| With the development of suspension bridges,their structure forms have become much more complex,and their scale have become much more extensive.Simultaneously,the calculating ability of computer have increased significantly,which make it become easier to analyze the suspension bridges.However,the calculating process of existing nonlinear finite element methods are very complex,it is necessary to propose a simply and practical approach to analyze the suspension bridges which is able to simplify the calculation procedures and improve the efficiency.In addition,the conventional deflection theories of suspension bridges need to be improved to obtain more precise results,which is not only beneficial for the preliminary design of suspension bridges,but also is convenient for the structure checking.In this study,the development of conventional earth-anchored and emerging self-anchored suspension bridges and deflection theories of suspension bridges are introduced firstly;the advantages and disadvantages of them are summarized respectively;the evolution of the deflection theory of suspension bridges and the complexity of the existing calculation methods are introduced in detail.Next,considering the horizontal deflection at the top of the towers,fabrication camber of the main girder and the nonlinear deformation of the main cable,deflection theories corresponding to earth-anchored and self-anchored suspension bridges under live loads are re-formulated by using the energy method,and the unreasonable point in the conventional deflection theory of the self-anchored suspension bridges are modified.Thirdly,in view of the disadvantages of the conventional analytical method which is difficult to solve the nonlinear deflection theory presented in this paper,and the disadvantages of the existing nonlinear finite element analysis method which is more complex and tedious in the actual operation,in this study,the practical finite element method(PFEM)considering only the structural elements of the main girder and the tower is firstly proposed by using the suspension bridge element and combining with the finite element theory.Furthermore,a preload method is newly proposed to reduce the maximum moment of the main girder,and the deflection theories of suspension bridges under preloads are formulated.Finally,in order to demonstrate the validity and accuracy of the proposed deflection theory and its practical FEM,based on the presented theory and method,the MATLAB is used to develop the PFEM program,and one three-span earth-anchored which is based on the Great Belt Suspension Bridge in Danmark and two three-span self-anchored suspension bridge models which are based on the Yeongjong Bridge in South Korea are analyzed under live loads.Then the results by the proposed method are compared with those by unstrained length method to demonstrate the validity and accuracy of deflection theory and FE solutions.Besides,a redeveloped program of PFEM program is used,and the presented earth-anchored suspension bridge model and one of the self-anchored suspension models are selected and analyzed to show how effective the preload method is in reducing the maximum bending moment of the main girder.The research results show that the two nonlinear deflection theories derived from energy method and the practical finite element method proposed in this study can reduce the calculation amount,improve the calculation efficiency and meet the accuracy requirements on the premise of fully considering the deformation characteristics of each component of the suspension bridge,and overcome the defect that analytical method is difficult to solve nonlinear deflection theory.At the same time,the preloading method proposed in this paper can significantly reduce the maximum bending moment of the main girder under live load,which provides a new idea for reducing the bending moment of the main girder and improving the safety and economy of the suspension bridges in the future. |
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