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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