Wire Ropes Under Bending and Tensile Stresses - Wire Ropes: Tension, Endurance, Reliability - page 307

Acceleration a 0 = 1.5 m/s 2
Diameter of traction sheave D T = 6,000 mm
Diameter of deflection sheave D R = 6,000 mm
Bending length l = 40,000 mm.

Analysis:
The rope pieces above the cage I and II are those
stressed most strongly. Under the action of
acceleration or deceleration, these pieces may
have a bending length l = 40 m. The loading
sequence shown in the figure on the left is taken
from the rope piece above cage I. The rope pieces
not running over a sheave and the attachment are
counted as part of the cage mass F.
The loading sequence shown in the figure on
the left is taken from the piece above cage I.
The loading sequence has been subdivided into
loading elements in a most unfavourable way.
They are finally transformed into the standard
loading elements and marked with symbols for
the acting forces (from the load mass Q; the
cage mass F, the mass of rope s or the balance
rope s b ; the moving resistance force K and the

Q Q S

Q

S

F up down F

loading sequence

loading elements

-a +a +a -a

+K -K +K -K

Q
s
F

Q
s
F
1

Q
s
F

s
F

2 3 4

standard loading elements

acceleration or deceleration a 0 ).
Tensile forces:
The tensile forces of the rope during bending are

S 1 ¼ ð F þ Q þ s Þð g a 0 Þþ K ¼ 266,000 N :
S 2 ¼ ð F þ s Þð g þ a 0 Þ K ¼ 230,000 N :
S 3 ¼ ð F þ Q þ s Þð g þ a 0 Þþ K ¼ 359,100 NS 0 ¼ F g ¼ 68,700 N
ð S 3 S 0 Þ= S 3 ¼ 0 : 8087 f S5 ¼ 2 : 246
S3equ ¼ S 3 f S5 ¼ 806,400 N :
S 4 ¼ ð F þ Q þ s Þð g a 0 Þ K ¼ 250,000 N

Number of bending cycles:
According to ( 3.55 ) for the mean discarding numbers of simple bending cycles and
together with ( 3.89 ) for reverse bending cycles, the bending cycles are