• Structural Engineering and Mechanics
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• v.88 no.1
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• pp.53-65
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• 2023

With the gradual implementation of long-span suspension bridges into high-speed railway operations, the main beam's bending stiffness contribution to the live load response permanently grows. Since another critical control parameter of railway suspension bridges is the beam-end rotation angle, it should not be ignored by treating the main beam deflection as the only deformation response. To this end, the current study refines the existing method of the main cable shape and simply supported beam bending moment analogy. The bending stiffness of the main beam is considered, and the main beam's analytical expressions of deflection and rotation angle in the whole span are obtained using the cable-beam deformation coordination relationship. Taking a railway suspension bridge as an example, the effectiveness and accuracy of the proposed analytical method are verified by the finite element method (FEM). Comparison of the results by FEM and the analytical method ignoring the main beam stiffness revealed that the bending stiffness of the main beam strongly contributed to the live load response. Under the same live load, as the main beam stiffness increases, the overall deformation of the structure decreases, and the reduction is particularly noticeable at locations with original larger deformations. When the main beam stiffness is increased to a certain extent, the stiffening effect is no longer pronounced.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.24 no.6
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• pp.645-654
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• 2011

Temporal supports is proposed for the large block construction of a double-deck truss girder of a bundle type cable-stayed bridge. The design force of the temporal bents cannot be evaluated by a conventional design procedure with gust factored static wind loads. The uplift forces in BS5400 also can not estimate the design forces of the temporal bents properly for the turbulent wind loads. A frequency-domain buffeting analysis is performed to evaluate the design forces of the temporal bents considering the interactions between the girder and temporal supports. Two cases of modeling are compared to estimate the stiffness contribution of temporal supports in determining design forces, i.e., an analysis model including temporal bents in the structural analysis modeling and an analysis model with fixed supports at the bent tops neglecting the stiffness of temporal bents. The consideration of bent stiffness usually generates smaller reaction forces than rigid support modeling. Consequently, the effectiveness and usefulness of the buffeting analysis procedure with full modeling of temporal supports are demonstrated for the design of a temporal bents of the construction of a bundle type cable-stayed bridge.

• Smart Structures and Systems
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• v.23 no.6
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• pp.653-667
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• 2019

Using cross-ties to connect cables together when forming a cable network is regarded as an efficient method of mitigating cable vibrations. Cross-ties have been extended and fixed on bridge decks or towers in some engineering applications. However, the dynamics of this kind of system need to be further studied, and the effects of extending cross-links to bridge decks/towers on the modal response of the system should be assessed in detail. In this paper, a system of two cables connected by an inter-supported cross-link with another lower cross-link extended to the ground is proposed and analyzed. The characteristic equation of the system is derived, and some limiting solutions in closed form of the system are derived. Roots of cable system with special configurations are also discussed, attention being given to the case when the two cables are identical. A predictable mode behavior was found when the stiffness of inter-connection cross-link and the cross-link extended to the ground were the same. The vector of mode energy distribution and the degree of mode localization index are proposed so as to distinguish global and local modes. The change of mode behaviors is further discussed in the case when the two cables are not identical. Effects of cross-link stiffness, cross-link location, mass-tension ratio, cable length ratio and frequency ratio on $1^{st}$ mode frequency and mode shape are addressed.

• Structural Engineering and Mechanics
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• v.87 no.3
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• pp.255-272
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• 2023

Spatial cable systems can provide more transverse stiffness and torsional stiffness without sacrificing the vertical bearing capacity compared with conventional vertical cable systems, which is quite lucrative for long-span earth-anchored suspension bridges' development. Higher economy highlights the importance of refined form-finding analysis. Meanwhile, the internal connection between the lateral and vertical sags has not yet been specified. Given this, an analytic algorithm of form-finding for the earth-anchored suspension bridge with spatial cables is proposed in this paper. Through the geometric compatibility condition and mechanical equilibrium condition, the expressions for cable segment, the recurrence relationship between catenary parameters and control equations of spatial cable are established. Additionally, the nonlinear general reduced gradient method is introduced into fast and high-precision numerical analysis. Furthermore, the analytic expression of the lateral and vertical sags is deduced and discussed. This is very significant for the space design above the bridge deck and the optimization of the sag-to-span ratio in the preliminary design stage of the bridge. Finally, the proposed method is verified with the aid of two examples, one being an operational self-anchored suspension bridge (with spatial cables and a 260 m main span), and the other being an earth-anchored suspension bridge under design (with spatial cables and a 500 m main span). The necessity of an iterative calculation for hanger tensions on earth-anchored suspension bridges is confirmed. It is further concluded that the main cable and their connected hangers are in very close inclined planes.

