Wire Ropes Under Bending and Tensile Stresses - Wire Ropes: Tension, Endurance, Reliability - page 249

Fig. 3.60 Longitudinal wire
stresses as the rope runs over
a sheave, Schiffner ( 1986 )

˃ zs3

˃ aB

2

˃ 2

˃ mB

˃ l

˃ zs4

time t

Fig. 3.61 Longitudinal wire
stresses under combined
fluctuating tension and rope
bending

2
aB

˃

a comb

2 ˃

˃

0,1

z

ʔ ˃ =1,1 ʔ ˃

˃

l z m comb

˃

z

)

˃ = 1,1( ˃ ʔ ˃ -

u z z

time t

Based on Sects. 2.1 and 3.1 [and using in particular the work of Andorfer ( 1983 ),
Schiffner ( 1986 ) and Wang ( 1989 )], these stresses will be derived with some
simplifications for the most interesting wires on the bottom of the sheave. By
bending the rope—taking the bending stress, the ovalisation stress and the sec-
ondary tensile stress into consideration—the amplitude of the longitudinal stress is

r aB ¼ 72 ; 500 d

d d D þ 300 d d þ 0 : 1 r z

ð 3 : 63 Þ

and the middle stress

r mB ¼ r z þ r aB : ð 3 : 64 Þ

For the combined fluctuating tension and bending, the amplitude of the lon-
gitudinal wire stress is

r a ; comb ¼ r aB þ 1 : 1 Dr z r z
2

ð 3 : 65 Þ

and the middle stress is
r m ; comb ¼ 1 : 1 ð r z Dr z Þþ r a ; comb : ð 3 : 66 Þ