• 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.

• Smart Structures and Systems
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• v.26 no.5
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• pp.575-589
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• 2020

For vibration control of stay cables in cable-stayed bridges, viscous dampers are frequently used, and they are regularly installed between the cable and the bridge deck. In practice, neoprene rubber bushings (or of other types) are also widely installed inside the cable guide pipe, mainly for reducing the bending stresses of the cable near its anchorages. Therefore, it is important to understand the effect of the bushings on the performance of the external damper. Besides, for long cables, external dampers installed at a single position near a cable end can no longer provide enough damping due to the sag effect and the limited installation distance. It is thus of interest to improve cable damping by additionally installing dampers inside the guide pipe. This paper hence studies the combined effects of an external damper and an internal damper (which can also model the bushings) on a stay cable. The internal damper is assumed to be a High Damping Rubber (HDR) damper, and the external damper is considered to be a viscous damper with intrinsic stiffness, and the cable sag is also considered. Both the cases when the two dampers are installed close to one cable end and respectively close to the two cable ends are studied. Asymptotic design formulas are derived for both cases considering that the dampers are close to the cable ends. It is shown that when the two dampers are placed close to different cable ends, their combined damping effects are approximately the sum of their separate contributions, regardless of small cable sag and damper intrinsic stiffness. When the two dampers are installed close to the same end, maximum damping that can be achieved by the external damper is generally degraded, regardless of properties of the HDR damper. Field tests on an existing cable-stayed bridge have further validated the influence of the internal damper on the performance of the external damper. The results suggest that the HDR is optimally placed in the guide pipe of the cable-pylon anchorage when installing viscous dampers at one position is insufficient. When an HDR damper or the bushing has to be installed near the external damper, their combined damping effects need to be evaluated using the presented methods.

• Wind and Structures
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• v.36 no.3
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• pp.149-160
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• 2023

Lightness and flexibility of membrane roofs make them very sensitive to any external load. One of the most important parameters that controls their behavior, especially under wind load is the sag/span ratio of edge cables. Based on the value of the pretension force in the edge cables and the horizontal projection of the actual area covered by the membrane, an optimized design range of cable sag/span ratios has been determined through carrying on several membrane form-finding analyses. Fully coupled fluid structure dynamic analyses of these membrane roofs are performed under wind load with several conditions using the CFD method. Through investigating the numerical results of these analyses, the behavior of membrane roofs with cables sag/span ratios selected from the previously determined optimized design range has been evaluated.

• Structural Engineering and Mechanics
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• v.39 no.5
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• pp.661-667
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• 2011

In the famous equivalent elasticity modulus method proposed by Ernst for the geometrical nonlinear analysis of stay cables, the cable shape was assumed as a parabolic curve, and only a part of the gravity load normal to the chord was taken into account with the other part of gravity load parallel to the chord being ignored. Using the actual catenary curve and considering the entire gravity load of stay cables, the present study has derived the equivalent stiffness method to analyze the sag effect of stay cables in cable-stayed bridges. The derived equivalent stiffness can be degenerated into Ernst's equivalent elasticity modulus method with some approximations. Therefore, the Ernst's method is a special and approximate formulation of the present method. The derived equivalent stiffness provides a theoretical explanation for the famous Ernst's formula.

• Structural Engineering and Mechanics
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• v.42 no.3
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• pp.291-311
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• 2012

The multi-span suspension bridge having double main cables in the vertical plane is investigated regarding endurance of live load distribution in the case of non-displaced pylon and pylon displacement. The coefficient formula of live load distribution described as the ratio of live load on the bottom cable to the top cable is obtained. Based on this formula, some function in respect of this bridge are derived and used to analyze its characteristics. This analysis targets the cable force, the cable sag and the horizontal displacement at the pylon top under live load etc. The results clarified that the performance of the live load distribution and the horizontal force of cables in the case of non-deformed pylon has a similar tendency to those in the case of deformed pylon, and the increase of pylon rigidity can increase live load distributed to the bottom cable and slightly raise the cable horizontal force under live load. However, effect on the vertical rigidity of bridge and the horizontal force increment of cables caused by live load is different in the case of non-deformed pylon and deformed pylon.

