Civil Engineering Reference
In-Depth Information
The elastic rope elongation is
DL
E
¼ e
E
L ¼
r
z
E
S
L ¼
S
0
þ
m
g
L
=
2
A
E
S
L
:
DL
E
¼
10
;
000
þ
2
;
180
87
:
5
71
;
000
500 ¼ 0
:
979 m
:
The shortening by twisting of the rope supported non-rotated at both ends is
much less than the elastic rope elongation. In comparable cases, this rope short-
ening can always be neglected.
According to (
2.99
) and with extension e
D
(x = 500) = 0.00378 according to
(
2.97a
), the lay angle of the twisted rope is on the upper end
b
0
ð
x ¼ 500
Þ
¼arctan
tan b
r
x
1
þ
e
D
¼ arctan
0
:
364
0
:
0059
1
:
789
1
þ
0
:
00378
¼ 19
:
40
and with the elastic rope extension e
E
(x = 500) = 0.00231 the lay angle is
b
00
ð
x ¼ 500
Þ
¼arctan
tan b
r
x
1
þ
e
D
þ
e
E
¼ 19
:
35
:
Example 2.13c: Suspended wire rope without rotation protection at the lower end,
continuation of Example 2.12
For the twisted wire rope, the integration of (
2.98
) leads to the rope elongation
DL
D
¼ 2
:
62 m
:
The elastic rope elongation is
DL
E
¼
e
E
L
¼
r
zm
E
S
L
¼
m
g
L
=
2
A
E
S
L
:
2180
87
:
5
59
;
000
500 ¼ 0
:
000422
500 ¼ 0
:
211 m
:
DL
E
¼
According to (
2.99
), the lay angle of the twisted rope on the upper end is
b
0
ð
x ¼ 500
Þ
¼arctan
tan b
r
x
1
þ
e
D
arctan
0
:
364
0
:
0059
4
:
765
1
þ
0
:
00979
¼ 18
:
40
and,
together
with
the
elastic
rope
extension
on
the
upper
rope
end
e
E
(500) = 0.000844, the lay angle is
b
00
ð
x ¼ 500
Þ
¼arctan
tan b
r
x
1
þ
e
D
þ
e
E
0
:
354
0
:
0059
4
:
765
1
þ
0
:
00979
þ
0
:
000844
¼ 18
:
38
¼ arctan
On the upper end, the lay length of the twisted and elastic elongated rope is
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