[pianotech] Tension and compression in soundboard panels

[Ron Nossaman]

On 7/6/2011 7:45 PM, David Love wrote:
> So it's the end of a long day and I was thinking about this and couldn't
> quite answer it--maybe a glass of wine will help.
>
> If you simply bend a panel around a set of curved ribs then the bottom of
> the panel (the concave side) is under compression and the top part of the
> panel (the convex side) is under tension.

Here we go. I don't know why this is so universal a question 
(eventually) but it's been a few years, so let's look at it again. I 
took the time to find the formulas and do the numbers to work this out 
to my satisfaction years ago, so I'm not interested in spending the time 
to do it again, but I highly recommend that anyone interested do so. It 
answers a lot of questions and puts what is otherwise a theoretical 
concern into much more practical perspective.


> But if you dry the panel down to some low EMC and then bend it around curved
> ribs and allow it take on moisture thus adding compression, there must be a
> point at which the top of the panel come under compression, i.e. when is it
> no longer under tension.  It first occurred to me, well no, as the panel
> expands the radius becomes tighter and so there is an increase in
> compression at the bottom part of the panel but also an increase in tension
> at the top of the panel.

The radius doesn't become tighter at a rate that offsets the expansion. 
Expansion overtakes it right away. Generate some numbers and see.


> In general, the target of this mental exercise was to determine where the
> panel starts out in terms of putting the top of the panel under compression
> at some EMC and what kind of change must take place (how much does the width
> of the panel when measured across the grain need to change as a function of
> compression set) in order to put the top part of the panel under tension at
> that same EMC.  It's leading to other questions as well but I must stop here
> for now.

It's been my experience that answers earned by chasing down the 
information and putting in the hours to generate the numbers tend to 
stick better than answers handed over, and I highly recommend you dig 
out the spreadsheet and chase down the appropriate formulas to put 
numbers to it, but the gist is this.

Wood changes dimension at x% per MC% change. Bending a, say 1M panel in 
a radius appropriate to a piano rib will put the concave under very 
light compression and the convex under make a very light tension. How 
much? Do the math. Pick a radius, and a circle segment length. Calculate 
the segment angle. Use, that angle to calculate segment lengths for 
radii 4mm shorter, and 4mm longer than the center line radius of the 
panel. Those numbers indicate the amount the top and bottom of the panel 
was stretched or compressed to make the bend, and you'll find there 
isn't much difference between the two. Now calculate how much the panel 
at it's starting width will change dimension with a given MC% change. 
You'll find the numbers bigger than the difference between the top and 
bottom lengths of the curved panel. In other words, it takes very little 
MC% over that at which the panel was ribbed, to put the entire panel 
under compression. Now calculate the top surface length of the panel 
with a radius giving a crown height of about half the unloaded original 
crown height. Compare that with the original panel width, and the 
potential for tension on top of the panel becomes even less than it was.

In the real world, this is a non issue in any practical way. For RC&S 
boards, we typically dry the panel to at least somewhat lower an MC than 
we expect it to experience in the climate it lives in, so it (hopefully) 
won't crack. Within reason, naturally. There are areas of the country 
and world that don't even give us a fighting chance. With the vast 
majority of soundboard installations being either pure CC, or largely 
panel supported RC assemblies, the entire panel is under considerable 
compression from birth.

Ron N