• Structural Engineering and Mechanics
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• v.8 no.1
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• pp.27-38
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• 1999

Cables are used in many applications such as cable-stayed bridges, suspension bridges, transmission lines, telephone lines, etc. Generally, the linear relationship is inadequate to present the behavior of cable structure. In finite element analysis, cables have always been modeled as truss elements. For these types of model, the nonlinear behavior of cables has been always ignored. In order to investigate the importance of the nonlinear effect on the structural system, the effect of cable stiffness has been studied. The nonlinear behavior of cable is due to its sag. Therefore, the cable pretension provides a large portion of the inherent stiffness. Since a cable-stayed bridge has numerous degrees of freedom, analytical methods at present are not convenient to solve this type of structures but numerical methods may be feasible. It is necessary to provide a different and more representative analytical model in order to present the effect of cable stiffness on cable-stayed bridges in numerical analysis. The characteristics of cable deformation have also been well addressed. A formulation of modified modulus of elasticity has been proposed using a numerical parametric study. In order to investigate realistic bridges, a cable-stayed bridge having the geometry similar to that of Quincy Bayview Bridge is considered. The numerical results indicate that the characteristics of the cable stiffness are strongly nonlinear. It also significantly affects the structural behaviors of cable-stayed bridge systems.

• Journal of the Korean Society for Railway
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• v.2 no.3
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• pp.36-45
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• 1999

The basic idea of cable-stayed girder bridges is the utilization of high strength cables to provide intermediate supports for the bridge girder so that the girder can span a much longer distance. In the cable-stayed bridge, the cables exhibit nonlinear behavior because of the change in sag, due to the dead weight of the cable, which occurs with changing tension in the cable resulting from the movement of the end points of the cable as the bridge is loaded. Techniques required for the static analysis of cable-stayed bridges has been developed by many researchers. However, little work has been done on the dynamic analysis of such structures. To investigate the characteristics of the dynamic response of long-span cable-stayed bridges due to various dynamic loadings likes moving traffic loads. two different 3-D cable-stayed bridge models are considered in this study. Two models are exactly the same in structural configurations but different in finite element discretization. Modal analysis is conducted using the deformed dead-load tangent stiffness matrix. A new concept was presented by using divided a cable into several elements in order to study the effect of the cable vibration (both in-plane and swinging) on the overall bridge dynamics. The result of this study demonstrates the importance of cable vibration on the overall bridge dynamics.

• Structural Engineering and Mechanics
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• v.25 no.2
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• pp.219-237
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• 2007

The effect of cable loosening on the nonlinear parametric vibrations of inclined cables is discussed in this paper. In order to overcome the small-sag limitation in calculating loosening for inclined cables, it is necessary to first derive equations of motion for an inclined cable. Using these equations and the finite difference method, the effect of cable loosening on the nonlinear parametric response of inclined cables under periodic support excitation is evaluated. A new technique that takes into account flexural rigidity and damping is proposed as a solution to solve the problem of divergence. The regions of inclined cables that undergo compression are also indicated.

• Structural Engineering and Mechanics
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• v.20 no.6
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• pp.609-630
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• 2005

A reliability analysis method is proposed in this paper through a combination of the advantages of the response surface method (RSM), finite element method (FEM), first order reliability method (FORM) and the importance sampling updating method. The accuracy and efficiency of the method is demonstrated through several numerical examples. Then the method is used to estimate the serviceability reliability of cable-stayed bridges. Effects of geometric nonlinearity, randomness in loading, material, and geometry are considered. The example cable-stayed bridge is the Second Nanjing Bridge with a main span length of 628 m built in China. The results show that the cable sag that is part of the geometric nonlinearities of cable-stayed bridges has a major effect on the reliability of cable-stayed bridge. Finally, the most influential random variables on the reliability of cable-stayed bridges are identified by using a sensitivity analysis.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.12 no.12
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• pp.956-963
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• 2002

In a recent construction industry, cable supported structures such as a cable-stayed bridge or space stadium have been increasingly constructed according to rapidly upgrade their related technologies. Generally stay cables as a critical member need to be rearranged for being satisfied with design tension forces. In this purpose, a vibration method has been applied to estimate the tension forces exerted on existing stay cables. In this study, cable vibration tests were tarried out to evaluate the cable tension forces comparing with theoretical and practical formulas. Using the measured frequencies obtained from free vibration and Impulsive tests, an accuracy of the estimated tension forces is confirmed according to use the first single mode only or higher multiple modes.