In order to study the sliding characteristics when the cable is connected with the other rods in the transmission line structures,a linear sliding cable element based on updated Lagrangian formulation and a sliding catenary element considering the out-of-plane stiffness coefficient are put forward.A two-span and a three-span cable structures are taken as examples to verify the sliding cable elements.By comparing the tensions of the two proposed cable elements with the existing research results,the error is less than 1%,which proves the correctness of the proposed elements.The sliding characteristics should be considered in the practical engineering because of the significant difference between the tensions of sliding cable elements and those of cable element without considering sliding.The out-of-plane stiffness coefficient and friction characteristics do not obviously affect the cable tensions.
In order to study the sliding characteristics when the cable structures are connected with other rods, a string of sliding cable dements （SCE） consisting of one active threenode SCE passing through the sliding point and multiple inactive two-node SCEs is put forward. Based on the updated Lagrangian formulation, the geometric nonlinear stiffness matrix of the three-node straight sliding cable dement is deduced. The examples about two-span and three-span continuous cable structures are studied to verify the effectiveness of the derived SCE. Comparing the cable tension of SCE with the existing research results, the calculating results show that the error is less than 1%. The sliding characteristics should be considered in practical engineering because of the obvious difference between the cable tension of the SCE and that of the cable element without considering sliding characteristics.
