At 07:10 -0600 24/11/07, Ron Nossaman wrote: >>The stiffness of the bridge increases as the _square_ of the >>height, to that a bridge of 33mm is about 70% stiffer than one of 1 >>inch and a bridge of 38mm is 33% stiffer than one of 33mm. > >Moment of inertia of the section for the flexure formula is >calculated on the cube of the height, but yes, a little added bridge >(or crowned rib) height makes for an assembly that's considerably >stiffer. Indeed! I was not making the distinction between strength and resistance to flexure, ie. stiffness, presuming erroneously that they were the same, so it can be said that "the strength of a rectangular beam varies as the square of the depth, and the stiffness to resist deflection varies as the cube of the depth" as you say, which means that a 38mm bridge is more than 50% stiffer than one 33mm tall and if one were to increase the height to 40mm. there would be a 78% stiffness advantage. > A similar net effect can be gotten with a short bridge with the >addition of more crowned ribs. That I am not qualified to calculate, but I am thinking of the whole length of the bridge and perhaps you are thinking more of remedial measures for weakness in a troublesome part of the scale as found commonly in old American Steinways (the "killer octave" ??). To stiffen the whole stucture by this means would surely mean adding quite a lot of unwanted mass, many times more than by increasing the bridge height or adding a "mirror bridge" as used by Grotrian, Rittmüller et al. To my mind a high ratio of stiffness to mass is of prime importance. JD -- ______________________________________________________________________ Delacour Pianos * Silo * Deverel Farm * Milborne St. Andrew Dorset DT11 0HX * England Phone: +44 1202 731031 Mobile: +44 7801 310 689 * Fax: +44 870 705 3241 ______________________________________________________________________
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