Analytical and experimental analysis of the capacity of steel wire ropes subjected to forced bending

Wire rope is used in numerous applications such as elevators, power lines, suspension bridges, ships and the mooring of offshore structures. In many of these applications wire rope needs to be bent. Currently the Norwegian certification instance Det Norske Veritas (DNV) prescribes a capacity reduction factor for bending wire rope. It is unclear how this formula is derived or what it is based on. Therefore the main question of this thesis is: How does the forced bending of a steel wire rope around a shackle affect the break load of the wire rope? A secondary research question is: How does the forced bending of a steel wire rope relate to the reduction factor for bending enforced by DNV? These questions are answered by constructing an analytical model. In addition experiments are performed at the laboratory of the civil engineering faculty to verify this model. The analytical model is based on the assumption that every single wire behaves as an Euler-Bernoulli beam. The reduction in capacity is dominated by the effect of individual wires being bent, similar to a bundle of loose beams being bent. Plastic deformation needs to be considered to accurately describe smaller D/d ratios. Due to the helix structure, axial tension causes friction forces to develop between the strands and the wires. This increases the stiffness of the wire rope and leads to higher stresses and strains when the wire rope is bent. As soon as the wires start slipping the stiffness lowers drastically and any further deformation causes a much lower increase in stress and strain. All experiments are performed on both a 14mm and a 20mm wire rope. First an experiment is carried out to verify the test set-up and obtain the break load of a straight steel wire rope. Then a second experiment is performed to find the break load of a bent wire rope under various D/d ratios. These two tests lead to a reduction factor for bending. The analytical model shows a good fit with the experimental results. From this it can be concluded that the model developed in this thesis is a promising way to model wire rope and leads to a fairly accurate answer for the capacity reduction due to bending. The model developed and the DNV formula show similar reduction factors. For very small D/d ratios the model predicts a 5% lower reduction, while at bigger D/d ratios a higher reduction factor is predicted. The experiments show a better match with the analytical model, but due to the small differences and large standard deviation a larger sample size would be necessary to confirm this. In addition to the main question a limited investigation was done on the bending stiffness of wire rope. With some additions to the model developed for capacity reduction it was possible to model the bending stiffness. The result is a stick slip model that defines the bending stiffness as a parameter of the axial tension and the curvature, this bending stiffness rapidly declines as the wire rope is bent and wires start slipping. Although this model is not experimentally validated, the fact that the original model it is based on is fairly accurate means it is worth investigating further.