ribs and stuff (was alternatives.)

[Doug Richards]

Stephen,
I agree that a yardstick (simple beam) stiffness should have linear
deflection for some range.  I think we are discussing an over-constrained
beam though.  If a soundboard has crown and glued at the perimeter, the
downward force of the string may not give a linear deflection due to the
soundboard edge constraints.  I haven't tested this, but would go out on the
limb far enough to say that I wouldn't be surprised to find a
non-proportional deflection for increasing force.  Any takers?

doug richards
San Jose, CA
mailto:doug.richards@quantum.com

> -----Original Message-----
> From:	Stephen Birkett [SMTP:birketts@wright.aps.uoguelph.ca]
> Sent:	Friday, December 04, 1998 7:50 AM
> To:	pianotech@ptg.org
> Subject:	ribs and stuff (was alternatives.)
> 
> Ron wrote:
> > ..fact is that a given load will deflect the beam a certain amount, but
> > double the load will not deflect it twice the distance. You can prove it
> > in the shop in a couple of minutes with an old wooden yardstick and your
> > set of gram weights, or in a piano with a couple hundred pounds of lead.
> 
> >
> Beg to differ here Ron. The stiffness parameter of a loaded beam *is*
> constant within loading to the proportional limit. I've demonstrated just
> these experiments you describe many times in teaching physics students. 
> Get out your metre-stick and weights. The deflection of a centre-loaded
> beam is directly proportional to the loading force until the region of
> plastic deformation is reached. The proportionality constant - stiffness
> parameter - depends on the material properties and the geometry of the
> beam, span length, width and depth, but it *is* constant (unlike a
> hardening spring which is non-linear *below* the plastic deformation
> region). I think you mentioned once you had Hoadley...this is all well
> described in the section on beams. 
> 
> A crowned soundboard is essentially a pre-stressed beam, the amount of
> crown being a measure of the pre-stressing. The purpose of the
> pre-stressing is simply so that the net of vertical forces will maintain
> the final deflection within functionally acceptable limits for the desired
> down-bearing. The physical means to produce the crown - whether through
> curved ribs, or compression, or a pre-stressed case while gluing in the
> soundboard, or some other technique - is really irrelevant to the beam
> mechanics. It will matter if the desired crown, produced say by
> compression crowning, exceeds the fibre stress limit of the soundboard
> panel. But that is bad design and could be corrected by using a different
> crowning technique; or reduced down-bearing and/or or stiffer ribs to
> reduce the required crowning. It is the ribs that are the beams that
> balance the down-bearing forces. The panel itself is of no consequence in
> that mechanics, except insofar as it is used as a means to pre-stress the
> ribs, and the thickness of the panel itself adds to the overall height of
> the "beams" somewhat. 
> 
> A modern soundboard panel loaded to the point that its stiffness is
> observed to be increased (as Del described), must be stressed past the
> proportional limit into the plastic deformation region, where the
> stiffness becomes much greater.  This is presumably a reason why some
> modern soundboards deteriorate over a relatively short time period, and
> why when a used soundboard is removed the original crown cannot be
> recovered completely (permanent set). 
> 
> Del wrote: 
> > Would you please define 'very wide and flat' (the Graf) and 'very tall,
> > thin' (the Streicher)?  I'm also curious about the thickness of the 
> > soundboard panels that these builders used. 
> > 
> Graf ribs are ca 50mm wide and 4-5 mm thick. Streicher ribs are heavily
> arched about 10-15 mm tall in the centre, ca 4-6 mm wide. Their soundboard
> panels are thinned to different thicknesses in different areas: Streicher
> 2-5.5 mm, Graf a bit more, maybe to 6-7 mm. 
> 
> Stephen
> 
> Stephen Birkett Fortepianos
> Authentic Reproductions of 18th and 19th Century Pianos
> 464 Winchester Drive
> Waterloo, Ontario
> Canada N2T 1K5
> tel: 519-885-2228
> email: birketts@wright.aps.uoguelph.ca
>