Wire Ropes Under Bending and Tensile Stresses - Wire Ropes: Tension, Endurance, Reliability - page 228

lg N z ¼ lg N E þ lg s 0 u f 1 ð 1 Q z Þ z g: ð 3 : 53c Þ

With the failure probability Q z = 0.5 we get the mean number of bending
cycles for the effective rope bending length L

lg N z ¼ lg N E þ lg s 0 u f 1 0 : 5 z g

ð 3 : 53d Þ

and the ratio of the mean numbers of bending cycles and also the endurance factor
f L for the influence of the bending length

f L ¼ N z
N E

¼ 10 lg s 0 u f 1 0 : 5 z g :

ð 3 : 54 Þ

With EXCEL the endurance factor is

f L ¼ 10 ð lg s 0 STANDNORMINV ð 1 0 : 5 ð 1 = z Þ ÞÞ

ð 3 : 54a Þ

The standard deviation for the rope bending length ratio z is

lg s 0 ð z Þ ¼ 1
2 u 0

ð lg N z f u 0 g lg N z f u 0 g Þ: ð 3 : 54b Þ

With Eq. ( 3.35c )is

h n o u1 ð 1 Q z f u 0 gÞ z n o i :

lg s 0 ð z Þ ¼ lg s 0
2 u 0

u1 ð 1 Q z f u 0 gÞ z

ð 3 : 54c Þ

With EXCEL the standard deviation as function of z is for the practically
selected standard variable u 0 = 1

lg s 0 ð z Þ ¼ lg s 0
2

ð STANDNORMINV ð STANDNORMVERT ð 1 Þ ð 1 = z Þ Þ

ð 3 : 54d Þ

STANDNORMINV ð STANDNORMVERT ð 1 Þ ð 1 = z Þ ÞÞ:

This standard deviation lgs 0 for pieces from the same rope under the same stress
condition (solo-distribution) has alone very seldom a practical meaning. Their
influence on the class standard deviation is neglectible small. The class standard
deviation lgs that is valid for a class of ropes with the length l = 60d will prac-
tically not be changed for other rope lengths, Feyrer ( 2011 ).
The endurance factor f L for the influence of the bending length depends only on
the solo standard deviation lgs 0 . The mean solo standard deviation is lgs 0 = 0.047,
Feyrer ( 2011 ). With that and the bending length ratio z of Eqs. ( 3.53a ), ( 3.54a ), the
endurance factor for rope length is