Wire Ropes Under Bending and Tensile Stresses - Wire Ropes: Tension, Endurance, Reliability - page 210

with forces F W10 and F Wcal in N and the global pressure p 0 in N/mm 2 . Over the
whole length of the rope, this high arc force F W10 is a frequent occurrence.
Wyss ( 1956 ) calculated the Hertz pressure between a wire arc and steel or cast
iron groove. He found that the outer arcs of the rope wires and the groove material
or both yield for relatively small forces. Häberle came to the same result. For
example, he found that the yield stress will be exceeded for a global pressure
smaller than p 0 = 2 N/mm 2 . Pantucek ( 1977 ) analysed the stresses in flattened
wire arcs in relation to the different breaking forms of the wires in running ropes.

Example 3.5 Wire arc force

Data:
Data the same as in Example 3.3 and additional data:
Strand lay length h S = 6d
Wire lay length h W = 3.1d
Results:
Global pressure, ( 3.27a )

p 0 ¼ 2 30,000

16 400 ¼ 9 : 38 N/mm 2 :

Pressure at the bottom of the groove, ( 3.33 )

¼ 18 : 4N/mm 2 :

17 : 4
117 0 : 229 ð 1 e 4 : 52 ð 0 : 54 0 : 5 Þ Þ

k 0 ¼ 150 1 þ

Max. pressure at the bottom of the groove, ( 3.33a )

k max ¼ 18 : 4 1 : 71 ¼ 31 : 5N = mm 2 :

Max. calculated wire arc force, ( 3.37 )

p 16 6 16

F Wcal ¼ 31 : 5 ¼ 501 N :

6
3 : 1 0 : 94 þ 1

6 18

The wire arc forces for 10 % of the wires on the bottom of the groove is
according to ( 3.37a ) greater than

501 ¼ 637 N :

0 : 614
9 : 38 þ 0 : 146

F W10 ¼ 1 þ 1,282