Civil Engineering Reference
In-Depth Information
• The mean standard deviation for the breaking number of bending cycles for
pieces of the same wire rope under the same stress condition (to see as example
in Fig. 3.45 )islgs = 0.047. Solo-distribution.
• Again for pieces from the same wire rope but under different stress condition (to
see as example in Fig. 3.34 ), the mean standard deviation for seventeen wire
ropes is lg s = 0.111 (and the mean coefficient of determination is B = 98.0 %).
• From several ropes of one class the standard deviation for the breaking number
is lg
s = 0.19 to 0.28 (to see as example in Fig. 3.36 ). Class-distribution
All these standard deviations belong to a bending length l = 60d.
The number of bending cycles N 10 at which—with a certainty of 95 %—not
more than 10 % of such wire ropes are broken or have to be discarded, can be
calculated by
lg N 10 ¼ lg N k T lg s :
ð 3 : 49a Þ
The constant k T stands for a mean ratio between N and N 10 that is in reality
smaller in the middle of the region being considered and greater at the edges,
Stange ( 1971 ).
From bending tests with Filler ropes 8 9 (19 + 6F) - FC - sZ, the breaking
numbers of bending cycles are drawn in Fig. 3.35 and the discarding number of
bending cycles in Fig. 3.36 . In addition to the test results (as points), these
Figs. 3.35 and 3.36 also include the lines for the calculated number of bending
cycles from ( 3.49 ) and ( 3.49a ). The thicker lines show the mean number and the
thinner lines the numbers of the 10 % limit. As Figs. 3.35 and 3.36 show, the 10 %
lines provide safe limits for the test results.
3.2.2.2 Strength
Woernle ( 1929 ) and Müller ( 1966 ) carried out some bending tests with wire ropes
of different strengths. They both found that the rope endurance only increases a
little with increased rope strength. For a nominal rope strengthR 0 = 1,370 N/mm 2
up to R 0 = 1,770 N/mm 2 , Shitkow and Pospechow ( 1957 ) observed an increase in
the numbers of bending cycles that does not continue into the next higher rope
strength R 0 = 1,960 N/mm 2 .
Wolf ( 1987 ) evaluated a large number of bending tests with wire ropes of
different strengths. He found that the endurance increases slightly with the
strength. A regression calculation has been derived from a new evaluation of these
and other results, Feyrer and Vogel ( 1992 ). For this regression calculation, the
tensile force S for ropes with the nominal strength R 0 has been defined in relation
to those with the mean nominal strength 1,770 N/mm 2 .
c
R 0
1,770
S ¼ S 1770
ð 3 : 51 Þ
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