms the accuracy and efficiency of the proposed approach.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 1997.10a
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• pp.134-141
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• 1997

A geometrically non-linear finite element formulation of spatial cable networks is presented using three cable elements. Firstly, derivation procedures of tangent stiffness and mass matrices for the space truss element and the elastic catenary cable element, and the isoparametric cable element are summarized. The load incremental method based on Newton-Raphson iteration method and the dynamic relaxation method are presented in order to determine the initial static state of cable nets subjected to self-weights and support motions. Furthermore, static non-linear analysis of cable structures under additional live loads are performed based on the initial configuration. Challenging example problems are presented and discussed in order to demonstrate the feasibility of the present finite element method and investigate static non-linear behaviors of cable nets.

• Journal of Ocean Engineering and Technology
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• v.18 no.6 s.61
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• pp.51-57
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• 2004

In this study, the improved three-dimensional analysis model designed for a more accurate analysis of marine cable-supported structures, is presented. In this improved analysis model, the beam elements, of which the stability function is derived using Taylor's series expansions, are used to model space frame structures, and the truss elements. The equivalent elastic modulus of the truss elements is evaluated on the assumption that the deflection curve of a cable has a catenary function. By using the proposed three-dimensional analysis model, nonlinear static analysis is carried out for some cable-supported structures. The results are compared with previous studies and show good agreement with their findings.

• Journal of Korean Society of Steel Construction
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• v.15 no.2
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• pp.175-185
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• 2003

The extended tangent stiffness matrices and force-deformation relations of the elastic catenary element were initially derived through the addition of the unstrained length of cables to unknown nodal displacements. A beam-column element was then introduced to model the deck and pylon of cable-stayed bridges. The conventional geometric nonlinear analysis, initial force method, and TCUD method were summarized, with an effective method combining two methods presented to determine the initial shapes of cable-stayed bridges with dead loads. In this combined method, TCUD method was applied to eliminate vertical and horizontal displacements at cable-supported points of decks and on top of pylons, respectively. The initial force method was also adopted to eliminate horizontal and vertical displacements of decks and pylons, Finally, the accuracy and validity of the proposed combined method were demonstrated through numerical examples.