The mechanics and mathematical modelling of wire rope
Wire rope is a structure formed by a large number of helical wires which combine in a complex manner to form a composite whole. The work presented in this thesis is concerned with unravelling the geometrical and mechanical complexities of stranded rope in a manner which promotes understanding of the mechanical behaviour and eventual failure of typical ropes. The thesis presents methods and computed results which provide detailed descriptions of single, double and triple helical shapes of individual wires in strands and ropes. Equations governing the possible spatial configurations of wires in multi-layered and stranded rope are also given and the dependence of the configuration on the number of wires per layer, wire diameter and helix angle is highlighted. This understanding of rope geometry is used to interpret extensive post-test examinations of full-scale ropes which have failed during systematic laboratory fatigue testing. Finally, closed-form mathematical models for the study of the mechanical behaviour of various rope and strand types are developed and presented. In all cases, these are built on the earlier geometric foundation described. In some cases, a modification of Costello's and Velinsky's approach is used. In single layer strand modelling, comparisons have been make between the author's analytical models and the experimental results from Martin and Packard as well as Machida and Durelli. Good agreement is shown.