An analytical approach to model the hysteretic bending behavior of spiral strands

Spiral strands are lightweight and flexible structural elements, widely employed in many different applications, moreover, they are the basic components of stranded wire ropes. Bending behavior can play an important role in modeling slack cables and in "critical" regions of flexible ropes, such as in the neighborhood of clamping devices. When a strand is bent, wires tend to slip relatively one to each other. In the present work, the critical conditions for the onset of inter-layer sliding are investigated by defining the limit domain for wire slipping (the domain of "admissible values" for the axial force of a generic wire, accounting also for the contribution due to bending of the strand). The special case of uniform bending of the strand is considered and a closed form expression of the limit domain is presented. The non-holonomic nature of the strand mechanical model developed in this work leads to a lacking of symmetry for the tangent stiffness matrix. In the paper it is proved that this condition can be de facto relaxed in practical applications and that an elastic potential function, relating the generalized stress and strain variables of the strand in bending, can be defined only under the limit kinematic hypotheses of "full stick-state" or of "full slip-state". The aforementioned results are used as the starting block from which the strand full mechanical behavior for coupled axial force and bending is derived. Knowledge in closed form of how the limit domain depends upon the strand construction parameters and current stress conditions paves the way to design optimization of the strand.