Wire Ropes Under Tensile Load - Wire Ropes: Tension, Endurance, Reliability - page 68

cos 2 a k E k A k
P n W F k ¼ S : ð 2 : 22a Þ

i¼0 Z i

cos 3 a i E i A i

By neglecting the contraction, the tensile force of the stranded rope is

!

X X

n Wj

n S

S ¼ DL
L

z j cos 3 b j z ij cos 3 a ij E ij A ij

ð 2 : 28a Þ

j¼0 i¼0

and the tensile force in the wire k of the strand l is

cos 2 b l cos 2 a kl E kl A kl

S :

F kl ¼ P n S

P n wj

ð 2 : 29a Þ

j¼0 z j cos 3 b j i¼0 z ij cos 3 a ij E ij A ij

The wire tensile stresses in the spiral rope and in the stranded rope are

r tk ¼ F k
A k

r tkl ¼ F kl and

A kl :

All wires have nearly the same tensile stress if a wire rope has a fibre core and
the same lay angle for all wire layers (except, of course, the centre wires in the
strands which have a higher stress than the other wires). This common tensile
stress is

S
A cos a cos b :

r t ¼ ð 2 : 31 Þ

This equation was previously given by Wiek ( 1980 ). In the outer wires, the
tensile stress is a little smaller than as calculated in ( 2.31 ).

Example 2.1: Wire tensile stress in spiral wire ropes

Calculation of the tensile stress in the wires of the open spiral wire rope 1 9 37
according to Fig. 2.4 with the global wire rope tensile stress r z = 300 N/mm 2 .
The tensile force of the spiral rope, is

S ¼ A m r z ¼ 1 : 431 þ 6 þ 12 þ 18 ð ð Þ 1 : 227 Þ r z ¼ 45 : 61 300 ¼ 13,680 N :

Using ( 2.23 ), the tensile stress in the centre wire is

45 : 61 r z

¼ 45 : 61 r t0 ¼

41 : 09 r z

0 : 9703 3
1 þ 0 : 3 0 : 2419 2

1 : 431 þ ð 6 þ 12 þ 18 Þ 1 : 227

r t0 ¼ 1 : 110 r z ¼ 333 N/mm 2 :

With the same Eq. ( 2.23 ), the tensile stress in the wires of the layers 1, 2 and 3
with the same lay angle a = 14 is