Civil Engineering Reference
In-Depth Information
Fig. 2.2 Tensile force of a
strand wire neglecting the
small shear force
S
i
F
i
ʱ
i
U
i
M
i
¼ F
i
r
i
sin a
i
or
M
i
¼ S
i
r
i
tan a
i
ð
2
:
11
Þ
These equations from Berg (
1907
) have since been used by nearly all
researchers, as for example Heinrich (
1937
), Costello (
1997
), Costello and Sinha
(
1977b
). Only Dreher (
1933
), who first did extensive investigations into wire rope
torsion has introduced a basic equation deviating from (
2.9
). But Dreher's equation
is of no value for use with real wire ropes as Heinrich (
1942
) has already shown.
Dreher's equation is only true for a simple wire helix not supported by a strand
centre.
A length-related radial force exists between the wire helix and the centre wire
or a wire layer (or between a helix strand and the core) in a wire rope under a
tensile force. The length-related radial force (when neglecting the bending moment
and torque) is
sin
2
a
i
r
i
q
i
¼
F
i
q
i
¼
F
i
:
ð
2
:
12
Þ
2.1.4 Wire Tensile Stress in the Strand or Wire Rope
2.1.4.1 Wire Tensile Stress in Strand or Spiral Rope
The first to work out a partition of the wire rope tensile force in wire tensile forces
was Benndorf (
1904
). The following determination of the tensile stress follows his
work. Out of the last chapter with (
2.9
), the wire tensile force component in strand
axe direction (neglecting the small shear force) is
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