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
Search WWH ::




Custom Search