Civil Engineering Reference
In-Depth Information
e ¼
Dl
S
l
S
;
the rope elasticity module for strands and spiral ropes is
X
n
E
S
¼
1
A
z
i
cos
3
a
i
1
þ
m
i
sin
2
a
i
E
i
A
i
:
ð
2
:
44
Þ
i¼0
Poisson's ratio can be set m = m
i
= 0.3 for all wire diameters and winding radii
in steel spiral ropes because the length-related force between the wire layers is
small and the lateral contraction is almost only caused by the tensile stress in the
wires.
Example 2.3: Elasticity module of an open spiral rope according to Fig.
2.4
According to (
2.44
) the rope elasticity module is
Þ
0
:
9703
3
E
S
¼
196
;
000
45
:
61
1
:
431
þ
6
þ
12
þ
18
ð
1
:
227
1
þ
0
:
3
0
:
2419
2
E
S
¼ 177
;
000 N/mm
2
:
The rope elasticity module for strands and spiral ropes calculated by (
2.44
)is
independent from the rope tensile stress. But in reality this rope elasticity module
always depends slightly on the stress level and it is always a little smaller than the
one calculated. This means, the smaller the stress level and the higher the number
of wires in the rope, the bigger the difference. The calculated rope elasticity
module can only be reached approximately with a strong pre-stressing.
A reference value for the elasticity modules of closed spiral ropes for bridges
which have not been pre-stressed is given in Fig.
2.10
by DIN 18809. This shows
elasticity modules with different definitions:
• E
g
rope elasticity module for the first loading up to the permanent load
• E
p
rope elasticity module for the traffic load
• E
A
rope elasticity module for defining the rope length
• E
B
rope elasticity module during bridge erection
2.2.3 Rope Elasticity Module of Stranded Wire Ropes
Because of its lateral contraction, the rope elasticity module of stranded ropes
cannot be calculated in the same way as that of strands or spiral ropes. The lateral
contraction of the stranded ropes depends on a large unknown quantity at the
tensile stress level. Therefore, the elasticity module of stranded ropes can only be
evaluated by taking measurements.
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