Bending of helically twisted cables under variable ... - Pfisterer

In In this we we assume assume that that the the wire wire in in this this layer layer does not not shift shift relative to the layer underneath and that
initially βL = 0.
Analogously for the associated bending stresses:
Fig. 2.6 Wire stresses as the cable bends
(a) wires not displaced (b) wires displaced
Here, dL is the average diameter of the wire layer L and φ is the “position angle” of the wire cross-section
cross
in the considered cable cross-section section Fig. Fig. 2.7, 2.7, which which can can only assume discrete values values in in this context,
differing from each other by 2π/nL in each case, depending on the position of the nnL
individual wires in
the cable cross-section. section. It is sufficient in this respect to co consider the range - ≤ ϕ ≤ + since the
conditions in the wire repeat periodically outside of these limits. ϕ is also the incremental angle of the
helix described by the centre of the wire cross-section, cross the so-called called strand rotation angle, Fig. 2.4. It
determines determines the the position position on the the cable axis and can assume any value, contiguous between 0 and 2 22π.
The “exact” calculation alculation of the bending stress σb,L, , which in its most simple form is approximated by the
Reuleaux Reuleaux equation equation (2.20), (2.20), has has been been carried carried out out by by various various authors already already [Leider, [Leider, 1977, Czitary, 1962,
Wiek, 1973, Schiffner, 1986, Wang, 1990] and need not theref therefore be repeated here.
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