Effect of interfacial contact forces in single layer cable assemblies

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The mechanical behaviour of cables and ropes used in engineering applications, though studied for the past three decades, varies widely depending on the numerical models adopted. Though these models predict the global response reasonably well, they differ widely in modelling the local contact conditions, the frictional effects at the interfaces and predicting the loss of stiffness of the cable assemblies. Three modes of contact can exist among the wires in a stranded cable assembly, i.e. the contact among the wires in the same layer (known as hoop or lateral contact), the contact among the wires in adjoining layers (radial contact) and the combined contact of all the wires (combined lateral and radial contact). The cables are hitherto modelled on the assumption of the presence of one of the contact modes only, though in reality the contact of modes change from one to the other, depending on the loading and the nature of contraction of the wires. The behaviour of the cable can be well understood if the appropriate mode of contact prevalent at every stage of loading is adopted in the model. This paper analyses the contact modes present in a single layer cable assembly and considers its response under an axial tensile load and an axial twisting moment. Based on the initial geometry, the contact mode is determined and depending on successive loading, the contraction of all the wires in the radial and lateral directions are ascertained and the threshold limits at which the contact modes change from one to the other are established. The overall response of the cables under the cascading effects of the presence of different contact modes, is compared with the works of the other authors who have adopted one type of contact mode only during their study. This has resulted in an overall reduction in the stiffness of the cable assembly, compared to the existing models. The force and moments in the individual wires are studied and the contact forces and the resulting contact stresses are established as a function of applied loads. The effect of the friction and the associated slip of the wires have been included. Apart from consideration of the radial contraction of the wires due to the Poisson effect, as accounted by few authors, this paper considers the radial deformation due to contact forces, as a special feature. This has resulted in refined expressions for the curvatures and twist of the wire and the associated forces in the normal and binormal directions. The predictions with these inclusions are compared with the existing works and the importance of the refinements to the cable designers are highlighted.