Wire Ropes Under Tensile Load - Wire Ropes: Tension, Endurance, Reliability - page 163

2

lg 2S ac

d 2 ¼ lg N c

1
a 1

a 0c þ a 2 S lower
d 2

S lower
d 2

þ a 3 þ a 4 lg d

a 1

!

þ a 5 lg z þ lg f L : ð 2 : 111 Þ

with N j ¼ N D ¼ 2 10 6 .
With ( 2.110 ), the number of load cycles will be calculated, directly valid up to
2 9 10 6 for all quantiles c. Numbers of load cycles above that should be corrected
with ( 2.104 ). By using the limiting number of load cycles 2 9 10 6 for all quan-
tiles, the standard deviation will be—as in reality—strongly extended in the region
above the limiting number of load cycles.
For the practical calculation of the numbers of load cycles the Excel-program
SWINGSP2.XLS can be used.

Example 2.15: Number of load cycles
Data:
Warrington-Seale rope 6 9 36—IWRC—sZ
Wire rope diameter d = 20 mm, nominal strength R 0 = 1, 770 N/mm 2 ,
lubricated
Rope length L = 120 m, terminated with resin sockets
The fluctuating tensile forces are
Lower tensile force S lower = 30 kN, S lower /d 2 = 75 N/mm 2
Upper tensile force S upper = 80 kN
The range of the specific force is

2S a = d 2 ¼ S upper S lower
d 2

¼ 125 N/mm 2 :

Results:
Using ( 2.110 ) and the constants from Table 2.11 , the numbers of load cycles are

N 50 ¼ 3 ; 690 ; 000 N 10 ¼ 1 ; 410 ; 000 N 1 ¼ 680 ; 000

From these numbers only

N 1 ¼ 680 ; 000 and N 10 ¼ 1 ; 410 ; 000

are directly valid. The mean number of loading cycles—greater than 2 9 10 6 —has
to be corrected. For that, using ( 2.111 ), the limit range of the specific tensile force is

2S aD50 = d 2 ¼ 146 N/mm 2 :