wrote:
While I was enjoying the current incarnation of the stand-or-hang
thread, I found myself wondering what the spokes and the rim will do
if you stick a wheel up in the air and hang a weight from the rim
section that would normally be the contact patch.

Cheers,

Carl Fogel

Dear CF

I am not completely clear on what the question is but if you are
thinking of a wheel, supported at the axle, with an outward radial force
applied to the rim to simulate the opposite of the inward radial loading
that a wheel usually sees while in use and the wheel is not a drive
wheel and brake is not applied and no spoke goes into compression ...

So long as the material remains elastic, exactly the opposite of what
happens with the usual loading.

If under the usual loading (UL) the tension in a particular spoke
decreases, the tension will increase when subjected to unusual (CF)
loading. This assumes that all material remains elastic and has linear
elasticity. Aluminum alloys do not truly have linear elasticity but for
the range of stress involved, which will be the case if the forces are
kept within a reasonable range, it is probably accurate enough to assume
linear elasticity for aluminum alloys. Steel is a very well behaved
material and displays very linear elasticity through compression and
tension. Some references provide a different modulus for aluminum alloys
in tension and compression but we won't go there unless someone can
support a theory of stress reversal in rims.

For UL, stress = (unloaded stress) + (delta stress)
For CF, stress = (unloaded stress) - (delta stress)

For UL, force = (unloaded force) + (delta force)
For CF, force = (unloaded force) - (delta force)

If anything goes into compression (total force or local stress), one
must consider stability. For a spoke I would use Euler's equation for
long slender columns.

Later,
Dan