Assembled Finite Element Method For Spatial Analyses Of Long-Span Suspension Bridges

J. Melan proposed the deflection theory for analyzing large-spanned suspension bridge early as in 1888. The finite element theory has been so advanced today and has been widely applied in analyzing suspension bridges. However, the analyses of suspension bridge structures are still preferred by finite displacement analysis based on 2D (two-dimensional) or spatial skeleton approximate models. This mainly dues that the conventional finite element method (FEM) usually deals with different material areas or members as separate elements, and consequently leads to a large number of elements and nodes involved in calculation that could not be performed by usual personal computers (PCs). The problem becomes prominent especially when FEM is applied to complicated engineering structures, for example the suspension bridge, which consist of a great deal of members as well as specifications.For complicated structures such as Tsingma Bridge, Hongkong, this paper particularly developed a so-called assembled element on the basis of the degenerated 3D (three-dimensional) solid element, which may consist of 3D blocks, beams, plates, shells, and bars etc. The assembled element breaks through the limit of conventional FEM that different material areas or members should be divided into different elements. This allows us to use much less elements to model complicated structures such as the stiffened beam and tower in suspension bridge, while it can still reflect various details such as the mechanical character, geometry, spatial position, the contribution to the system stiffness and mass, of each member involved. By adopting the assembled element, we can use usual PCs to perform the nonlinear analysis of long-span suspension bridges. Furthermore, the assembled element holds the superiority characterized by FEM such as agility of objects and unification of program. It can be used to analyze structures with arbitrary shapes, interior structures, boundaries as well as arbitrary loads. It is a new type FEM that is extremely suitable for the global analysis of complicated structures.In order to consider the geometrically nonlinear behavior of suspension bridge structure, the tangential stiffness matrix of the assembled element and that of the spatial bar element were formulated. The later was specially developed to model the main cables and suspenders.Taking the Runyang Yangtse River Highway Bridge as the engineering background, this paper presented the nonlinear spatial finite element analysis in view of construction order of suspension bridge. Especially, three different states were considered, i.e. the designed state of free cable, the state of first stage dead load, and that of the second stage of dead load. The tensile forces of main cable, the geometric alignments, the stresses of tower, suspenders, and stiffened beams in various stages were obtained. The error between the calculated values and the design ones of elevations at controlling points in the designated status is very small. Further, static analysis under four different design loads was performed.Vibration analysis of Runyang Yangtse River Highway Bridge and Hongkong Tsingma Bridgewas also given. The consistent mass matrix for the assembled element was derived to transform the dynamic equation to the generalized eigenvalues problem that can be solved using the inverse iterative method. Moving frequency technique was also adopted in the calculation. By comparing with the results calculated using the spatial skeleton model involving 44000 DOFs (degrees of freedom), it was found that the results calculated by the present method involving only 26000 DOFs agree better with the experimental results.