Civil Engineering Reference
In-Depth Information
a c
1 F R = F m
1 S 0 = F m
A c ¼
:
ð 3 : 74 Þ
The wire rope force S 0 is the tensile force that is used during the bending fatigue
test. In practice the measured rope breaking force F m , which is unknown, can be
replaced on the safe side by the calculated breaking force F m & F c = F min /k
(minimum breaking force/spinning loss factor). The exponent is a c = 0.203
1.664 uc . For the relative number of bending cycles with the limits c = 10, 50 and
90 %, the exponents are a 10 = 0.106; a 50 = 0.203 and a 90 = 0.39.
Parallel bearing wire ropes (redundant bearing ropes) have the advantage that if
one of these ropes breaks, the other wire ropes can survive. The probability that the
other rope or the other ropes do not break depends mainly on the relative number
of bending cycles A c at which the residual breaking forceF R is still the same as the
impact force S S . This impact force occurs in the survival ropes when one of the
ropes breaks, Feyrer ( 1990c ).
With Eq. ( 3.74 ) and equations for the impact force and the rope endurance the
survive respectively failure probability can be calculated, see Fig. 3.78 , Sect. 3.3 .
3.2.8.2 Rope Diameter Reduction
During the life time of a wire rope running over sheaves, the rope diameter will be
continually reduced. The relative rope diameters measured in the course of
bending fatigue tests with different tensile forces are shown in Fig. 3.65 for a rope
with fibre core and in Fig. 3.66 for a rope with steel core. The wire rope diameter
in these figures is the rope diameter measured under the tensile force used for the
bending fatigue tests.
Both of these figures show that a large diameter reduction of about 10 % only
occurs for the very small specific tensile force S/d 2 = 29 N/mm 2 with a very high
rope endurance. In practical applications, diameter reduction can be much greater
with outside wear. Such a rope diameter loss can cause a severe reduction of the
rope breaking force. Therefore, in rope inspections the diameter of the wire rope
has to be looked at as a possible discard criterion.
3.2.8.3 Wire Rope Elongation
In the course of bending fatigue tests, an elongation of the rope occurs. This
elongation has been measured by Woernle ( 1929 ), Hankus ( 1985 ), Winkler (1988)
and others. The historical Fig. 3.67 shows the typical course of rope elongation.
During the first bending cycles, the wire rope will be strongly elongated, then over
a longer period the rope elongation is small and only close to the end of its
working life will the rope be progressively elongated again. In principle, this
progressive increase in the elongation shows the imminent breakage of the rope.
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