Wire Ropes Under Tensile Load - Wire Ropes: Tension, Endurance, Reliability - page 71

The stresses in the wires induced by the alteration of the wire curvature are of
special interest. Together with the tensile stresses, they determine the endurance of
the strand or spiral rope in the case of fluctuating tensile force.
The bending stress is

d
2 E

1

q 1

r b ¼ ð 2 : 37 Þ

q 0

or with ( 2.35 )

d
2 E :

sin 2 a
r

sin 2 a 0
r 0

r b ¼ ð 2 : 37a Þ

The torsion stress is

Þ d s ¼ T T 0 ð

2 G

ð 2 : 38 Þ

and with ( 2.36 )

d
2 G :

sin a cos a
r

sin a 0 cos a 0
r 0

s ¼ ð 2 : 38a Þ

In addition to the symbols already known, d is the wire diameter. The index 0 is
again of value for the initial state and the symbols without indices designate the state
under the effect of tensile force. E is again the elasticity module and G is the shear
module. The bending and torsion stresses were first calculated by Schiffner ( 1986 ).

Example 2.2: Additional stresses in a spiral rope
Calculation of the bending and torsion stresses in the wires of an open spiral rope
according Fig. 2.4 with the global wire rope stress r z = 300 N/mm 2

(neglecting

the influence of the point pressure between the crossing wires).
The winding radius under the effect of the tensile force is (neglecting the small
higher tensile stress in the centre wire) with r t = r t,1,2,3

¼ 0 : 99953r 0i

¼ r 0i

1 m r t
E

308
196 ; 000

r i ¼ r 0i 1 0 : 3

and the lay angle

1 0 : 3 308
196 ; 000

1 m r t
E

sin a ¼ sin a 0 ¼ sin a 0

:

1 þ r t
E

308
196 ; 000

1 þ

a 0 ¼ 14 ; sin a 0 ¼ 0 : 24192; cos a 0 ¼ 0 : 97030
sin a ¼ 0 : 9980 sin a 0 ¼ 0 : 9980 0 : 24192 ¼ 0 : 24144
cos a ¼ 0 : 97042 :