Wire Ropes Under Tensile Load - Wire Ropes: Tension, Endurance, Reliability - page 59

2.1.2 Real Stresses
The real stress in wires of the layer k is named r tk in opposition to the (global) rope
tensile stress r z . The real wire tensile stress r tk is bigger than the rope tensile stress
r z . In addition to the tensile stresses, the wires in ropes under tensile force are
strained by bending and torsion stresses and normally slightly by pressure. The
stresses in all the individual wires are different:
• Systematically according to the different lay angles of the wire and the strand
layers and
• Unsystematically because wires or strands very often are lying loosely on their
base and therefore do not start to take up the load from the beginning by
increasing the tensile force of the rope.
The unsystematic working stresses may be bigger in some cases than the sys-
tematic ones. Of course, they cannot be calculated but their influence can always
be observed especially in the rope endurance under fluctuating tensile forces.
Conditions for calculating wire stresses
The working stresses will be determined in the following chapter. Thereby, an
ideal wire rope will be presupposed:
• The wire rope is of perfect geometry.
• The wires are without self-contained stresses.
• No wires or strands are loose, so that all wires start to bear when the wire rope
will be under a slight tensile force.
• All stresses remain in the elastic region.
The self-contained stresses of the wires resulting from their manufacture have
no importance in the case of static loads. In case of fluctuating loading, they
influence the endurance like an increasing or a decreasing of the middle stress.
2.1.3 Basic Relation for the Wire Tensile Force in a Strand
A tensile force loading a strand induces a torque because of the helix form of the
wires. Therefore the strand will be turning if the strand ends are not secured
against this. In practical usage, the turning of strands and ropes must be prevented
because otherwise the strand loosens its structure and because of this very unequal
stresses would be induced in the wires. For normal ropes, the turning can be only
prevented securing the rope ends. In so-called non-rotating ropes, the turning is
more or less prevented because the torque of different right or left wound wire
layers or strand layers compensate each other. In the following it will be pre-
supposed that the turning of the strands and ropes are prevented.
For one wire, the portion of the tensile strand force S i in strand axis direction
and the corresponding portion of the circumference force U i out of torque act as