Curve on Bridge Bottom

[Ron Nossaman]

>The only bridge I had laying around was from an upright and it was notched 
>at the tenor/treble break, so I followed your suggestion over the 39" tenor 
>segment - it bowed 5/16" with 100 lbs applied in the middle (my son stood on 
>it).
>
>I'm not sure what I was supposed to observe. Kinda seemed to act like a big 
>rib.
>
>Terry Farrell

Holding one end of the bridge with one hand, setting the other end on a
bench top or something solid, and pressing down with the other hand in the
middle of the bridge, you were supposed to observe that you couldn't hold
the bridge top level. Using just the relatively straight tenor segment
didn't illustrate the principal. The rotation is the key point. When you
find a piano known to have a crowned bridge, with a nice 3mm soundboard
crown in the low tenor and negative crown in the killer octave, what
happened there? Why didn't the bridge support the crown in the killer
octave? Why is there negative front string bearing and positive rear
bearing in the killer octave? Lay a straightedge from low tenor to high
treble of the bridge and locate the point of the bridge that furthest
deviates from that line. Where is that point in the scale? When you tear
the soundboard out and look at the bridge, you will find it is still
crowned. So why didn't it support the crown in the killer octave? Consider
that the string bearing loads in the top half of the scale are typically
over twice those in the lower half, and the loading per mm of bridge length
is much higher in the top half of the long bridge, where the bend is most
extreme, than in the bottom half.

Lay your upright bridge on a flat bench surface. Does it conform to the
surface pretty closely? Now prop the killer octave up with a pencil. Don't
the ends of the bridge still touch the bench top, while the middle is a
pencil's width high? How is that different from a crowned bridge?

So my point is that, while the bridge does distribute and support load
locally from rib to rib, it doesn't from end to end because of it's shape.
The killer octave gets the brunt of the load, relative to rib dimensions
and load capacities, because of the bridge curvature, and regardless of
bridge crown. That's the way I see it, for what it's worth.

I would love to see a real live pedigreed structural engineer's analysis of
this thing, to see just where and to what degree the board loading is
affected by the leverages from that curved bridge. Any FEM enabled,
qualified and curious soul(s) out there who are willing?
 
Ron N