Coupling Behavior of Wire Ropes Subjected to Tensile Impulses

To determine the stress state of a wire rope is tedious although analytical solution of a simple rope subjected to static load is available. While facing the problems involving complex ropes, it is usual practice to take approximations based upon the concepts of an average stress state for the constitutive ropes or for every wire. For a statically loaded cable superimposed with a tensile impulse, practically in sudden lifting of a heavy weight, the coupled axial-shearing strain waves in the cable has rarely been studied and explored through analytical approaches. Based on Costello’s force-deformation relationship and elastic wave propagation theory, analysis procedures and results are presented in this paper. Time-dependent coupled axial-torsional displacements and axial-shearing strain waves in a simple straight wire rope, due to a longitudinal impact at one end, are obtained. At the instance of the strike, a pair of coupled primary axial-torsional waves is created and begins to travel in the cable independently with different speed. Meanwhile, a coupling induced secondary torsional wave and an axial wave were observed to travel with the primary axial wave and the primary torsional wave, respectively. Phenomenon such as the traveling, reflections from ends, and intersections of the primary waves as well as the secondary wave are presented. Information provided in this paper would be useful in the study of unexpected overstress and/or fatigue problems.