piano soundboard beam deflection

[chickering]

I'm trying to find a formula to determine max deflection @ center of a simply supported beam, rectangular section, with 2 point loads located at non-center location.

Jim

 

[electricpete]

For starters, you need only find the formula for one point load and then combine results by superposition.

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[desertfox]

Hi chickering

I would use the Macauley method and here is a link:-

http://www.freestudy.co.uk/strength of materials/tutorial 2 1.pdf

then go to worked example number 6 on page 13 of 18

desertfox

 

[IRstuff]

Your title and your question appear to be differing. A piano sounding board does not experience point loads, I don't think.

While the end result is a deflection, the equivalent point load that causes such a deflection has little relevance to the tension applied to the wires.

TTFN

FAQ731-376

 

[chickering]

Viewed as a system, you are correct.

However as independent small artisan types we don't have ready access to finite systems or other complex/expensive modeling products. The price point of this work doesn't allow for that kind of consulting for each board, so we come up with trends which are ballparked with # crunching, and back it up with empirical tests and experience. There are definitely trends.

The bridge or bridges are located in discreet positions along the ribs. They transfer string loads at each intersection of bridge and rib. The total load is 700lbs or more down force exerted by the strings on the soundboard.

WHile calling these points "point loads" is not precisely correct, calling them as such does allow me to narrow down the "guess" range, and clean up small discreencies after the board and strings are all put together. Seat of the pants engineering.

So anyway my question remains...I will see if I can deal with the Macauley math.

 

[msquared48]

irstuff...

Any deflection in the soundboard affects the pitch of the strings, and the achievable region of adjustment of the stringe to the desired pitch. It also affects the ability of the strings to hold the pitch with time. The stiffer the soundboard, the less dampening, and the pitch loss over time tends to be in the string itself rather than the deflection of the soundboard.

We have a Kawai studio piano, but Chickerings are good too. Have played on them in the last too.

Mike McCann
MMC Engineering

 

[zekeman]

You will have quite a problem if the loads are not symmetric and equal, and the maximum deflection will not be located at the beam center. If they are symmetric and the same then

y=F*A(3*L^2-4*A^2)/(24*E*I)
where
L = beam length
A= distance of each load from ends
F = point load value

E modulus of elasticity
I section modulus (B*D^3/12)rectangular beam
B= beam width
D = beam depth

 

[msquared48]

If the soundboard beam has a changing section shape, then it has a variable I, and the solution is a lot more complicated, but solveable.

Mike McCann
MMC Engineering

 

[GregLocock]

So at a guess you want to know how much tensioning one string detensions another? That's in the realms of hand calculation, for the two string case, but I think it is a little trickier than the beam under 2 point load calculation suggests.

Is the far end of the frame much stiffer than the end that deflects, or are they roughly similar, or in between?



Cheers

Greg Locock

SIGlease see FAQ731-376 for tips on how to make the best use of Eng-Tips.

 

[IRstuff]

The issue was that the tension applied by the strings is not a direct correlation to point load application. According to:

http://en.wikipedia.org/wiki/Piano#Development_of_the_modern_piano

http://www.frederickcollection.org/works.html

the applied tension is in the many tons range.

Additionally, the stiffness of the soundboard structure is provided by separate load-bearing metal ribs, in additional to off-angle wood ribs on the bottom:

http://www.absolute-piano.com/structural/soundboard.htm

http://www.absolute-piano.com/structural.htm

TTFN

FAQ731-376

 

[GregLocock]

Just an idle observation - the detensioning effect is greater the stiffer the string, and the stiffer the beam at the other end.



Cheers

Greg Locock

SIGlease see FAQ731-376 for tips on how to make the best use of Eng-Tips.

 

[IRstuff]

From what I've read, detuning appears to be a bigger issue with RH effects on the wood itself:

http://www.kenfoster.com/PianoTuning/Why.html

TTFN

FAQ731-376