evaluating sdbd. crown & bridge downbearings in a new piano

[Frank Weston]

I admit their was a certain amount of "bait" in my previous post, but.....

Ron wrote:

>* Ok engineer. A spruce panel that is 24" wide at 4% EMC will grow to
24.14"
>at 8% EMC. Glued to an infinitely flexible rib 1" tall, it would bow to
>approximately a 101" radius curve. With a real world spruce rib, it will
bow
>to a (roughly) 600 - 700" radius curve. That's in an unloaded condition.
The
>resistance of the ribs to bending is enough to compress the entire panel,
>top included, before string load is applied. If not, where did the extra
>panel width go?

No matter how the panel is constructed, the extra size will have to be
accomodated either by expansion of the the entire structure or by
compression of the fiber in the panel.  For a "compression" crowned board,
the top portion of a panel starts out in tension, as it flattens out, the
ultimate compression load will be less than if the top of the panel is
unstressed or in compression to begin with.  As a panel bends toward flat,
the original compression load in the bottom half will also be diminished at
a rate somewhat less than compression is being increased on the entire
panel.

For a soundboard constructed by any other method, the extra panel width
still has to be accomodated.  Ultimate compression in the top half of the
panel will be greater than for a "compression" crowned board, while ultimate
compression in the bottom will be less by the same amount.

>* As load is applied, the compression throughout the panel will be
>increased, more at the top than at the bottom. The leverage from this
>compression is what provides the resistance to downbearing.


No argument here, in fact, this statement fully supports my thesis.

>
>* The panel in a rib crowned board is also entirely under compression, only
>somewhat less. The rib is under similar stress to the compression crowned
>board (countering the panel's bending leverage), only less so. The forces
>are less because the panel is typically not dried down as much in a rib
>crowned assembly.


Given that a "compression" crowned soundboard assembly is at zero stress due
to deformation when it is flat, and a "rib" crowned soundboard assembly is
at zero stress due to deformation when it is crowned, then it follows that
as download is applied to a "compression" crowned soundboard and it is
displaced to a flatter shape, stress due to deformation will be decreased
toward zero.  For a "rib" crowned board, this stress will be increased.
There will be an additional stress placed upon each board as a result of
resisting downbearing loads.  This stress will be the same, no matter how
the board is constructed.  So, with a "compression" crowned board, total
stress, which is the sum of stress due to deformation and stress due to
compression required to resist downbearing, will be less than total stress
in a "rib" crowned board.

>>In theory, if a "compression" crowned soundboard is loaded to a perfectly
>>flat shape, it will have no internal stress.
>
>* The rib will be (cumulatively) at rest, but the panel will be under
>extreme compression.


My phrasing threw you off.  When I say "internal" stress, I am refering to
stress due to deformation as described in my paragraph above.

>
>* The total force required to support string bearing load is the same with
>either crowning system. The point in a rib crowned system is to have the
>ribs help hold up the string load, instead of adding their own load to the
>already over stressed panel. It's a more equitable distribution of abuse.

What's good for the panel is good for the ribs, and the same logic in terms
of stress applies to ribs as it does to panels.


>
>* Regardless of the wood selection process, or the care taken in the
>assembly, the fact is that the design of a compression crowned soundboard
>puts a compressive force on the panel that is very near, or exceeds the
>fiber stress proportional limit of the spruce. Try to compute the expansive
>force per linear inch across the top of a 1"x1"x48" and see what kind of
psi
>load it would put on a 3/8" panel to both bend the rib and lift another
>twenty pounds or so. If your arrived at figure is anywhere near 580 psi,
the
>panel is in trouble. Early failure is designed into a compression crowned
>board. The surprise is that some last as long, and perform as well as they
do.

As I have argued, the ultimate stress on a "rib" crowned soundboard is even
greater than on one "compression" crowned.  Could it be that there are just
not as many  old "rib" crowned boards around to observe in failure?

There is another whole issue that we can argue.  I say that because of the
differences in stress on "compression" crowned boards (almost zero internal
stress due to deformation) they are more lively and more responsive.  I have
no figures to prove this.

Frank Weston