The Richard Gertz myth

[Phillip Ford]

>>
>>I believe he means the chord of a circle or arc, in this case, the 
>>straight line connecting the two points where the lower edge of the 
>>soundboard touches the rim (right, Ron?).
>>
>>--Cy--
>
>That's correct Cy. Sorry for the delay in getting back to you with a 
>reply Phil. I got distracted gluing ribs together.
>
>Ron O.
>--

At 11:49 PM -0500 10/29/04, Ron Nossaman wrote:
>
>I expect he means the line of neutral stress through the rib. The 
>centroid, assembly centerline, Zen.
>
>Ron N

Perhaps we need a little more discussion on this.  I'm not sure that 
we're all on the same page.  In my view, the reason that a soundboard 
assembly would want to pull in under the effects of downbearing is 
because the line through the neutral axes of the rib-panel assembly 
is taking a negative curve (lower in the center than at the ends), 
not because some portion of the rib, at any point along its length, 
lies above or below the top plane of the inner rim.  The main reason 
for the negative neutral axes curve for any given flat rib (assuming 
constant cross section for the main part of its length) is the 
feathering at the ends, and for any positively crowned rib is its 
moderate amount of crown (or large radius of curvature) and the 
feathering at the ends.  If the rib had a constant cross section 
along its entire length, and was cut or laminated to have a positive 
crown, then the line through the neutral axis would have a positive 
curve, or crown.  Also, if you had ribs that were cut or laminated in 
a very tight curve (say, a 300 cm radius rather than a 2000 cm 
radius) and had moderate feathering, you would probably end up with 
the neutral axis line having a positive curve.  If the neutral axes 
of the rib-panel assembly has positive curve (forms an arch if you 
like) then the ends would want to push out under the effects of 
downward load.

I think you can see that if you had constant cross section ribs of 
large radius of curvature that were let-in to the rim, then you could 
have a situation where a good portion of the rib is below the top 
plane of the inner rim and yet still has a positive neutral axes 
curve for the rib-panel assembly.

A couple of additional comments here:

1.  I think we're assuming that all downbearing load is being taken 
by the ribs and not by the panel, except perhaps that portion of the 
panel directly over the ribs which wants to act with the ribs.  If 
the panel is in fact taking some significant portion of the load, 
what's happening between the ribs?  The panel in these areas does in 
fact have a positive neutral axes curve and would want to push out 
under load.  What's the net effect of the assembly wanting to pull in 
at the ribs and push out in between?

2.  How does compression crowning affect this?  When we talk about 
pushing out or pulling in we're basically talking about movement from 
an equilibrium position.  If you compression crowned a board, let it 
fully stabilize, and then glued it to the rim, then when you applied 
your downbearing load you might expect to see the board trying to 
pull the rim in from its neutral stable position (which was what Ron 
O was alluding to in the original post - that the M-H tension 
resonator would then not be providing its claimed function of 
preventing the rim from spreading).  If, however, you dried the 
board, glued on the ribs, and immediately glued it into the rim, what 
would happen?  I assume that the panel-rib assembly is going to try 
to spread the rim.  In this case the M-H tension resonator is sort of 
doing its claimed job (it's trying to keep the rim from spreading), 
but at the same time it's trying to inhibit the crown from forming 
(although it's pushing back against whatever crown is formed, so in 
that sense I guess it's trying to 'support' the crown).  As 
downbearing load is applied, the board wants to pull in, thus 
removing some of the load applied by the crowning procedure.  If the 
movement from the pulling in is smaller than the outward movement 
from the board crowning, then the tension resonator would not fully 
unload (for whatever good that does).

Phil Ford