Wire Ropes Under Bending and Tensile Stresses - Wire Ropes: Tension, Endurance, Reliability - page 177

Chapter 3
Wire Ropes Under Bending and Tensile
Stresses

3.1 Stresses in Running Wire Ropes

3.1.1 Bending and Torsion Stress

3.1.1.1 Global Stresses

The global tensile stress in wire ropes is the so called rope tensile stress r Z as a
quotient between the tensile force S and the nominal metallic cross-section A of the
rope

r Z ¼ S

A :

ð 3 : 1a Þ

Another global form describing the tensile stress is the specific tensile force S/d 2
as a quotient between the tensile force S and the square nominal rope diameter d.
The corresponding global bending stress of a wire in a bent wire rope is the

bending stress from Reuleaux ( 1861 )

r b ¼ d

D E :

ð 3 : 1b Þ

In this equation, d is the wire diameter, D is the middle curvature diameter
(diameter of the rope axis bent over a sheave), and E is the elasticity module (of
material).
With ( 3.1b ), the bending stress is calculated as if the wire in the rope did not
have a helix form. For a long time, there was a dispute about whether this equation
was able to supply a result which was more or less true. The main contributions
here came from the famous Bach ( 1881 ) with his correcting factor 3/8 and in
opposition from Benoit ( 1915 ). Now it is clear that the real bending stress of wires
in a rope is both partly smaller and greater than—and well represented by—the
global bending stress according to Reuleaux.