Wire Ropes Under Tensile Load - Wire Ropes: Tension, Endurance, Reliability - page 76

T ¼ du w

cos a
ds

¼ h S cos a
h W cos b

1
x 0 2 þ y 0 2 þ z 0 2

p :

Then according to ( 2.38 ), the torsion stress from the winding change is

: d

s ¼ T T 0

2 G :

When loaded by a tensile force, the wires elongate and contract. The strands
will be bent up like the wires in the straight strand under a tensile force. The wires
displace each other under the strand bending in core direction. The friction
between the wires induces a secondary tensile stress in the wires. Andorfer ( 1983 )
calculates this secondary tensile stress to be as Schmidt ( 1965 ) first indicated.
When the rope tensile force increases, the secondary tensile force increases in
the strand wire of the wire rope from the outside to the inside in the opposite
direction to the displacement. The displacement is restricted to the half lay length
of the strand wires. The resulting wire tensile force is bigger than the mean tensile
force in the wire sections lying directly on the core and smaller than that of the
outer wire sections. Contrary to the statement of Andorfer ( 1983 ), this is also valid
for ordinary lay ropes as well. The force induced by friction will be called sec-
ondary tensile force although the force can be either tensile or compression.
On the other hand, the secondary tensile force reverses its direction when the
rope tensile force decreases so that the resulting tensile force in the inner wire
sections is smaller and in the outer wire sections bigger than the mean wire tensile
force. The rope force reversal increases the wire stress amplitude in the case of
wire ropes loaded with fluctuating tensile forces.
The secondary tensile stress in a straight stranded rope can reach a considerable
size. This stress is especially responsible for the fact that well-lubricated stranded
wire ropes have a longer endurance under fluctuating tensile force than unlubri-
cated ones. The lubrication reduces the friction and because of that the secondary
tensile stress.
Supplementary to the fluctuating tests, Wang ( 1989 ) calculated the stresses in a
simple stranded rope ordinary lay FC-6 9 7-sZ with the diameter 12.2 mm. At
about the half endurance for the lower wire rope stress r z unt = 100 N/mm 2 (with
the indices of Wang) the rope extension is e sunt = 1.5 % and the lateral contraction
e q unt = 5.2 % and for the upper wire rope stress r z oben = 675 N/mm 2 the rope
extension is e s oben = 5.8 % and the lateral contraction e q oben = 9.8 %. For this
rope with fibre core between the lower and the upper rope tensile force the
transverse contraction ratio is m = 1.69 for the rope diameter and m = 1.88 for the
winding radius of the strand axis.
Wang ( 1989 ) presented the results of his calculation, done with the relatively
high friction coefficient l = 0.25, in Fig. 2.8 . The (global) rope tensile stress
range is 2r za = 575 N/mm 2 between 100 and 675 N/mm 2 . After Fig. 2.8
the maximum range of longitudinal stresses in the fibres of the lay wires is