Equivalent Plane Algorithm for Static Analysis of Cable-Stayed Bridge with Spatial Cables

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.