• Smart Structures and Systems
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• v.24 no.1
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• pp.83-94
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• 2019

Passive negative stiffness dampers (NSDs) that possess superior energy dissipation abilities, have been proved to be more efficient than commonly adopted passive viscous dampers in controlling stay cable vibrations. Recently, inertial mass dampers (IMDs) have attracted extensive attentions since their properties are similar to NSDs. It has been theoretically predicted that superior supplemental damping can be generated for a taut cable with an IMD. This paper aims to theoretically investigate the impact of the cable sag on the efficiency of an IMD in controlling stay cable vibrations, and experimentally validate superior vibration mitigation performance of the IMD. Both the numerical and asymptotic solutions were obtained for an inclined sag cable with an IMD installed close to the cable end. Based on the asymptotic solution, the cable attainable maximum modal damping ratio and the corresponding optimal damping coefficient of the IMD were derived for a given inertial mass. An electromagnetic IMD (EIMD) with adjustable inertial mass was developed to investigate the effects of inertial mass and cable sag on the vibration mitigation performance of two model cables with different sags through series of first modal free vibration tests. The results show that the sag generally reduces the attainable first modal damping ratio of the cable with a passive viscous damper, while tends to increase the cable maximum attainable modal damping ratio provided by the IMD. The cable sag also decreases the optimum damping coefficient of the IMD when the inertial mass is less than its optimal value. The theoretically predicted first modal damping ratio of the cable with an IMD, taking into account the sag generally, agrees well with that identified from experimental results, while it will be significantly overestimated with a taut-cable model, especially for the cable with large sag.

• Journal of Korean Association for Spatial Structures
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• v.16 no.3
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• pp.47-58
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• 2016

Cable network system is a flexible lightweight structure which curved cables can transmit only tensile forces. The weight of cable roof dramatically can reduce when the length becomes large. The cable network system is too flexible, most cable systems are stabilized by pretension forces. The tensile force of cable system is greatly influenced by the sag ratio and pretension forces. Determining initial sag ratio of cable roof system is essential in a design process of cable structures. Final sag ratio and pretension depends on initial installed sag and on proper handling during installation. The design shape of cable system has an affect on the sag and pretension, and must be determined using well-defined design philosophy. This paper is carried out the comparative data of the deflection and tensile forces on the geometric non-linear analysis of cable network systems according to sag ratio. The study of cable network system is provided to technical informations for the design of a large span cable roof, analytical results are compared with the results of other researchers. Structural nonlinear analysis of systems having cable elements is relatively complex than other rigid structural systems because displacements are large as a reason of flexibility, initial prestress is applied to cables in order to increase the rigidity, and then divergence of nonlinear analysis occurs rather frequently. Therefore, cable network systems do not exhibit a typical nonlinear behavior, iterative method that can handle geometric nonlinearities are necessary.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.28 no.5A
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• pp.657-664
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• 2008

Rain-wind induced cable vibration can cause the damages in the cable-stayed bridge due to very little inherent damping characteristics and low fundamental frequency. External Dampers attached to stay cables near anchorages have been shown to be effective means at short stay-cables. However, installation locations of external dampers are limited to a particular range due to aesthetic and practical reasons for very long stay-cables. A recent study by the authors showed that the stay-cable vibration system can perform better than the optimal passive viscous damper, thereby demonstrating its applicability in large cable-stayed bridges. This paper extends the previous study on the taut string representation of the cable by adding cable sag and inclination. The response of the proposed system compared to those of the cable with and without an external damper, and the movable anchorage system provides very effective mitigation of cable vibration. Cable damping ratio is seen to be remarkably reduced by movable anchorage system for a wide range of cable sag. This result shows that the sag effects of the proposed system should be considered.

• Structural Engineering and Mechanics
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• v.20 no.3
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• pp.363-380
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• 2005

The cable tension plays an important role in the construction, assessment and long-term health monitoring of cable structures. The cable vibration equation is nonlinear if cable sag and bending stiffness are included. The engineering implementation of a vibration-based cable tension evaluation is mostly carried out by the simple taut string theory. However, the simple theory may cause unacceptable errors in many applications since the cable sag and bending stiffness are ignored. From the practical point of view, it is necessary to have empirical formulas if they are simple and yet accurate. Based on the solutions by means of energy method and fitting the exact solutions of cable vibration equations where the cable sag and bending stiffness are respectively taken into account, the empirical formulas are proposed in the paper to estimate cable tension based on the cable fundamental frequency only. The applicability of the proposed formulas is verified by comparing the results with those reported in the literatures and with the experimental results carried out on the stay cables in the laboratory. The proposed formulas are straightforward and they are convenient for practical engineers to fast estimate the cable tension by the cable fundamental frequency.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.32 no.5A
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• pp.255-266
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• 2012

Main cable of a suspension bridge is the important member which shows the overall structure integrity at bridge completion. Configuration of main cable is a free hanging state at cable erection completion and is different from that at bridge completion supporting the dead loads such as hanger, girder, and so on. Accordingly, the configuration control under cable erection is considerably significant because the configuration at cable erection completion has direct influence on that at bridge completion. That is performed by sag adjustments at center, side span and tension adjustments at anchor span. The former needs the sag sensitivity which represents the control quantity of strand length corresponding to that of sag. The latter requires the tension sensitivity which shows the change of strand tension according to that of strand temperature. In this study, the fundamental equations of cable were derived with the assumption of either catenary or parabola shape, the differential-related equations using chain rule on horizontal tension were drawn from those and finally the estimation methods of the sag / tension sensitivity were proposed from both those. The nonlinear numerical analysis flow charts of sag sensitivity based on the catenary equations were proposed and the sag sensitivities grounded on the differential-related equations were compared with the results using them for various parameters of sag change. Also, considering the combinations of sag change parameters, the calculation method of the final variation for the cable sag was suggested. For the real suspension bridge under construction with PPWS method, the sag/tension sensitivity were estimated considering the construction conditions like the change of PPWS length, PPWS temperature, bridge span, etc.. We hope that this study will be a systematic guideline for the configuration control under main cable erection and improved highly by field verification in the real bridge site.

• Smart Structures and Systems
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• v.23 no.6
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• pp.537-551
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• 2019

In this paper, a method for analyzing the damping performance of stay cables incorporating magnetorheological (MR) dampers in the passive control mode is developed taking into account the cable sag and inclination, the damper coefficient, stiffness and mass, and the stiffness of damper support. Both numerical and asymptotic solutions are obtained from complex modal analysis. With the asymptotic solution, analytical formulas that evaluate the equivalent damping ratio of the sagged cable-damper system in consideration of all the above parameters are derived. The main thrust of the present study is to develop an general design formula and a universal curve for the optimal design of MR dampers for adjustable passive control of sagged cables. Two sag-affecting coefficients are derived to reflect the effects of cable sag on the maximum attainable damping ratio and the optimal damper coefficient. For the cable configurations commonly used in cable-stayed bridges, the sag-affecting coefficients are directly expressed in terms of the sag-extensibility parameter to facilitate the control design. A case study on adjustable passive vibration control of the longest cable (536 m) on Stonecutters Bridge is carried out to demonstrate the influence of the sag for the damper design, and to figure out the necessity of adjustability of damper coefficients for achieving maximum damping ratio for different vibration modes.

• 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.

• 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.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2011.10a
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• pp.432-433
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• 2011

• 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.