Wire Ropes Under Tensile Load - Wire Ropes: Tension, Endurance, Reliability - page 65

Dl S cos 2 a i
l S 1 þ m i sin 2 a i

S i ¼ E i A i : ð 2 : 20a Þ

Using ( 2.13 ) the strand tensile force is

:

X

n

z i cos 3 a i
1 þ m i sin 2 a i

S ¼ Dl S
l S

E i A i ð 2 : 21 Þ

i¼0

The tensile force in a wire of a specific wire layer k is found by combining
( 2.20 ) and ( 2.21 ) with the elimination of Dl S /l S

cos 2 a k
1 þ m k sin 2 a k

E k A k

F k ¼ S : ð 2 : 22 Þ

z i cos 3 a i
1 þ m i sin 2 a i

P i¼0

E i A i

The tensile stress in this wire is

cos 2 a k
1 þ m k

E k

r tk ¼ F k
A k

sin 2 a k

¼ S : ð 2 : 23 Þ

P i¼0

z i cos 3 a i
1 þ m i sin 2 a i

E i A i

2.1.4.2 Wire Tensile Stress in Stranded Ropes

As before, the same derivation can be used for the stranded rope by now observing
a strand as a wire. The wire layers keep the counting index i and a certain wire
layer the index k, whereas the strand has the respective indices j and l. The total
number of wire layers in a strand is n W and the total number of strand layers is n s .
The wire rope tensile force is according to ( 2.13 )

S ¼ X

ns

F j z j cos b j

j¼0

and with the strand tensile force

n wj

F j ¼ X

F ij z ij cos a ij

i¼0

the wire rope tensile force is