In an attempt to understand where the 'weak and strong' sides of a shaft
concept came from it occurs to me that one of the problems with
understanding this concept is that it is easy to visualize a shaft that is
stronger on one side than the other; a thicker wall on one side in a steel
shaft, or more fibers on one side in a composite shaft. This will, indeed,
result in a shaft that is 'stronger' on that side - to a tensile (or
compressive) load applied parallel to the axis of the shaft! Assuming the
shaft remains straight the strain and stresses in the shaft material will
be the same through a cross section but, because of the greater cross
sectional area on the 'thick' side of the shaft more of the reaction force
to the axial shaft load will be carried on that side of the shaft, so, in a
sense, it is 'stronger'. In a bending situation, however, because of the
redistribution of stresses that occurs in the shaft to balance the forces
on either side of the neutral axis, this does not result in a shaft being
stiffer in one direction than in the opposite direction. In a given
bending plane the shaft has the same stiffness in both directions. The
'neutral axis' is defined, by the way, as the line of zero stress through
the cross section of a shaft under bending load and is not always at the
geometric center of the shaft. The stresses in the material on one side of
the neutral axis are compressive and tensile on the other for bending in
one direction and then reverse for bending in the other, but the neutral
axis remains in the same location, hence the resistance to bending
(stiffness) is the same. I hope this helps.
Regards,
Alan
At 04:58 PM 12/26/02 -0500, you wrote:
At 04:32 PM 12/26/02 -0500, Al Taylor wrote:
I'm impressed. I have no clue if you answered my question, but I was
impressed. John, you still there? ;-)
Al
OK, John and Alan and I all said, counterintuitive as it may seem, yes it
bends exactly the same TOWARD and AWAY FROM the spine, as long as it's in
the same plane.
You could weld a small steel rod to the shaft, to give it as stiff a spine
as you want. It will still have exactly the same stiffness in BOTH
DIRECTIONS in the same plane.
Twirling it in a spine finder might or might not say that. But measuring
the REAL stiffness will. I have posted here how to measure true stiffness,
several times over the past week.
Hope this answers it.
DaveT
