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


Over the years, the world has witnessed a continuous trend in the design and construction of cable-stayed bridges with relatively longer length spans. Some of the world’s longest cable bridges, like the Russky Bridge, have a much longer center span and stay cable length of 1104 m and 580 m, respectively. While such structures are big engineering breakthroughs, they have numerous design challenges. For example, such cable-stayed bridges are highly susceptible to vibrations induced by various human activities and environmental disturbances that could potentially degrade the safety and functionality of the bridges. Indeed, the length of the cables posed a significant engineering challenge because they had to be strong enough to support the weight of the bridge deck and withstand the harsh environmental conditions of the area, which include typhoons and earthquakes.

There are several methods to suppress unwanted cable vibrations. Among them, cross-tie solution is a popular and widely used vibration control strategy in cable-stayed bridges owing to its remarkable performance compared to other methods. When a vulnerable cable is tied with neighboring ones to form a cable network, it is beneficial in improving its in-plane stiffness and facilitating energy transfer from the former to the latter. In addition, it is effective in increasing the modal mass of the vibration system and reducing cable sag.

While most available cable network analytical models assume rigid cross-ties, this is not true as cross-ties in real applications are not rigid, and their stiffness could influence the dynamic response of cable networks. Although the mechanism of cable networks has been extensively studied, very few studies have separately studied the effects of cable bending stiffness or cable sag on the modal responses of cable networks. Further, the investigation of their combined effects is still missing.

To overcome these challenges, Dr. Amir Younespour and Professor Shaohong Cheng from the University of Windsor investigated the combined influence of cable sag and bending stiffness on the in-plane dynamic behavior of cross-tied cable networks on relatively longer cable-stayed bridges with different configurations. The authors extended their previously proposed analytical model of a flexible two-cable network and applied linear theory of shallow cables to take into account the combined effect of cable sag and bending stiffness. Their work is currently published in the peer-reviewed journal, Engineering Structures.

The authors demonstrated the effectiveness and feasibility of the proposed model in evaluating both isolated effects of cable sag and bending stiffness parameters and their combined effects on the modal response of shallow-cable networks. While cable sag influence only the symmetric modes, cable bending stiffness influences all the network modes. However, both exhibited a stiffening effect on the affected modes, with the impact of cable sag being greater. Additionally, modal cross-over in cable networks was observed to occur not only between two global modes but also a global and a local mode.

Dr. Younespour and Professor Cheng evaluated the effects of different system properties like cross-tie installation location and axial stiffness. The frequencies of symmetric cable networks with unequal length cables were affected by the cable length ratio, while changes in the cross-tie installation location, axial stiffness and properties of the neighboring cables did not affect the frequency of the first anti-symmetric mode. Additionally, the frequencies of symmetric global modes increased with the growth of sag, while those of anti-symmetric modes were not dependent on sag. Furthermore, the stiffening effects of the sag were more substantial for sag values below 50, especially for more rigid networks.

In summary, the study successfully investigated the modal response of two-cable networks using a newly proposed shallow-flexible-cable network model. Considering cable bending stiffness and sag improves the in-plane stiffness of shallow-flexible-cable networks. In addition, the occurrence of modal cross-over at a smaller sag could be advanced by increasing cross-tie axial stiffness and/or connecting a vulnerable cable to a stiffer or shorter neighboring one. In a statement to Advances in Engineering, the lead and corresponding author, Professor Shaohong Cheng explained their study contributes to advancing the functionality and safety of long-span cable-stayed bridges.

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

About the author

Amir Younespour is a Ph.D. candidate in Civil Engineering at the University of Windsor, Canada. He has twelve years of engineering experience in industry and academia.

Dr. Younespour graduated in 2011 from Azad University of Tabriz, Tabriz, Iran, with a bachelor’s degree in civil engineering. In 2013, he acquired his MSc degree from the University of Tabriz in earthquake engineering. Then, he worked for two consulting companies designing steel, concrete, and wood structures for almost five years while studying at the University of Tabriz as a Ph.D. student in earthquake engineering. The University of Tabriz, Iran awarded him a Ph.D. in earthquake engineering in 2018. His research work for MSc and Ph.D. was primarily focused on exploring various strategies for mitigating the vibrations of engineering structures against earthquakes and stay cables on cable-stayed bridges.

In his current position at the University of Windsor, Dr. Younespour is working on his second Ph.D. in Civil Engineering. His fields of interest are vibration control, structural rehabilitation strategies, system control and health monitoring.

About the author


Dr. Shaohong Cheng is a Professor in the Department of Civil and Environmental Engineering at the University of Windsor, Windsor, Ontario, Canada. She is a Professional Engineer of Ontario, a member of the American Society of Civil Engineers, the American Association for Wind Engineering, and the International Association for Bridge and Structural Engineering.

Dr. Cheng received her Ph.D. degree in Structural Engineering from Carleton University in Canada in 2000, studying wind-induced response of long-span bridges. She then worked as a post-doctoral research fellow at the University of Ottawa, during which she was in charge of an NSERC CRD research project in collaboration with the National Research Council Canada, the RWDI Inc., and the US Federal Highway Administration, and conducted extensive wind tunnel studies to investigate some newly identified wind-induced vibration problem of bridge stay cables. After working for eight months as a senior consulting engineer in a private company specialized in wind, she joined the Faculty of Engineering at the University of Windsor in 2005.

Dr. Cheng is the founder of the Boundary Layer Wind Tunnel Laboratory at the University of Windsor. She conducts research and supervises students in a broad range of projects, mainly in the areas of bluff body aerodynamics, fluid-structure interaction, vibration control and concrete technology. In recent years, her research is focused on Wind-induced response of structures, in particular, the bridge stay cables; Mitigating excessive stay cable vibrations using external dampers, cross-ties and hybrid systems; Mechanisms associated with dry inclined cable galloping and high-speed vortex excitation; Enhancing the aerodynamic stability of a new small ducted-fan type VTOL UAV model for precision agriculture; Evaluating the design wind load for building guardrail systems; Simulating atmospheric boundary layer effect in the wind tunnel; Shear strengthening of prestressed precast concrete hollow core slabs using carbon fibre reinforced polymer.


Younespour, A., & Cheng, S. (2022). Combined effect of cable sag and bending stiffness on in-plane modal behavior of two horizontal shallow cables connected by an elastic cross-tie. Engineering Structures, 266, 114617.

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