Analytical Model Of Parallel Wire Cables Considering Bending And Torsional Stiffnesses And Its Applications

Cable structures are usually regarded as tension-only members,ignoring their flexural and torsional stiffnesses.However,relevant researches show that disregarding the bending and torsional stiffnesses will introduce unnegligible errors.Thus,further investigations are required on this topic to provide references for related engineering applications.This paper firstly proposed an analytical model for the bending of parallel wire cables considering the slips and interaction forces among wires.The parallel wire cable was transformed into a plane stress model of multi-layered composite beam considering slip between layers.Then the state space method was utilized to solve this model,the results of bending deformation and stress of the cable were obtained.The numerical solutions were compared with the experimental results,and key parameters in the proposed model were also calibrated by experiment datas.Then the bending stiffness of parallel wire cables considering interlayer slips among wires was obtained through transforming the cable into an equivalent multi-layered composite beam with slip between layers.The governing equation was obtained,so as the analytical solution of deflection.The equivalent bending stiffness of the cable was given by the reduced stiffness method.The linear relationship between the slip rigidity among wires and the average stress of the section was calibrated by the experimental data,and the relevant parameters were analyzed.The equivalent bending stiffness of several common parallel steel cable sections under different average stresses and lengths were given.Finally,the significant influence of bending stiffness on the natural frequency of cables was calculated and discussed.The torsional stiffness of parallel wire cables considering the slips among wires was also investigated.An analytical model for torsion of parallel wire cables was proposed according to the contact relationship among wires,in which the slips and interaction forces were simulated by a virtual spring.Based on the principle of Saint Venant torsion,the finite element method was utilized for the calculation of torsion stiffness of cables.The numerical results showed that torsional stiffness owned upper and lower bounds as the bending stiffness.If the linear relationship between the section average stress and the slip rigidity was introduced,the torsion stiffness would increase.The ratio of the torsion stiffness of parallel wire cable to the upper or lower bound torsion stiffness was only related to the number of steel wires and the composition of their arrangement and was independent of the diameter of steel wires.In the end,the numerical method for cable structures considering bending and torsional stiffnesses was derived,which was based on the geometrically exact beam theory and was capable to simulate the geometrical nonlinear effects of cables with large deformations and small strains.Moreover,the relationship model between the average section stress and the bending and torsional stiffnesses was proposed,thus the bending and torsional stiffnesses were updated according to the stress in the calculation.The numerical results showed that the method presented in this paper converged to the catenary solution at the minimum bending and torsional stiffnesses,while the classical beam theory solution was obtained at the maximum bending and torsional stiffnesses.The bending and torsional stiffnesses impacted little on the shape and internal force of cables.However,for the main cable of suspension bridges,although the reasonable constructed state of the bridge was not influenced by bending and torsional stiffnesses,the construction control parameters would be considerably affected.