Civil Engineering Reference
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rope diameter. Of the two 8 9 19 ropes, one has a fibre core and the other a steel
core. The contact angle for the rope with a fibre core is 5-20 % greater than for the
rope with a steel core.
As an example the relative rope pressure k/p 0 over the sheave groove (winding
angle # and groove angle c) is drawn in Fig. 3.25 from Häberle.
3.1.8 Force on the Outer Arcs of the Rope Wires
The rope-pressures k and k max are only comparable values but not really existing
pressures. The real wire pressure (the material pressure) can be derived from the
contact force between the outer arcs of the rope wires and the groove. In the
following this force executed by the outer wire arcs of a rope will be called wire
arc force. The maximum wire arc force on bottom of the groove can be calculated
using the maximum rope pressurek max from ( 3.33 )
F Wcal ¼ k max A f :
ð 3 : 34 Þ
In this, the area A f related to the arc force of one wire as a part of the rope
surface A rope in one lay length h S is
A f ¼ A rope
z K
:
ð 3 : 35 Þ
According to Recknagel ( 1972 ), the number of wire arcs on the rope surface in
one lay length h S is
:
h S
h W cos b 1
z K ¼ z S z W
ð 3 : 36 Þ
In this, z S is the number and h S the lay length of the outer strands of the rope, z W
is the number of outer wires and h W the lay length of these outer wires, b is the lay
angle of the outer strands. Then, using ( 3.34 )-( 3.36 ), the calculated maximum
force on the wire arcs is
p d h S
z S z W h S
:
F Wcal ¼ k max
ð 3 : 37 Þ
h W cos b 1
This calculated maximum arc force F Wcal is only true for a perfectly round rope.
This is normally not the case. This means that in a real wire rope some of the arcs
of the wires bear a very high force and others even do not come into contact with
the groove at all. Between these two extremes, there are varying degrees of force
existing for the arcs. Häberle ( 1995 ) measured the real forces for the arcs of the
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