By replacing each long stick by several short ones, we can make the Euler load for each stick greater than the applied compressive load. Clearly, this stick model is no longer adequate. If the compressive load reaches the Euler load for an individual stick, then the real line which the stick represents will start to deform at a shorter wavelength, and deflections within the stick length become significant. Provided the wavelength of the deflection is longer than the length of the individual sticks then the rigid stick model can approximate it: shorter sticks give a better approximation. Under compression, the line deflects: the sticks remain straight and the joints rotate.
#Orcaflex hockling series#
Why are these two statements equivalent? Imagine the real line replaced by a series of rigid sticks connected by rotational springs at the joints – this is essentially how OrcaFlex models the line. Another way of saying the same thing is that the compressive load in any segment of the line should never exceed the Euler load for the segment. provided the segments are short enough to model the deflected shape properly. OrcaFlex is fully capable of modelling this behaviour provided the discretisation of the model is sufficient, i.e. Under dynamic loading conditions, the transverse deflection is resisted by a combination of inertia and bending. The Euler load is derived from a stability analysis: it tells us the value of axial load at which transverse deflection will occur but nothing about the post-buckling behaviour. For a simple stick of length $l$, bend stiffness $EI$, with pin joints at each end, the Euler load is $\pi^2 EI / l^2$. The Euler load is a function of the length of the straight section, the bend stiffness and the end conditions. This defines the maximum compressive load – the Euler load – which a particular length of line can withstand before transverse deflection occurs. Under static conditions, the behaviour of an initially straight section of line under pure axial loading is described by classic Euler buckling theory. When a flexible line experiences compression, it responds by deflecting transversely: the magnitude of the deflection is controlled by bend stiffness.
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