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

Wire stiffness
Independent of the magnitude of the wire slippage, the first component of the stiffness, the wire stiffness
(EJ)wire, , has a constant value. Applying equation (2.31), we get:
EJwire
EJwire
Secondary stiffness
In Region I (no wire wire displacement), displacement), the the secondary stiffness of of an an individual wire depends on the position
of the individual wire in the conductor cross cross-section. section. This is represented by the factor sin 2 ϕ in (2.33).
The stiffness of an individual wire along the axial directi direction on of the conductor is therefore a function of this
factor, since the angle ϕ assumes values of ϕ = 0 to ϕ = 2π along the lay length of a wire.
If we now sum these stiffness values over the wires, mutually displaced by ϕ = 60° within the same
conductor cross-section section (Fig. 2.19), the sum remains remains constant for for every every conductor conductor cross cross-section,
independent of the position of the individual wires, since:
Wires
The general proof of this was discussed in Section 2.4 for an arbitrary numbe number of wires nL L in a wire layer
L and is given in Annexure II.
Wires
No. of layer wires
This yields a constant value for the secondary stiffness EJ EJzusI in Region I in acc. with (2.33):
Alum. wires
39