Wire Ropes Under Tensile Load - Wire Ropes: Tension, Endurance, Reliability - page 97

6,75

‰

Warrington 8 19-CWR, sZ
after 10 th loading
main mass M = 2000 kg
dropping mass M A = 500 kg

6,50

6,25

6,00

5,75

5,50

5,25

5,00

4,75

0 5 10 15 20 s 25

time t

Fig. 2.17 Decay behaviour of a mass hanging on a wire rope, Wehking et al. ( 1999 )

E S ð 435 r a Þ ¼E S ð 400; 400 Þþð E S ð 600; 600 Þ E S ð 400; 400 ÞÞ 435 400

600 400 þ DE

E S ð 435 r a Þ ¼ 134 þð 141 134 Þ 35 kN/mm 2 :

200 11 ¼ 124

For the rope elasticity modules—evaluated using ( 2.50 ) and ( 2.52 )—the spring
constants according to ( 2.58 ) are

c S87 ¼ 83,000 45 : 1
12,000

¼ 312 N/mm ! 312,000 N/m and

c S435 ¼ 125,000 45 : 1
12,000

¼ 470 N/mm ! 470,000 N/m :

Without taking the damping into consideration, according to ( 2.57 ) the fre-
quency is then

f 0;87 ¼ 4 : 45 Hz and f 0;435 ¼ 2 : 44 Hz :

Under the influence of the damping, the amplitude (stress or extension) is
continuously reduced and the frequency is somewhat less. With the small damping
of the inner rope friction, the amplitude is