Wire Ropes Under Tensile Load - Wire Ropes: Tension, Endurance, Reliability - page 162

2

lg N c ¼ a 0 þ a 1 lg 2S a

d 2 þ a 2 S lower

S lower
d 2

þ a 3 þ a 4 lg d þ a 5 lg z

d 2

þ lg f L k Tc lg s :

This equation is also valid for the Warrington-Seale ropes if here the constant
a 5 is set a 5 = 0. For the failure quantiles of 50, 10 and 1 %, the constant parts can
be summarised to

a 0c ¼ a 0 k Tc lg s : ð 2 : 109 Þ

With this constant a 0c the number of load cycles N c —where with a certainty of
95 % at most a quantile c of wire ropes has been broken—is

2

lg N c ¼ a 0c þ a 1 lg 2S a

d 2 þ a 2 S lower

S lower
d 2

þ a 3 þ a 4 lg d

d 2

þ a 5 lg z þ lg f L : ð 2 : 110 Þ

In Table 2.11 , the constants a i for ( 2.110 ) are listed Casey ( 1993 ), Paton et al.
( 2001 ), Klöpfer ( 2002 ) Feyrer and Wehking ( 2006 ). The constants a 1 -a 5 have
been taken from Table 2.8 for the open spiral ropes and from Table 2.9 for the
Warrington-Seale ropes. The constant a 0c —listed in Table 2.11 —has been cal-
culated with ( 2.109 ) for the different quantiles f L is given in Eq. ( 2.107 ).
Equation ( 2.110 ) and the constants of Table 2.11 are valid up to the limiting
number of load cycles N D . With the reduced gradient of Haibach ( 1989 ), the number
of load cycles above N D = 2 9 10 6 is (as explained under Woehler Diagram)

2 a1 þ 1

2S a = d 2
2S aD = d 2

N k ¼ N D : ð 2 : 104 Þ

S aD is the amplitude of the tensile force for which the limiting number of load
cycles N D = 2 9 10 6 has to be expected. This limiting amplitude of tensile force
can be calculated with the following equation (inverted from Eq. ( 2.110 )).

Table 2.11 Constants for calculating the number of load cycles, ( 2.110 )

Wire ropes c

(%)

a 0c a 1 a 2 a 3 a 4 a 5

Open spiral ropes 50 15.401

10 15.039 -3.910 0.00118 -0.0000037 -0.793 0.399

1 14.774

Warr-Seale ropes
IWRC—sZ

50 16.302

10 15.883 -3.939 0.00326 -0.000012 -1.180 0

1 15.568