Civil Engineering Reference
In-Depth Information
According to these equations with rotary bending stress r rot = ± 90 0 N/mm 2 as
an example, the mean number of bend in g cycles for new wires is N ¼ 13,000
( 1.2d ) and for wires taken from ropes N ¼ 34,000 ( 1.2a ). As an additional test
result Briem ( 2000 ) found a 19 % smaller endurance for zinc-coated wires than for
bright wires.
The endurance of the wires depends on the size effects of the two parameters,
the wire diameter and the wire length where the wire is stressed (bending length or
stressing length). The wire diameter cannot change in isolation. That means, with
the wire diameter, the other parameters which influence endurance will always
also be changed. Therefore, to find out the influence of the wire diameter, the other
parameters which influence wire endurance should be kept as similar as possible
and there should be a wide range of different wire diameters. As already men-
tioned, the influence of the wire diameter on the wire fatigue endurance is only
known in a first form using the given results represented by Eqs. ( 1.2b ) and ( 1.2c ).
The influence on wire endurance of the wire length, which is the other
parameter affecting the size, can be evaluated reliably by conducting tests with
parts of one and the same wire and theoretically with the help of the reliability
theory. A series of wire fatigue tests done by bending over one sheave have been
used to evaluate the influence of the bending length, Feyrer ( 1981 ). The wire
diameter is d = 0.75 mm, the measured tensile strength is R m = 1,701 N/mm 2 .
The wire bending diameter over the sheave is 115.75 mm; with these conditions
the wire bending stress is r b = 1,270 N/mm 2 . The constant tensile stress from a
loaded weight is r t,m = 400 N/mm 2 . For the test bending over one sheave, the
wire is loaded by
the middle stress r m ¼ r t ; m þ r b = 2 ¼ 1,035 N/mm 2
and the stress amplitude r a ¼ r b = 2 ¼ 635 N/mm 2 :
The test results are shown in Fig. 1.13 . Together with the points taken from the test
results, t he figure shows the curves calculated for the mean number of bending
cycles N and the limiting number of bending cycles for 10 and 90 % probability.
The calculation of these curves is based on the reliability theory.
The survival probability is the smaller the larger the bending length l (as a
string of bending lengths l 0 ) of the wire being considered is. For a given survival
probability P 0 of the wire bending length l 0 , the survival probability P(l) of the
wire with the bending length l is
P ð l Þ¼ P ð l Dl Þ=ð l 0 Dl Þ
0
:
ð 1 : 2e Þ
The bending lengths l and l 0 are the theoretical lengths without considering the
bending stiffness of the wire. These lengths would occur for bending limp yarn.
For the wire near the sheave, the fluctuating bending stress is small. The short
bending length Dl is introduced to take this into account. Dl is the shorter part of
the bending length having the smaller radius difference of the rope curvature than
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