Wire Ropes Under Bending and Tensile Stresses - Wire Ropes: Tension, Endurance, Reliability - page 186

Using ( 3.3a ) and ( 3.3c ), the length of the wire in the bent strand (lay angle
a = const.) is

r
sin a du

r
sin a u ;

dl ¼ and l ¼

and it has the same length as a wire in a straight strand. For every wire winding
angle u, a wire element will be displaced over a winding angle D #

D # ¼ # u

p #ð u ¼ p Þ:

ð 3 : 4a Þ

According to ( 3.4 ), the winding angle # for u = 180 is

p

s

D
2 r

#ð u ¼ p Þ ¼ :

2

tan a 1

Using ( 3.3b ) and D # from ( 3.4a ), the length of the displacement bow is

:

D
2 þ r cos u

DL ¼ D #

The equations for the displacement of the wires in the strand are also valid for
the displacement of the strands in the rope. For this, the lay angle a is to be
replaced by b and r = r S and u = u S .
The clearance between the wires is always small and the clearance between the
strands is normally small or the strands are more or less fixed laterally by the core.
Therefore, at most, the wire and the strand helix show a nearly constant ratio of the
winding angles.

Example 3.1 Strand displacement by bending the rope

Data:
Diameter ratio of sheave and rope D/d = 25

Lay angle b = 20

Winding radius (8 strand rope with steel core) r/d = 0.363

Results:
For a rope with a constant ratio of the winding angles, the strand displacement in
strand direction for u = 90 is s/d = 0.0273
Theoretical ratio of strand length in bent or straight rope l/l 0 = 1.0000218
Theoretical tensile stress in the strand r th = 4.27 N/mm 2