Wire Ropes, Elements and Definitions - Wire Ropes: Tension, Endurance, Reliability - page 46

• The wire is bent with the binormal helix as a neutral axis (this is only of
importance for wires which are not round) and twisted in such a way that the
neutral axis is located stationary to the wire.

Hruska ( 1953 ) calculated the cross-section of round wire strands using the sim-
plification of taking ellipses as the section contour of the round wires. Using the
same simplification, Shitkow and Pospechow (German translation 1957 ) gave a
detailed presentation of this method of calculation. For a long time, their topic was
a guide for the practical calculation of rope geometry. Jenner ( 1992 ) established
that the results calculated with the ellipse simplification are accurate enough for
the lay angles normally used.
Groß ( 1954 ) calculated the first realistic contour (based on the two given pre-
suppositions) for round wires in the cross-section of a strand. Shitkow and
Pospechow ( 1957 ) and Wiek ( 1985 ) came to the same result as Groß. Wolf ( 1984 )
and Wang and McKewan ( 2001 ) presented the geometry of round strand ropes in
vector form. The use of computers for these methods in practice brought a great
progress for the rope quality, Wiek ( 1977 ), Fuchs ( 1984 ) and Voigt ( 1985 ) etc.
One method of calculating a realistic cross-section of a round wire in a straight
strand is presented in a clear parameter form. Using u for the wire winding angle
u W , the wire winding radius r W and the lay angle a, the equations for the wire axis
in a strand are

x M ¼ r W sin u
y M ¼ r W cos u
z M ¼ r W u cot a :

ð 1 : 7 Þ

(These and the following equations are also valid for round strands in straight
ropes with u = u S for the winding strand angle, with r S for the winding strand
radius and with the strand lay angle b instead of a.)
The surface of a wire with the diameter d in a strand is defined by the equations

x ¼ r W sin u þ d

2 sin u cos ð u 0 u Þþ d 2 cos u sin ð u 0 u Þ cos a

y ¼ r W cos u þ d

2 cos u cos ð u 0 u Þ d

ð 1 : 8 Þ

2 sin u sin ð u 0 u Þ cos a

z ¼ r W u cot a d

2 sin ð u 0 u Þ sin a :

These equations are to be found in a slightly different version in Andorfer ( 1983 )
and Schiffner ( 1986 ). There, the cross-section is to be found, for example, with
z = 0. From that the last Eq. ( 1.8 ) is derived