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Re: cavendish expt



I wrote:

"C) Conclude that a round solid fiber gives
minimal stiffness for a given strength."

Bernard Cleyet wrote:

If "a given strength", is the same as a given cross sectional area,
then not true. Aux contraire, a cylinder has the highest stiffness
strength (tensile) for a solid member than any other simply connected
cross-sectional shape. St. Venant showed this some time ago (ca.
1855). continuing:

Given strength means given tensile strength in the
vertical tape, as should be clear from my original
posting. Also, it seems self-evident that tensile
strength in such situations is proportional to the
cross-sectional area; I hope we can agree on that.

I don't know what means "highest stiffness strength
(tensile)". First of all, stiffness is not equivalent
to strength, as I noted in my original post. Secondly,
the thing I asserted was lowest was not tensile but
torsional.

So what I said was true: a solid cylindrical fiber
has the minimal torsional stiffness for a given
tensional strength (assuming constant length in
the Z direction).

"B) Again split the tape, but rather than
moving them apart, move them together so they
share the same attachment point. This will
give less stiffness than the original full-width
tape."

I stand by that, too.

why do you think the split tape will have significantly less stiffness
than the original?

Uhh, because of elementary physics?

1) I can't imagine a case where splitting something
gives it more stiffness.

2) After splitting it, moving the two halves together
reduces the stiffness.

Do the calculation. You don't even need to bother
with a full St. Venant analysis; just imagine a
swing-set supported by two very thin vertical ropes.
The resistance to torsion goes like the square of
the distance between the ropes, again assuming
constant length in the Z direction.

p.s. a quick calc. for the torsion constants (per unit length and
same shear modulus) of a cylinder (r= 0.0178 inch) and a ribbon two
mills thick and 1/2 inch wide give a factor of 120 X (the cylinder
being the more rigid)

That's preposterous. Does that perhaps come from
misapplying the formula for flexional stiffness
across the width of the tape, rather than the
formula for torsional stiffness?

Let's get real:
-- Birds have hollow bones. Do we really think
they would do so if solid bones were stiffer?
-- The driveshaft on your car is hollow. Flagpoles
are hollow. Do we really think that people would
build such things if solid rods were stiffer?
-- Why would people bother to fabricate I-beams
if solid rods were stiffer?
-- Et cetera...............