Wire Ropes Under Tensile Load - Wire Ropes: Tension, Endurance, Reliability - page 67

radius or circumferences in the strands, in the spiral ropes and in the strands of the
stranded ropes are practically only caused by the elongation of the wires. This is
especially true for the most frequently used parallel lay ropes.
The transverse contraction ratio of the strand helix m j in stranded ropes is
difficult to estimate. Especially in wire ropes with a fibre core, this ''Poisson ratio''
is very large. In any case of fluctuating force, there is a great part of the rope
contraction and the rope elongation remaining.
The influence of the Poisson ratio of the wires and the ''Poisson ratio'' of the
winding radius or circumferences of wires on the calculated distribution of the
wire tensile forces is normally not very large. For strands, the influence reduces
with the increasing number of wires. For a parallel wire strand with 19 wires, the
calculated stress of the outer wires is at the most 2 % more and that of the centre
wire 3 % less if the Poisson ratios are neglected.
The influence of the Poisson ratios of wires and of winding circumferences of
wires and strands on the wire tensile stress is also small for the stranded ropes.
This is true for ropes with steel cores because the ''Poisson ratio'' m j is also small.
For ropes with fibre cores, the contraction can be quite large. However, the
influence on the distribution of tensile forces of the strands is small.
However, unlike with the calculation of the wire tensile stresses, the ''Poisson
ratio'' m j must used as precisely as possible if the equations given here are to be
used later on to calculate the additional stresses, the rope elongation or the rope
elasticity module. The Poisson ratio m = 0.3 can continue to be used for the strands
and spiral wire ropes. But that is not valid for the strand helix (strand axis) in
stranded ropes.
The cross-section of fibre cores and their effective diameter are very greatly
reduced under the effect of the length-related radial force of the bearing strands.
This is also true to a lesser extent for wire ropes with steel cores especially for wire
ropes with several strand layers especially if the strand layers lie parallel. The
''Poisson ratio'' of the strand winding radius of these wire ropes is not constant as
it depends on the wire rope stress. The ''Poisson ratio'' of the stranded wire ropes
can generally only evaluated by measurement and not by calculation.

2.1.4.4 Wire Tensile Stress Neglecting the Poisson Ratios

If the tensile force of the wires in strands or wire ropes is calculated by neglecting
the ''Poisson ratios'', the equations are much simpler. The tensile force in a strand
is in this case

X

n W

S ¼ Dl S
l S

cos 3 a i

z i E i A i ð 2 : 21a Þ

i¼0

and the tensile force in the wire k is