Stress-strain state of composite multi-layer stay rope considering breakages in reinforcing elements and nonlinear distribution of mechanical properties

Abstract

Purpose. Formulation of an algorithm for considering the influence of continuity breakages in fiber reinforcing elements on stay rope strength. Methods. Construction and analytical solution of a mathematical model of interaction for parallel fiber reinforcingelements connected through elastic material, in a case of continuity breakage of individual elements in reinforcement. Findings. A static strength calculation algorithm for a multi-layer stay rope with breakages in one cross-section of reinforcing elements is developed. It is established that a continuity breakage of an arbitrary element of a stay rope reinforcement leads to a significant change in internal loads of only the adjacent reinforcing elements and is practically independent of a nonlinear deformation character of cable components. Greater loads on reinforcing elements occur in a case of breakage of a corner reinforcing element, and the smallest loads – in a case of breakage of a central one.It is established that a number of rows of reinforcing elements in a stay rope and location of a damaged reinforcing element do not significantly affect displacement of cable end and do not affect distribution of loads among reinforcing elements in a damaged cross-section. Displacements depend on a ratio of shear modulus of elastic material and Young's modulus of reinforcing elements; the ratio is varied along cable length. It is established that a reinforcing element location with discontinuity does not significantly affect the character of relative growth of stay rope deformations in a case of nonlinear character of elastic shell deformation. Deformation nonlinearity of cable components does not affect redistribution of forces in stay rope with damaged reinforcing elements. Maximum relative displacements of reinforcing elements and the resulting maximum shear angles of material located between reinforcing elements are smaller than a value of the assumed nonlinearity coefficient. Characters of displacements of reinforcing elements are qualitatively similar. Scientific novelty. An analytical algorithm is developed for calculating a stress-strain state of a multilayer stay rope considering its design, nonlinearly of mechanical properties of its components distributed along the cable with damage to an arbitrary group of reinforcing elements in one cross-section. Practical significance. The developed algorithm allows considering a nonlinear deformation character of stay rope components on its stress state in a case of breakages in an arbitrary number of reinforcing elements arbitrarily located in a stay rope with a continuity breakage in one cross-section. The algorithm can be applied to determine a stress-stress state of a stay rope with breakage in a cross-section infinitely distant from rope ends. The algorithm allows considering the influence of breakages in reinforcing elements on rope strength, which increases rope reliability in a structure.