Wire Ropes Under Tensile Load - Wire Ropes: Tension, Endurance, Reliability - page 100

the acceleration due to gravity in m/s 2 ; g

q the length-related rope weight force in N/m;

the rope elasticity module in N/m 2 ;

E

the equatorial moment of inertia in m 4 ;

I

k is the wave length in m.

If a wire rope is knocked with a lead hammer, transverse waves of different
wave lengths will be initiated and run along the rope. As ( 2.61 ) shows, the velocity
of the wave increases with the decreasing length of the wave. The velocity of a
wave package with different wave lengths is therefore inhomogeneous with a
scatter which increases with time. The lead hammer method is therefore unsuitable
for evaluating the tensile force of a rope. Instead of this, Zweifel ( 1961 ) recom-
mended using the kind of impulse which produces a wave length which is as large
and homogeneous as possible so that the bending stiffness of the wire rope can be
neglected and ( 2.61 ) can be simplified to

s

g S
q

t ¼ :

With the length-related rope mass m r = q/g, the wave velocity is

r

S
m r

t ¼ : ð 2 : 62 Þ

The failure for the rope tensile force calculated is smaller than 1 % if the wave
length is at least k [ 250; 300 and 450d for the tensile rope stress r z = 600; 400
and 200 N/mm 2 , Zweifel ( 1961 ). The desired wave length k will be obtained if the
impulse brought on the rope is not too sharp and k/4 away from the end of the rope.
Zweifel recommended winding a fibre rope around the wire rope and pulling on
that shock-wise by hand. He supposed that the force of one hand was sufficient for
a wire rope of 20 mm diameter. For thicker wire ropes, it would be necessary to
have several persons pulling (increasing in number with the rope diameter
squared). After pulling, the fibre rope should be slightly stressed by hand, so that
the waves coming back can be sensed. For n cycles in the measured time t and for
the rope length L, the length of the rope from one end to the other, the wave
velocity is

t ¼ 2 n L
t

: ð 2 : 63 Þ

According to that and ( 2.62 ), the rope tensile force in the middle of the rope
field is