Wire Ropes Under Bending and Tensile Stresses - Wire Ropes: Tension, Endurance, Reliability - page 184

3.1.2 Secondary Tensile Stress

3.1.2.1 Displacement of Wires and Strands

Strands and wire ropes can only be bent over sheaves because the wires in the
strands and the strands in the rope are able to move against each other. When a
strand is bent the wires generally move in the direction of the wire axis as shown in
Fig. 3.6 . For reasons of symmetry, it follows that the inner and the outer wire
element of the strand bow lie unchanged in the same position before and after the
strand is uniformly bent, Schmidt ( 1965 ). By changing the bending state uni-
formly, the wire elements will be only displaced in the wire bow between both of
these fixed points. The displacement of the wire elements are calculated using the
position of the wire before and after the bending of the strand.

(a) Constant ratio of the winding angles # /u

For constant ratio of the winding angles # /u in a strand (shortened symbols
u = u W and r = r W ), ( 3.3 ) is valid

#
u ¼

r

: ð 3 : 3 Þ

D
2

tan a 0

Together with ( 3.3b ) the circle bow length dL around the sheave centre as
component of the wire element length dl in the bent strand is

D
2 þ r cos u

r

dL ¼ du :

D
2

tan a 0

The wire element length is

q

dL 2 þð r du Þ 2

dl ¼

Fig. 3.6 Wire displacement in a uniformly bent strand