Wire Ropes Under Tensile Load - Wire Ropes: Tension, Endurance, Reliability - page 101

2

2 n L
t

S ¼ m r : ð 2 : 64 Þ

For very large rope fields, Zweifel presented equations to calculate the rope
tensile force considering the chain line.

Example 2.6: Rope tensile force from the running time of the transverse wave

Data:
Seale rope 6 9 19-NFC-zZ
rope diameter d = 20 mm
distance between rope terminations L = 250 m
number of cycles n = 12
running time t for n cycles t = 40 s

Results:
According to Eq. ( 1.5b ) and Table 1.9 , the length-related mass m r of the rope is

1
100 W 1 d 2 ¼

1
100 0 : 359 20 2 ¼ 1 : 436

m r ¼ kg/m

Then according to ( 2.64 ), the rope tensile force in the middle of the rope field is

S ¼ m r ð 2 n L
t

Þ 2 ¼ 1 : 436 ð 2 12 250
40

Þ 2 ¼ 32 ; 300 N :

2.2.4.4 Transverse Vibrations

Transverse vibrations are to be understood as standing waves. The equations for
the velocity of the waves can be used to calculate the frequency. Because the wave
length is large, the influence of the bending stiffness is very small and can be
neglected. So ( 2.62 ) can be used and the running time of the wave, there and back,
is

r

m r
S

t L ¼ 2 L
t

¼ 2 L : ð 2 : 65 Þ

In this, L is once again the rope length (or the distance between the ends of the
rope for a small curvature). The period T of a standing wave is

T ¼ t L
i