Civil Engineering Reference
In-Depth Information
Fig. 3.58 Course of
longitudinal stress under
independent bending and
fluctuating tension
2 ˃ aB
2 ˃ aZ
fluctuating
tension
rope bending
time t
Fig. 3.59 Course of
longitudinal stress under
combined fluctuating tension
and bending
rope bending
change of rope
tensile force
2 ˃ a comb
time t
bending is shown. In this type, the stress amplitudes of the two loadings—the
fluctuating tension and the bending—do not influence each other. The rope
endurance can be calculated for the independent loadings and summarized with the
help of the Palmgren-Miner-Rule. This independent tension and bending—which
is very rare—will not be considered in the following passage.
Combined fluctuating tension and bending causes increased amplitude in the
longitudinal wire stress. The course of the longitudinal wire stress is shown in
Fig. 3.59 . In the case of combined loadings, the endurance could be evaluated by
means of tests. However, because of the numerous possible combinations of
tensions and bending cycles, it is necessary to find a method which is a combi-
nation of the results of bending tests and a theoretical back-up. From the stresses of
the two combined loadings, an equivalent tensile stress r equ or equivalent tensile
force S equ
r equ ¼ f S5
r z
or
S equ ¼ f S5
S :
ð 3 : 62 Þ
will be derived, with that the number of bending cycles N comb for combined
tension and bending can be calculated using ( 3.55 ), Feyrer ( 1993 ).
As can be seen in Figs. 3.60 and 3.58 , the amplitude and the middle of the
fluctuating longitudinal stress both increase under combined tension and bending.
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