• Structural Engineering and Mechanics
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• v.74 no.5
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• pp.635-655
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• 2020

The sag effect of long stay cables is one of the key factors restricting further increase in the span of cable-stayed bridges. Based on the formerly proposed concept of long stay cables lifted by an auxiliary suspension cable in cross-strait cable-stayed bridges, corresponding static approximate calculations and analytical theory based on catenary and parabolic cable configurations are established. Taking a main span 1400 m cable-stayed bridge as the research object, three typical lifting conditions and the whole process of auxiliary cable lifting are analyzed and discussed. The results show that the sag effect is effectively reduced. The support efficiency is only improved when the cables are lifted above the original cable chord. Reduction of the horizontal component force of the cable is limited. The equivalent elastic modulus and the vertical support stiffness of the lifted cables are significantly increased with increased horizontal projection length and not sensitive to the change of the lifting point position. The scheme of lifting the cable to the chord midpoint is more economical because of the less steel required for the auxiliary suspension cable, but its effect on improving the vertical support efficiency is limited. The support efficiency is better when the cable is lifted to the cable end tangential to the original cable chord, but the lifting force and the cross-sectional area of the auxiliary suspension cable are doubled. The approximate calculation results of the lifted cables are very close to the numerical analysis results, which verifies the applicability of the approximation method proposed in this study. The results of parabolic approximation calculations are approximately equal to that of catenary cable geometry. As the parabolic approximation analysis theory of lifted cables is more convenient in mathematical processing, it is feasible to use parabolic approximation analysis theory as the analytical method for the conceptual design of lifted cables of super-long span cable-stayed bridges.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.25 no.3
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• pp.195-202
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• 2012

Two nonlinear frame elements taking into account geometric nonlinearity is presented and compared based on the Lagrangian co-rotational formulation. The first frame element is believed to be geometrically-exact because not only tangent stiffness matrices is exactly evaluated including stiffness matrices due to initial deformation but also total member forces are directly determined from total deformations in the deformed state. Particularly two exact tangent stiffness matrices based on total Lagrangian and updated Lagrangian formulation, respectively, are verified to be identical. In the second frame element, the deformed curved shape is regarded as the polygon and current flexural deformations in iteration process are neglected in evaluating tangent stiffness matrices and total member forces. Two numerical examples are given to demonstrate the accuracy and the good performance of the first frame element compared with the second element. Furthermore it is shown that the first frame element can be used in tracing nonlinear behaviors of cable members.

• Journal of Korean Association for Spatial Structures
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• v.17 no.1
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• pp.31-40
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• 2017

The objective of this study is to analysis the mechanical characteristics and nonlinear behaviors on the geometric nonlinear behavior of a cable spoke wheel roof system for long span lightweight roof structures. The weight of a cable spoke wheel roof dramatically can reduce and the cable roof system can easily make the required rigidity and shape by the sag ratio and pretension forces. Determining the pretension and initial sag of cable roof system is essential in a design process and the shape of roof is changed by pretension. The nonlinear behavior of flexible cable system has greatly an affect on the sag and pretension. This paper will be carried out analyzing and comparing the tensile forces and deflection of a cable spoke wheel system for the large span retractable roof, and analyzed to deflections and tensile forces by the post height of center hub. The double arrangement of a spoke wheel system with reverse curvature works more effectively as a load bearing system, the pretension can easily increase the structural stiffness. The cable truss system can carry vertical load in up and downward direction, and act effectively as load bearing elements.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.24 no.5 s.176
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• pp.1246-1253
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• 2000

Wire ropes are widely used in cable car, suspension bridge and elevator, etc. and there has been a growing need for ropes of large diameter. The theoretical procedures to obtain the stiffness coefficients of wire ropes, using previously reported theory, are programmed and the verification of the program is made. The effects of lay angle on the stiffness of strand are researched and comparisons on stiffness of rope are made according to the lay type. Axial stiffness optimization problems with coupling and torsional stiffness constraints are formulated and the effects of constraints on other stiffness coefficients on axial stiffness optimization are investigated.

• Proceedings of the Korea Concrete Institute Conference
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• 2002.05a
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• pp.531-536
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• 2002

The design of anchorage zone in prestressed concrete cable stayed bridges is very important area due to the more accurate analysis is needed to estimate the behavior. In the study, since the cable anchorage zone in the prestressed concrete cable-stayed bridge is subject to a large amount of concentrated tendon forces, it shows very complicated stress distributions and causes a serious local cracks. Accordingly, It is necessary to investigate the parameters of affecting the stress distribution, such as the cable inclination, the position of anchor plate, the modeling method and the three dimensional effect. The tensile stress distribution of anchorage zone is compared to the actual design condition by varing the stiffness of spring element in the local modeling and an appropriate position of anchor plate is determined. These results would be elementary data to the stress state of anchorage zone and more efficient design.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.11 no.4
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• pp.231-237
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• 1999

A geometric non-linear finite element formulation of spatial ocean cable under currents is presented using multiple noded curved cable elements. Tangent stiffness and mass matrices for the isoparametric cable ele¬ment are derived and the initial equilibrium state of ocean cable subjected to self-weights, buoyancy, and current as well as support motions is determined using the load incremental method. Free vibration analysis of ocean cables is performed based on the initial equilibrium configuration. Numerical examples are presented and discussed in order to demonstrate the feasibility of the present finite element method and investigate dynamic characteristics of ocean cables.