True or false? Non-circular cross sections can be non-planar when torsion is applied. This was on a quiz today and I wasn't sure of the answer. I guessed true by intuition, but does anyone have a better answer/justification?
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This is a manifestation of the Poisson effect. Suppose we take a beam and stretch it, then we are only applying a force along one axis:
You might think that the response of the beam can only be along the axis of the force, but in practice experience tells us that when stretched the beam will (usually) get thinner i.e. we see a response at right angles to the axis of the force. The magnitude of the thinning is described by Poisson's ratio.
This is where my ability to draw is going to let me down, since I can't draw a very convincing diagram:
When we apply a torque to the beam the forces are (as I've drawn it) in a horizontal plane, but the Poisson effect means there can be a response in the vertical plain. Exactly what motion will occur depends on the geometry.
The reason a non-circular cross section is required is that in circular cross sections the symmetry means there can be no net vertical force acting.
John Rennie
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