Soundboards/stress

[Ron Nossaman]

Hi Bob and all,

Ringing in a little late in the discussion, but it just came back around to
some of the things I've got some opinions on. I've interspersed comments
through the following. Sorry, it's the only way I could think to address
various points.




 
>First the wood basics:  wood expands and contracts with 
>changes in moisture at least twice as much per unit dimension in the
tangential 
>direction (soundboard thickness) as the radial (ribbing direction), changes in 
>length are negligible.  A normal piece of  spruce, allowed to expand and 
>contract in the air developes no stresses (discounting the cellular level).
>

Correct, according to Mr. Hoadly.


>When a rib is glued across the grain (radially) to a dried and shrunken spruce 
>panel, and then the whole thing is allowed to absorb moisture, the panel tries 
>to expand in width and the rib doesn't change in length.  This creates 
>_compression_ on the bottom surface of the panel, _tension_ on the top surface 
>of the rib, and huge shearing stress on the glue joint.  It is the action of 
>this compression and tension which causes the system to arch (if it is free to 
>move) until these stresses are balanced by _compression_ on the bottom surface 
>of the rib.  The shearing stress on the glue joint is what makes failure of
the 
>joint so common.  
>


I'll take exception here. If the spruce panel is merely bent, the convex
side is under tension and the concave side under compression, with (roughly)
the center of the board being relatively unstressed. Seems to me that the
crown being the result of wood swelling with ribs on the back limiting
movement would put the neutral stress centerline somewhere near the center
of the *rib*, being levered by a soundboard that is entirely under
compression not by bending, but by expansion with re-hydration. If true, the
convex surface of the board would be under *less* compression than the back,
but still compressed. The compression ridges seen on (the top of) new
soundboards in dealer showrooms would seem to support this view. Also,
you're talking about a sixty foot radius curve, there about, which wouldn't
put a heck of a lot of tension on the convex side of a soundboard panel even
if it was *just* bent. 




>snip>
>However, pursuing that question, I have made quite a few "model" 
>soundboard/ribs  in different configurations and  evaluated the stresses on 
>every surface of the panel and ribs.  How this is done would take too long to 
>describe here.  But every configuration I have tried has resulted in _tension_ 
>on the top surface of the soundboard. 
>


How determined? How does one measure tension, or compression in wood?



>There is another factor which sheds some light on the top surface of a 
>soundboard: cracking can reveal a lot about the stresses.  Cracks mean
tension. 
> Compressed wood _cannot_ crack.  This is not to say that excess compression 
>can't set up a condition that results in tension/cracking.  In any case, if 
>soundboards were "compressed" as many seem to believe, cracks would not form.  

>As Brent Fisher said, "Each board reacts differently".    I believe the 
>question is not, "Do some soundboards have tension on the top surface?" but 
>rather, "Is it possible to make a crowned soundboard which is not tensioned on 
>the top surface?"  This is an opinion based largely on my models, which are
not 
>real-life soundboards, and would be difficult to verify conclusively in 
>assembled pianos.
>
>All of my comments refer to unloaded soundboards.  So what does loading do to 
>the stresses?  Applying downbearing does not simply put the board into 
>compression:  if it did, boards would not crack.  I thought I might go into 
>this here, but this message is already kind of long.  Maybe another time.
>
>Bob Hohf
>Wisconsin
>
>
When the movement of a wood panel is constrained, like gluing ribs on the
back and loading weight on top, swelling with humidity crushes wood cells,
killing resiliency. Dry cycles open up cracks in the damaged wood. The
reason a board under compression can have cracks is because wood isn't
uniform in density. You are right in saying there can't be a crack where
there is compression, but the compression isn't uniform across the board.
The softer layers (growth rings) will crush more than the harder layers, and
develop cracks in the dry cycles while the majority of the wood in the board
is still solid enough to maintain the crown. It's all glued to the ribs, so
it can't redistribute the load and even out the stresses. The softer
portions, panel joints, and any other part of the board where annular ring
orientation changes abruptly will be where the cracks show up. You will also
see small cracks along the treble bridge where the bridge direction isn't
quite parallel to the soundboard grain. This should be an indication that
this area is taking a lot of abuse with humidity swings. 


Sorry about the length of this turkey. Any comments?

 Ron Nossaman