Wire Ropes Under Tensile Load - Wire Ropes: Tension, Endurance, Reliability - page 123

u ¼ c 1 ð L x Þ

c 2 d c 1 c 3 d G

c 2 m g sin b F
ln c 2 d 2 ð m g x sin b F þ S 0 Þþ c 3 G d 4
c 2

G d 4 :

ð 2 : 86a Þ

d 2 ð m g L sin b F þ S 0 Þþ c 3

The maximum rotary angle u max occurs at the lower end of the rope, that means
for x = 0. The most interesting maximum twist angle x max occurs at the upper
rope end, for x = L.
According to ( 2.85 ), the maximum twist angle is

c 1 d ð S 0 þ m g L sin b F Þ
c 2 d 2 ð S 0 þ m g L sin b F Þþ c 3 G d 4 :

x max ¼ ð 2 : 85b Þ

For the practical calculation of the rotary angle u and the twist angle x, the
Excel-program FREEDRE2.XLS can be used.

Example 2.12: Suspended wire rope without rotation protection at the lower end

Data:
The same data will be used as in Example 2.11, but the tensile force at the lower
rope end is S 0 = 0.

Results:
According to ( 2.93 ), the maximum rotary angle at the lower rope end is

u max ¼ 15,202 81 ; 795 ln 0 : 8433 ¼ 15 ; 292 þ 13 ; 943
u max ¼ 1 ; 259 rad :

With that, the number of rope turns at the lower end is

n max ¼ u max

2p ¼ 1 ; 259

¼ 200 : 4 :

2p

According to ( 2.94 ), the maximum twist angle (rotary angle per length unit at
the upper rope end) is

x max ¼ 4 : 766 rad = m ! x max ¼ 273 ^ = m ! x max ¼ 437 = 100d

The numbers are given with four or more digits to make it easier to follow the
calculation. But, of course, the results are only valid in a scattering following the
standard deviation of the constants c from Table 2.6 . Above that, the maximum
twist angle 437/100d exceeds the limit 360/100d for the validity of the constants.
But for the rope considered here according to Fig. 2.23 , there is practically no
change of the constants c to be expected.