Civil Engineering Reference
In-Depth Information
Fig. 3.10 Ovalised rope in a
sheave groove
d
s
ʴ
r
s,ov
r
the rope takes on the radius of the groove. Outside this contact bow, the cross-
section is deformed in unknown way.
Schiffner (
1986
) calculated the bending and torsion stress due to rope ovali-
sation. For this, he substituted the round rope cross-section by an ellipse with the
same area and then calculated the stresses arising from the curvature changes of
the space curves before and after ovalisation. In contrast to the bending stress, the
torsion stress arising from ovalisation is small enough to be neglected.
As an example the bending stress at the bottom of the groove can be found
calculate the bending stress
d
sin
2
b
ov
r
S
;
ov
sin
2
b
r
S
r
b
;
ov
¼
2
E
:
The winding radius of the strand with a round form is
r
S
¼
d
2
d
S
:
2
In Fig.
3.10
, with r for the groove radius (and supposing that the strand cross-
section remains unchanged), the winding radius of the strand in an ovalised rope is
r
S
;
ov
¼ r
d
S
2
:
The lay angle of the strand is hardly changed at all by rope ovalisation and so it
can be set as b = b
ov
. The groove radius is normally r = 0.53d. If, for example,
the rope diameter is equal to the nominal rope diameter d, the centre wire diameter
is d = d/16, the strand lay angle is b = 18, then the bending stress of the strand
centre wire due to ovalisation is
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