Theoretical Analysis And Secondary Development Of Frictional Sliding Catenary Cables Under Two-Span Continuous Conditions

As a tension component in a large-span structure,the cable plays an important role in cable hoisting systems,suspension bridges and other large-span structures with its high efficiency,economy,and light weight.However in the calculation theory of cable the problems of self-weight form-finding and friction-slip of two-span continuous cables are always unavoidable.In response to such problems,on the basis of studying and summarizing the research of domestic and foreign scholars,under the premise that the total original length of the two cable segments is known and unchanged,the internal force of the cable segment is solved by redistributing the original length of the two cable segments.And based on this,a friction-slip catenary cable element under two-span continuous conditions and considering the weight of the cable was created in ANSYS to simulate the frictio-slip problem of the cable,without complicated form-finding calculations.First,based on the iterative solution theory of single-span catenary cables,the stiffness matrix and mid-span sag of the single-span catenary cable in the local coordinate system are obtained.Through the coordinate conversion matrix,the stiffness matrix of the single-span catenary cable in the global coordinate system is obtained,and then it is expanded and superimposed to obtain the stiffness matrix of the two-span continuous catenary cable in the global coordinate system.Taking into account the friction between the cable and the slip node in the actual project,according to the friction theory at the slip node,the expression of the force transmission coefficient at the friction slip node is obtained.Then,under the premise that the total original length of the two cable segments is known and remains unchanged,the initial value of the original length of the two cable segments is determined from the original length variation range of the two cable segments of the friction-slip catenary cable element under the two-span continuous conditions.According to the calculation theory of single-span catenary cables and the expression of force transmission coefficient,the internal force of the cable segment and the force transmission coefficient at the slip node are obtained,and then the slip state of the cable segment is judged and described in numerical form.According to the value described for the slip state of the cable segment,the original length of each cable segment is redistributed and update the internal force and force transmission coefficient of the cable segment.And the original lengths of the two cable segments are redistributed again until the internal force of the cable segment meet the balance relationship.After the original length of the final cable segment is obtained,other basic quantities such as the internal force of the cable element are obtained.Secondly,using FORTRAN language to write the algorithm of friction sliding catenary cable element under the two-span continuous conditions,into the core file for secondary development of UPFs,and develop a customized version of ANSYS.It not only enriches the ANSYS element library,but also can combine custom elements with ANSYS self-contained elements to meet engineering needs.Finally,a simple calculation example of two-span continuous cable is verified by calling the friction-slip catenary cable element under two-span continuous conditions in ANSYS.It also simulates and analyzes simplified models of transmission conductor deployment construction,suspension bridge main cable erection,and cable hoisting system.The analysis results are compared with other documents,which prove the reliability of the calculation of the algorithm and the correctness of the results.At the same time,it verifies the feasibility of the proposed algorithm to solve the friction slip problem of two-span continuous catenary cables in actual engineering,and avoids complicated form-finding calculations.