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

Fig. 2.16 Cable bending processes in the M-B M diagram
The M-B B diagram, diagram, Fig. Fig. 2.16, 2.16, allows allows us us to to easily easily determine the curvature status status (and therefore also the
stress status) and the associated effective bending stiffness of the cable under any external load, i.e.
any external bending moment.
If, for instance, the cable experiences an external loading moment MMb,
, then this state diagram shows
that the cable will assume a curvature κb. To reach the “end” point Mb/κb, , the cable can only assume deformation conditions along the MM-B
curve
if the original condition was friction-free free (initial loading). loading). The The cable therefore at at first reacts to to an an external
external
load load with its initial initial stiffness, stiffness, corresponding corresponding to to the the cable with with undisturbed wires wires and maximum cable
stiffness (EJ)max – see see (2.36). This This stiffness remains up to the average transition transition curvature curvature κm, which, as
described described above, is is the approximate approximate transition point between the undisturbed cable condition and a
cable with fully slipped wires. From this point onwards, the external bending moment is opposed only by
the minimum stiffness, or wire stiffness (EJ) (EJ)min as in (2.31), which could also be called the final stiffness
of the cable.
Region I
Region II
If, therefore, bending of the cable has caused wire slippage along th the e entire length of the cable, then
further bending involves only the wire stiffness in (2.31).
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