Wire Ropes Under Tensile Load - Wire Ropes: Tension, Endurance, Reliability - page 130

q

1 2 r j

DL j
L

x tan b j r j ¼ x 2 1 : ð 2 : 97d Þ

r j is winding radius of a strand j and

b j is lay angle of a strand j.

The length changes of the wire helix and the strand helix can be calculated
independently from each other.

2.4.6.3 Longitudinal Stress

With practically all rope terminations the relative motion of the wires and strands
in straight ropes are prevented and the cross-sections remain plane when the rope
is twisted. By preventing the relative motions, longitudinal forces are induced by
extensions e of the wires and strands. The sum of the components in the rope axis
direction of all these forces is

X S i ; j ¼ 0 :

ð 2 : 97e Þ

The stress in a wire i of a wire rope with fibre core and only one strand layer
will be looked at a great detail as an example. The unimpeded wire elongation Dl i,1
is transformed to the common strand elongation Dl 1 as a real elongation. Then the
component in the strand axis direction from the necessary longitudinal force of the
wire i is with the same elasticity module E for all wires

S i ; 1 ¼ Dl 1
l 1

E Dl i ; 1
l 1

A i ; 1 A i ; 1 E : ð 2 : 97f Þ

With the abbreviation

A i ; 1 ¼ z i ; 1 cos i ; 1 d i ; 1

p = 4

and

A 1 ¼ X A i ; 1

is according to ( 2.97e )

0 ¼ X

n w

Dl i ; 1
l 1

A i ; 1 Dl 1
l 1

A 1 :

i¼0

From that the common extension of the strand is