Wire Ropes Under Tensile Load - Wire Ropes: Tension, Endurance, Reliability - page 78

2.2 Wire Rope Elasticity Module
2.2.1 Definition
The elongation behaviour of materials under the effect of mechanical stresses is
described by elasticity modules. The elongation of a wire rope depends, of course,
on elasticity module for wire materials, but the wire rope elasticity module
describing wire rope elongation differs from the wire elasticity module. The rope
stress-extension curve is not linear. Therefore, for a certain wire rope, the wire
rope elasticity module is not constant but depends on the tensile stresses.
As far as strands and spiral ropes are concerned, there is only minimal non-
linearity and this can be neglected in most cases. The wire rope elasticity module
for these ropes can be calculated approximately using analytical methods (see
Sect. 2.2.2 ), but this is not true for stranded ropes as their rope elasticity modules
can only be evaluated by measurements, and—because of the non-linear stress-
extension curve—the wire rope elasticity module resulting from these measure-
ments can only be given with a correct definition of the loading.
The main rope elasticity modules which are of importance for practical usage
are:
• E S (r lower , r upper ) as secant between both of the wire rope stresses with a load
reverse at the beginning stress (this is especially the case for fluctuating tensile
stresses) and, as a special case of this,
• E S (0, r upper ) with the lower stress 0.
Here, and in the following, the stresses refer to the wire rope stresses r z = S/A
with the rope tensile force S and the metallic cross-section A of all rope wires. The
index z normally used for the global wire rope stress is left out here for simpli-
fication (r z,lower = r lower and r z,upper = r upper ).
The rope elasticity modules defined in this way are always meant if they have
not been described expressly in a different way. Here it is important that a stress
reverse takes place at the starting stress. The rope elasticity module as secant
between two points on a stress-elongation curve (without stress reverse at the
beginning) is of no practical importance.
The tangent elasticity module defined by a tangent on the stress-extension curve
will be only used in special cases. But later on this tangent elasticity module E t
will be used as an assisting parameter for evaluating the stress-extension curve to
find out the rope elasticity module E S (r lower ,r upper ), see Sect. 2.2.3 . The mea-
surements of the stress-extension curves for this have always been taken between
the lower stress r lower = 0 and the upper rope stress r upper = 800 N/mm 2 .
Because of this, it is not necessary to show either of these end stresses in the
symbol of the tangent elasticity module. The tangent elasticity module (as assisting
parameter) on the stress-extension curves between the rope tensile stresses 0 and
800 N/mm 2 in the up-and-down direction are therefore given by the symbols
where only the rope tensile stress in the tangent point is nominated: