Bending of an Axially Loaded Strand With Friction and the Mechanics of Wire Rope Reinforced Cylinders
Leclair, Raymond A.
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https://hdl.handle.net/2142/71688
Description
Title
Bending of an Axially Loaded Strand With Friction and the Mechanics of Wire Rope Reinforced Cylinders
Author(s)
Leclair, Raymond A.
Issue Date
1986
Department of Study
Theoretical and Applied Mechanics
Discipline
Theoretical and Applied Mechanics
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Engineering, Mechanical
Abstract
A theory is presented which will predict the stresses in a single lay strand subjected to axial, bending, and torsional loads when friction is present. Similar to the solution for the axial loading of a strand, the curvatures and twist of the wires in bending are estimated and the loads required for equilibrium are obtained by solving the six nonlinear, differential equations of equilibrium of a thin wire. The stresses due to bending are then superimposed on the stresses in the wires due to the axial loading.
In addition, a solution for the stresses in a cylinder reinforced with a wire rope is presented. The case of a uniform stress applied to the ends of the cylinder is of particular interest. The displacements corresponding to no end rotation are approximated using the principle of minimum potential energy. It must be understood a torque is present to restrain the ends from rotating. A strength of materials approach, in which plane sections remain plane, is taken to determine the stresses produced by releasing this torque, allowing the ends to rotate. This leads to the unexpected conclusion that the bond shearing stresses approach infinity at the ends.
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