Equivalent Plane Algorithm for Static Analysis of Cable-Stayed Bridge with Spatial Cables
Publication: Journal of Bridge Engineering
Volume 27, Issue 6
Abstract
This paper proposes an equivalent plane algorithm of spatial stay cables using spatial rigid arms and the stay cable corotational coordinate system. The equivalent equations for the cable displacements and force elements are established, and the equivalent plane-element stiffness matrix of the spatial-cable element and its transfer matrix are derived. The matrix is automatically transformed into the plane-cable element model with rigid arm when the cable plane of the cable-stayed bridge is parallel. The spatial characteristic parameters of the cable plane are proposed, and the spatial effect of the spatial-cable plane on the internal force and deformation of the cable-stayed bridge is also analyzed. This equivalent plane algorithm is programmed into the bridge design and construction monitoring system procedure, and a comparison analysis with MIDAS software is also conducted. The proposed method can simplify the calculation model for the entire construction process of cable-stayed bridges with spatial cables and yield a good calculation accuracy. The equivalent plane algorithm has been successfully applied to the Jiayu Yangtze River Bridge (a kilometer-scale cable-stayed bridge). The results show that the number of stay-cable elements in the calculation model is reduced by 50%. The difference between the proposed method and the calculation result of a spatial-cable plane model is very small for a cable-stayed bridge with a spatial-cable plane, whether the initial tension is used or an unstressed cable is used. The proposed method provides an efficient and reliable calculation method for the design and construction of spatial-cable-stayed bridges.
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Acknowledgments
This work reported here was conducted with the financial supports from the National Natural Science Foundation of China (51678070, 51878073), the Science Fund for Creative Research Groups of Hunan Province (2020JJ1006), and the Training Program for Excellent Young Innovators of Changsha (kq2106039). The support is gratefully acknowledged.
Notation
The following symbols are used in this paper:
- A
- unstressed cross-sectional area of the cable element;
- c or c0
- projected length along the direction in the element plane;
- E
- modulus of elasticity of cable material;
- components of tension in the element at the end i in and directions;
- components of tension in the element at the end j in and directions;
- l or l0
- projected length along the direction in the element plane;
- q
- mass per unit length of cable element;
- q0
- weight of the cable element per unit unstressed length (note: the direction of gravity is always in the negative Z direction);
- s
- actual length of the cable element (stressed between i and j);
- s0
- unstressed length of the cable element between i and j;
- tension at end i and the end j of the cable element;
- H = Hj = −Hi, Vi + Vj = qs0, , ; and α
- angle between the element plane and global YZ plane.
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Published In
Journal of Bridge Engineering
Volume 27 • Issue 6 • June 2022
Copyright
© 2022 American Society of Civil Engineers.
History
Received: Dec 28, 2020
Accepted: Feb 27, 2022
Published online: Apr 15, 2022
Published in print: Jun 1, 2022
Discussion open until: Sep 15, 2022
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