• Journal of Korean Society of Steel Construction
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• v.15 no.2
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• pp.219-229
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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.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.29 no.8 s.239
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• pp.1123-1131
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• 2005

In this paper, a formulation for a spatial sliding joint, which a general multibody can move along a very flexible cable, is derived using absolute nodal coordinates and non-generalized coordinate. The large deformable motion of a spatial cable is presented using absolute nodal coordinate formulation, which is based on the finite element procedures and the general continuum mechanics theory to represent the elastic forces. And the non-generalized coordinate, which is neither related to the inertia forces nor external forces, is used to describe an arbitrary position along the centerline of a very flexible cable. In the constraint equation for the sliding joint, since three constraint equations are imposed and one non-generalized coordinate is introduced, one constraint equation is systematically eliminated. Therefore, there are two independent Lagrange multipliers in the final system equations of motion associated with the sliding joint. The development of this sliding joint is important to analyze many mechanical systems such as pulley systems and pantograph/catenary systems for high speed-trains.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.1 no.1
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• pp.93-101
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• 1989

A geometrically nonlinear cable finite element is presented to use in the static or dynamic modeling of offshore and onshore structures such as guyed tower, tension leg platform or mooring buoy, submarine cable, cable-stayed bridge, suspension bridge, cable roof and so on. The cable finite element is derived directly from the compatibility equations and flexibility matrix of elastic catenary cable theory for the arbitary plane loading and geome try. A general and virsatile computer program has been developed to perform the analyses of cable member itself or cable guyed or suspened structures, in which Newmark-$\beta$ method is used to obtain a time domain solution and Newton-Raphson iteration method is used to solve the nonlinear system of compatibility equations of cable and algebraic static or dynamic equations at each time step. The results from the static and dynamic analysis of a cable member by the computer program are summarized and presented.

• International Journal of Precision Engineering and Manufacturing
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• v.5 no.4
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• pp.50-60
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• 2004

A very flexible beam can be used to model various types of continuous mechanical parts such as cables and wires. In this paper, the dynamic properties of a very flexible beam, included in a multibody system, are analyzed using absolute nodal coordinates formulation, which is based on finite element procedures, and the general continuum mechanics theory to represent the elastic forces. In order to consider the dynamic interaction between a continuous large deformable beam and a rigid multibody system, a combined system equations of motion is derived by adopting absolute nodal coordinates and rigid body coordinates. Using the derived system equation, a computation method for the dynamic stress during flexible multibody simulation is presented based on Euler-Bernoulli beam theory, and its reliability is verified by a commercial program NASTRAN. This method is significant in that the structural and multibody dynamics models can be unified into one numerical system. In addition, to analyze a multibody system including a very flexible beam, formulations for the sliding joint between a very deformable beam and a rigid body are derived using a non-generalized coordinate, which has no inertia or forces associated with it. In particular, a very flexible catenary cable on which a multibody system moves along its length is presented as a numerical example.

• Journal of Korean Society of Steel Construction
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• v.14 no.4
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• pp.539-547
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• 2002

The study proposed the initial equilibrium state analysis method that considers axial deformation, in order to accurately determine the initial shape of a cable-stayed bridge. Sepecifically, the proposed method adopted the successive iteration method. In order to evaluate appropriate initial cable force introduced in the initial equilibrium state analysis, parametric studies were performed and a useful linear analysis method proposed. The geometrically nonlinear static behaviors of cable-stayed bridges were considered, using three-dimensional frame element and elastic catenary cable element. The usefulness and applicability of the analytic method proposed in this study were demonstrated using numerical examples, including a real cable-stayed bridge. The algorithm, is applicable in cases wherein axial deformation is not adopted in the fabrication camber, or final cable force is adjusted to eliminate construction and fabrication errors occurring during construction.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.25 no.1
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• pp.101-108
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• 2012

Initial shape analysis for cable-stayed bridges should be able to find optimizated initial cable forces and unstrained length that minimize deflection and bending moments of the deck and pylon. Comparison study of an improved initial force method and TCUD method for determination of initial cable forces in cable-stayed bridges is presented in this paper. For this purpose, an elastic catenary cable element and a nonlinear frame element are firstly described. And concepts and algorithm of two analysis methods are then presented. Finally to demonstrate the validity and the accuracy of two methods, numerical examples for initial state problems of cable-stayed bridges are given and compared based on these methods.

• Journal of Korean Society of Steel Construction
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• v.12 no.1 s.44
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• pp.103-110
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• 2000

The suspension bridge is divided by an earth anchor and a self-anchor type according to the anchorage type. This study is to evaluate the dynamic effect of moving vehicles to suspension bridges. The results were presented with the dynamic magnification factor (DMF) by the effect of vehicle speed and weight according to the anchorage type. The vehicle model has 6 degrees of freedom to idealize nonlinear multi-leaf suspensions and elastic tires of tractor-trailer. The bridge was modelled with the 3-dimensional frame element and 3-dimensional elastic catenary cable element. The condition of deck surface is considered using the actual road spectra.

• Journal of the Earthquake Engineering Society of Korea
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• v.9 no.2 s.42
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• pp.47-58
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• 2005

Dynamic response analysis in time dimain is conducted for floating bridges with discrete pontoons subject to spatial variation of ground motions. The Spatial variation of ground motions is considered with the coherency function model which represents wave passage, incoherence and local site effects. The superstructure of the bridge is represented by space frame and elastic catenary cable elements, the abutment us modelde with the spring element of FHWA guideline for considering soil structure interaction and the concept of retardation function is utilized to consider the frequency dependency of the hydrodynamic coefficients which are obtainde by boundary element method. multiple support excitations considering the spatial variation. The noticeable amplification of the response can be shown when the spatial variation of ground motions is incorporated in the anallysis of floating bridges.