Civil Engineering Reference
In-Depth Information
B ¼ C
0
þ
X
n
C
i
x
i
and with
C ¼ C
1
;
i¼2
the tangent elasticity module for the rope tensile stress r
z
on the stress-extension
curve between the tensile stresses r
z
= 0 and 800 N/mm
2
in an ''up-and-down''
direction is
C
r
z
þ
A
:
E
t
r
ðÞ
¼B
þ
ð
2
:
46
Þ
The constants A, B and C are listed in Tables
2.1
and
2.2
. The constant B for
wire ropes with fibre-covered steel cores in Table
2.1
has been changed unlike
constant B in Feyrer and Jahne (
1990
).
2.2.3.3 Rope Elasticity Module with the Lower Tensile Stress r
z
= 0
The extension e of a wire rope is
e ¼
Z
1
E
t
ð
r
z
Þ
dr
z
:
Using (
2.46
), the extension of a wire rope between the two stresses r
lower
and
r
upper
—in the stress-extension curve coming from r
z
= 0—in the ''up'' direc-
tion—is
r
upper
r
upper
e ¼
Z
dr
z
¼
Z
1
r
z
þ
A
up
dr
z
C
up
r
z
þ
A
up
B
up
r
z
þ
A
up
B
up
þ
C
up
B
up
þ
r
lower
r
lower
and after integration
e ¼
r
upper
r
lower
B
up
C
up
B
up
ln
r
upper
þ
A
up
þ
C
up
=
B
up
r
lower
þ
A
up
þ
C
up
=
B
up
:
ð
2
:
47
Þ
According to (
2.47
), the important rope elasticity module with the lower stress
r
lower
= 0 and the upper stress r
upper
is
E
S
ð
r
z
Þ
¼E
S
ð
0
;
r
z
Þ
¼
r
z
e
or
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