Dead Load Allocation in Triple-Cable Suspension Bridges by Adjusting the Unstrained Lengths of Hangers: A Novel Analytical Approach
Publication: Journal of Bridge Engineering
Volume 27, Issue 11
Abstract
Triple-cable design of suspension bridges with an ultrawide main girder can improve their mechanical properties, making it lucrative for numerous engineering scenarios. However, its realization requires assigning an appropriate share of the dead load of the main girder supported by three main cables to avoid the middle main cable overload by the main girder’s dead load since the latter would impair the mechanical behavior of the upper transverse beams in the towers and deteriorate the whole bridge’s torsional stiffness. Therefore, this study proposes an analytical approach for dead load allocation to the suspension bridge with three main cables, which adjusts the share of the main girder’s dead load supported by three main cables via changing the unstrained lengths of the hangers. The main advantage of the proposed approach is that it can consider both uniform and nonuniform allocations. The spatial model for the suspension bridge with three cable planes is first converted into a plane model. The relationship between unstrained lengths of the three hangers in the same cross section is determined via the deformation compatibility conditions and one of the following options: (1) equality of stiffness of the two side hangers in the case of a symmetrical plane model; or (2) energy conservation conditions in case of an asymmetrical one. The proposed method was applied to an example of a triple-cable suspension bridge with a main span of 2,100 m and a width of 75 m, and its analytical solutions were compared against finite-element method calculation results. An increase in the share of the main girder’s dead load supported by the two side main cables increased the torsional stiffness of the whole bridge and reduced the vertical load exerted by the middle main cable on the top transverse beam of each tower. Meanwhile, variation of the share of the main girder’s dead load supported by the side and middle main cables only slightly influenced the whole bridge’s vertical and lateral stiffness values. The aforementioned adjustment by the proposed method could be accomplished without increasing the steel consumption of the bridge cables. The results could provide references for the design, static, and dynamic response analysis of similar triple-cable ultrawide suspension bridges.
Practical Applications
Installation of an ultrawide deck in a conventional two-cable suspension bridge requires resolving the following two major problems: (1) the main girder has a significant spatial effect, which considerably adds to the difficulty of design and analysis; and (2) at the midpoint of the main girder section, the deflection may be excessively large. The height of the main girder has to be increased to improve the stiffness, leading to high steel consumption and high construction cost. These problems may be solved by adding a cable plane (one more main cable and the corresponding hangers). Based on the findings and the major contributions of this paper, we can achieve random dead load allocation ratios by just adjusting the unstrained lengths of hangers. The application of triple-cable systems may be a great potential approach to increase the overall torsional stiffness. Meanwhile, changing the share of the dead load supported by the side and middle main cables has a slight effect on the total cable-steel consumption. It shows that the method presented in this paper will not increase the construction cost.
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Acknowledgments
Financial support from the National Natural Science Foundation of China (Grant No. 52078134) is gratefully acknowledged.
Notation
The following symbols are used in this paper:
- Ai
- cross-sectional area of the ith hanger;
- Eb
- elastic modulus of the transverse beam;
- Eh
- elastic modulus of the hangers;
- Fi
- ith reaction force of the multipoint rigidly supported continuous beam;
- hi
- unstrained length of the ith hanger;
- I
- moment of inertia of the transverse beam;
- ki
- support stiffness provided by the ith hanger;
- M(x)
- bending moment function of the transverse beam;
- P1
- force acting on the left hanger;
- P2
- force acting on the middle hanger;
- P3
- force acting on the right hanger;
- q
- dead load intensity of the transverse beam;
- q′
- dead load intensity of the main girder in the longitudinal direction;
- w
- deflection curve of the transverse beam;
- w′
- rotational angle of the transverse beam;
- w″
- curvature of the transverse beam;
- Δi
- elongation of the ith hanger; and
- Δ0
- length of the middle hanger exceeding the line connecting the bottoms of the left and right side hangers.
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Published In
Journal of Bridge Engineering
Volume 27 • Issue 11 • November 2022
Copyright
© 2022 American Society of Civil Engineers.
History
Received: Mar 23, 2022
Accepted: Aug 2, 2022
Published online: Sep 15, 2022
Published in print: Nov 1, 2022
Discussion open until: Feb 15, 2023
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Cited by
- Wen-ming Zhang, Han-xu Zou, Jie Chen, Jia-qi Chang, An analytical method for adjusting dead load allocation between side and central cables in a cable-stayed bridge with three cable planes, Structures, 10.1016/j.istruc.2023.01.097, 48, (1761-1771), (2023).