Wire Ropes Under Tensile Load - Wire Ropes: Tension, Endurance, Reliability - page 64

Fig. 2.3 Elongation of a
strand wire

U i

U i

l i U i tan

ʱ i
l i /cos ʱ i

l s

ʔ

l i

ʱ i

l s

m i ¼ Du i = u i
Dl i = l i

:

Here u i is the winding circumference and Du i its contraction. Using this and
( 2.15 ), the contraction of the winding circumference is

Du i ¼ e i m i u i

and with u i ¼ l i sin a i is

Du i ¼ e i m i l i sin a i : ð 2 : 18 Þ

Using ( 2.17 ) and ( 2.18 ), the wire elongation is then

Dl i ¼ Dl S cos a i e i m i l i sin 2 a i

or

Dl i þ Dl i m i sin 2 a i ¼ Dl S cos a i :

Following this, the elongation of a wire in the wire layer i is

Dl S cos a i
1 þ m i sin 2 a i :

Dl i ¼ ð 2 : 19 Þ

This equation together with ( 2.14 ) and ( 2.16 ) supplies the tensile force of a wire
in the wire layer i as a function of the strand elongation

Dl S cos 2 a i

E i A i

F i ¼ ð 2 : 20 Þ

sin 2 a i l S 1 þ m i

or its component in the direction of the strand