The Richard Gertz myth

[Ron Nossaman]

>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.

Agreed.


>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.

Yes.


>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.

You could, depending on rib length and depth.


>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.

Yes, if the neutral axis extends above the plane of measurement.


>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.

Yes, at least in the center rib length between the feathering which, with a 
large radius would still be below the plane of support.


>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.

I'm not. I tried it with both compression crowned, and rib crowned models 
with very similar results. It doesn't matter how the crown is formed, the 
assembly still doesn't act like an arch, and the assembly is what we're 
working with.


>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?

Since the panel is still part of the assembly, it doesn't act like an 
isolated strip between the ribs. It's still glued to and constrained by the 
ribs. The compression in the panel between ribs is going to be essentially 
the same as that directly above the ribs because of the longitudinal 
stiffness of the panel material, and the close spacing of the ribs. In a 
compression crowned board, for instance, the panel is shrunk down at 4%MC 
(or whatever) to less than 99% of it's 10%MC (or whatever) unconstrained 
width, and glued to the ribs. Taking it back to 10%, it doesn't scallop out 
between ribs to the original width. I haven't measured, but it gives no 
visible indication that it scallops out at all, though it probably does 
some tiny amount, which compression set will take care of in short order 
after installation anyway.


>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).

Not noticeably, by my experiments.

>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

All of which means that the tension resonator doesn't support crown. Be it 
an arch, or be it a cable suspension, and be the rim absolutely rigid, the 
fact still remains that spruce is too plastic a material to support the 
bearing load from either arch, or cable suspension. Do the math, and see 
what the tensions are to support bearing loads from a cable of the length 
and sag of any particular rib.  The crown is formed and maintained, or not, 
by the assembly and the shaping of the ribs and panel together. The rim 
still has very nearly nothing to do with it in the long term.


Ron N