Wire Ropes Under Bending and Tensile Stresses - Wire Ropes: Tension, Endurance, Reliability - page 252

To be on the safe side, the evaluated rope breaking force F e (which is no longer
standardised) is evaluated as the sum of the wire breaking forces and can be
replaced by the smaller calculated breaking force F c . Normally, the minimum rope
breaking force F min has to be used today. With the spinning loss factor k, the
minimum breaking force is

F min ¼ k F c :

With that, the constants q related to the minimum breaking force are
q ¼ q 0 = k ;

which means the Donandt force is then

d S D ; sim ¼ q 0 F min þ q 1

D F min :

ð 3 : 71 Þ

In the case of reverse bending cycles, the Donandt force is of course smaller
than that of the simple bending cycles. The test results have also been evaluated
with the basis ( 3.71 ). A more or less constant difference has been found by
comparing the constants q i for simple and reverse bending. This means that the
Donandt force for reverse bending is, Feyrer and Jahne ( 1991a )
S D ; rev ¼ ð q 0 0 : 035 Þ F min þð q 1 0 : 25 Þ d

D F min :

ð 3 : 72 Þ

The constants q i for the different rope constructions are to be found in
Table 3.17 (Sect. 3.4.5 ).
In reality, the transition of the two straight endurance lines marking the
Donandt force is rounded. If the number of bending cycles and the tensile force are
drawn in a diagram in linear and not in logarithm scale as done by Nabijou and
Hobbs ( 1994 ) the Donandt force can hardly be detected.

3.2.7.2 Discard Limiting Force

The discard limiting forceS G is the rope tensile force at which, with sufficient
probability, a number of wire breaks of at least B A30 = B A30min has to be expected.
B A30 means the discard number of visible wire breaks on a rope reference length of
thirty times the rope diameter L = 30d. The discard limiting force can be calculated
using an equation which is regrouped from ( 3.83 ) in Sect. 3.2.9 for a given discarding
number of wire breaks. This regrouped ( 3.94 ) is presented in Sect. 3.4.5 .

3.2.7.3 Optimal Rope Diameter

For a given tensile force S and a given sheave diameter D, the tensile stress for
small rope diameters is high and the bending stress low. In the case of large rope