Civil Engineering Reference
In-Depth Information
or
R
0
1,770
:
lg S ¼ lg S
1770
þ
c
lg
S
1,770
is the tensile force in (
3.49
) and their constants a
i
for the mean nominal
tensile strength 1,770. Using (
3.49
) the ratio of the bending cycles N/N
1,770
is
given by
lg
N
1
;
770
¼ b
1
þ
b
3
lg
D
N
S
S
1
;
770
lg
ð
3
:
51a
Þ
d
With (
3.51
)in(
3.51a
) the ratio of the numbers of bending cycles as a function
of the rope strengths is
lg
N
N
1
;
770
¼ c
b
1
þ
b
3
lg
D
d
R
0
1
;
770
lg
ð
3
:
51b
Þ
The regression calculation has been based on (
3.51b
). The mean exponent
c found for all bending tests is c = -0.408. The part-results for the diameter ratios
D/d = 10; 25 and 63 for the breaking number of bending cycle is c = -0.370; -
0.348 and -0.408 and for the discarding number of bending cycles c = -0.561; -
0.390 and -0.355. The influence of the constant -0.561 is very high and relatively
unsafe because of the small gradient for small diameter ratios D/d. Therefore, the
constant has been finally set at c = -0.4.
An example is given in Fig.
3.37
showing the ratio of the number of bending
cycles for different nominal tensile strengths. A line has been drawn for c = -0. 4
and for c = -1. The line for c = -1 means that the ratio of the bending cycle
would increase proportionally with the nominal tensile strength, which is appar-
ently not the case.
3.2.2.3 Rope Diameter, Size Effect
The endurance factor for the rope diameter f
d
can be lead back to Shitkow and
Pospechow (
1957
) who, in their topic ''Drahtseile'', presented a chart in which the
relationship f
d
¼
ð
d
=
16
Þ
0
:
32
is to find. This relation has been integrated so far in
the calculation of the numbers of rope bending cycles in the first edition. Ciuffi and
Roccati (
1995
) stated—with reference to the Fig.
3.38
of Müller (
1966
)—that the
exponent should be greater than -0.32. A study, carried out from Virsik (
1995
)
under Feyre´s supervision, confirmed still this exponent. However, the doubts have
been arisen whether that relation with the exponent -0.32 will show the realistic
rope diameter influence on the rope endurance. Therefore an investigation has
been started with a great number of rope endurance data, Feyrer (
2011
), to find a
realistic endurance factor for the rope diameter influence. The data for the
investigation come from the archivs of the Institut für Fördertechnik und Logistik,
Universität Stuttgart (Fig.
3.39
).
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