Wire Ropes Under Tensile Load - Wire Ropes: Tension, Endurance, Reliability - page 79

Fig. 2.9 Definitions of the
wire rope elasticity modules
used

800
N
mm 2

˃ upper

E s ( ˃ lower, ˃ upper )

˃ lower

E t down ( ˃ z )

˃ z

E s (0, ˃ z )

E t up ( ˃ z )

rope extension ʵ

• E t,up (r z ) rope elasticity module as tangent on the stress-extension curve in the
up direction at the rope tensile stress r z
• E t,down (r z ) rope elasticity module as tangent on the stress-extension curve in
the down direction at the rope tensile stress r z
The rope elasticity modules in the different definitions used here are shown in
Fig. 2.9 .

2.2.2 Rope Elasticity Module of Strands and Spiral Ropes,
Calculation

As already mentioned, the non-linearity of the stress-extension curve is relatively
small for strands and spiral ropes. There is also only a small increase of the rope
elasticity module with the number of loadings. The smaller the number of wires in
the rope, the more likely this is to be true. Buchholz and Eichmüller ( 1988 ) found
that there was only the very small difference of DE = 600 N/mm 2 between the
first, second and third measurements with an almost constant rope elasticity
module E S = 198,000 N/mm 2 . Taking all these observations into consideration, it
is possible to make reliable calculations for the rope elasticity module for strands
and spiral ropes with a small number of wires. A method of calculation was first
devised for this by Hudler ( 1937 ).
The calculation can be done with the help of the equations from Sect. 2.1 . The
rope elasticity module is by definition

E S ¼ r z
e

:

With ( 2.21 ) for the tensile stress and the definition of the strand extension