Derivation of the resolving system of equations for flat bending of a rod with variable bending stiffness

Abstract

The theory of the stress-strain state of a rectilinear plumb line of a round rope, taking into account the interaction between its wires, was developed by prof. Glushko M.F. [1]. This theory was applied to plumb lines of round balancing ropes in [2]. At the bottom of the shaft, two plumb lines of the balancing rope bend substantially under their own weight, forming a pear-shaped loop. Tension devices for the rope in this part of the shaft, where groundwater flows, turned out to be inoperative. Plumbs of round ropes are delimited by wooden log cabins up to 10 m high to prevent overlapping (entanglement) of plumb lines of adjacent ropes due to their significant torsional deformations. Due to the large torsional deformations of round ropes, their wires in one section are loaded very unevenly [2]. During the operation of the lifting machine, the ropes saw through the demarcation logs, the zinc protective coating of the wires of the rope is broken, this is also facilitated by the displacement of the wires due to significant deformations of the torsion of the ropes, so their service life does not exceed 3 years, despite the fact that they are loaded only by their own weight.