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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