Civil Engineering Reference
In-Depth Information
M
i
¼ F
i
r
i
sin a
i
Q
i
r
i
cos a
i
þ
M
b
;
i
sin a
i
þ
M
tor
;
i
cos a
i
:
ð
2
:
5
Þ
The most recent equations for bending and torsion moment for a wire of the
wire layer i were developed by Czitary (
1952
) as follows
sin
2
a
i
r
i
sin
2
a
0i
r
0i
M
b
;
i
¼ E
i
J
i
ð
2
:
6
Þ
and
:
sin a
i
cos a
i
r
i
sin a
0i
cos a
0i
r
0i
M
tor
;
i
¼ G
i
J
pi
ð
2
:
7
Þ
In addition to the known symbols, there is E
i
the elasticity module, G
i
the shear
module, J
i
the equatorial and J
pi
the polar moments of inertia of a wire in the wire
layer i. The index 0 means the state before loading by a tensile force. As before,
the parameters without the index 0 show the loaded state.
The portion of the strand torque for one wire of the wire layer i can be cal-
culated from (
2.3
), (
2.5
)-(
2.7
)
þ
M
tor
;
i
1
þ
cos
2
a
i
cos
3
a
i
:
M
i
¼ F
i
r
i
sin a
i
M
b
;
i
sin a
i
ð
2
:
8
Þ
Both of the moments M
bi
and M
ti
are very small, because the lay angle and the
winding radius alter only slightly under the tensile load. Therefore, the shear force
Q
i
is also very slight. As demonstrated by Czitary (
1952
), both moments and the
shear force can be neglected for the calculation of the wire tensile force F
i
.This
neglect only results in a very minimal deviation. With this, out of (
2.1
) the simple
relation for the tensile force in a wire in the layer i depicted in Fig.
2.2
is
S
i
cos a
i
F
i
¼
ð
2
:
9
Þ
and the circumference force out of (
2.2
)is
U
i
¼ F
i
sin a
i
or
U
i
¼ S
i
tan a
i
:
ð
2
:
10
Þ
According to (
2.4
), the portion of the strand torque for a wire in the layer i is
now
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