of spline and catenary

[Michael Spalding]

Ron,

If by "end supported" you mean freely pivoting supports, the beam
deflection formula is 

y=-(F/48EI)(3lx^2-4x^3)

where F=center load, E=Young's modulus, I=moment of inertia, l=length of
beam, x=distance from the end to the point where deflection is measured.

If the end support is not freely pivoting, as in a piano string, the
formula is different.  If the load is not a single centered load, as in a
piano string, the formula is different.

Definitely not a catenary, but by eye they would be pretty hard to
distinguish.  What's up?

Mike


> [Original Message]
> From: Ron Nossaman <RNossaman@cox.net>
> To: Pianotech <pianotech@ptg.org>
> Date: 9/4/2003 11:26:44 PM
> Subject: of spline and catenary
>
>
> A question for the math, engineering, and geometry folks out there. A 
> constant cross section beam, end supported and center loaded, describes a 
> curve. What curve? I suspect it's catenary, but I haven't found anything 
> anywhere giving even a clue one way or another. If no one out there can 
> produce a reference, I'll resort to attempting to work out the math 
> describing the catenary and comparing deflection rates at various points 
> along the beam with available formulae. But math is hard on me, and I'd 
> appreciate any specifics anyone out there may have that would help
minimize 
> the inevitable frustration.
>
> Thanks, just in case...
> Ron N
>
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