Combined effect of cable sag and bending stiffness on in-plane modal behavior of two horizontal shallow cables connected by an elastic cross-tie

Abstract

Cross-tie solution is commonly employed to mitigate stay cable vibrations, especially the long ones. Therefore, cable sag could have a sizable impact on the dynamic response of the formed cable network and should not be neglected. Besides, the reduced cable effective length due to the installation of cross-ties and the larger diameter of longer cables would render the cable bending stiffness to have a more pronounced effect on the dynamic behavior of cable networks consisting long cables. Though the mechanism and effectiveness of cable networks have been studied by numerous researchers, majority of these work employed the taut cable assumption in modeling cable behavior. Only a few recent studies investigated the influence of either cable bending stiffness or cable sag separately on the modal response of cable networks, whereas the evaluation on their combined effect has yet to be fulfilled. In the current study, an analytical model of a flexible two-cable network proposed earlier by the authors is refined by including the sag effect. The combined effect of cable sag and bending stiffness on the dynamic behavior of cable networks with different configurations are examined, using the linear theory of shallow cables. Besides, the effect of cross-tie axial stiffness and installation location, as well as the length ratio and the bending stiffness ratio between the consisting cables, on the occurrence and characteristics of modal cross-over are discussed. Results show that while cable bending stiffness would influence all network modes, sag would only influence the symmetric modes. Both of them have a stiffening effect on the affected modes with that of the latter being more sizable, in particular, on the high order modes. Besides, modal cross-over in cable networks is observed to occur not only between two global modes, but also a global mode and a local mode. Enhance the stiffness of a cable network is found to advance the occurrence of modal cross-over at a smaller sag.