Robert W. Hohf wrote: > ...It sounds like you are not disputing my description of the way downbearing > changes the shape of a crowned soundboard, but rather the way that the force > of downbearing effects the stresses that are built into an unloaded soundboard. > I wouldn't compare a soundboard to a rippled potato chip since the shape of the > chip is made with a rippled cutter. OK, I should have said a “wavy” potato chip which takes on its waviness later during cooking. Actually I wasn’t referring to the process by which the potato became rippled or wavy at all, but its appearance afterward the fact. —ddf Robert W. Hohf wrote: > ...Most people seem to agree > that the equilibrium shape of an unloaded soundboard is > maintained by a balance of the stresses between the ribs and soundboard > panel. Taken by itself, the fact that most people agree about something is not a particularly strong argument in favor of anything, especially things concerning pianos. Much of what most people agreed on twenty or thirty years ago is now understood differently. Including much about how soundboards work. As may be...your statement is correct in the case of a "compression-crowned" soundboard assembly. Soundboards that are crowned using pre-crowned ribs are another matter. —ddf Robert W. Hohf wrote: > A rib has a gradient of stress through its thickness which goes from > compression on the bottom, through zero stress somewhere in the middle, and > to tension on the top. The soundboard panel also has a gradient of stress from > greater compression on the bottom to (perhaps) lesser compression on the top. > I have expressed the belief before that the stress gradient in the panel may go, > at least in some cases, from compression on the bottom, through zero, to > tension on top. The rib (in a compression-crowned soundboard system) is the bent member. It started out straight (or nearly so) and is forced into a curve by the expansion of the soundboard panel that it is glued to so, yes, it will have the force gradient you describe. The soundboard panel itself, however, is quite another matter. It is not “bending” in the traditional sense. The entire panel is trying to expand (across grain) because the wood fiber (cells) expand as they absorb moisture subsequent to being dried to a very low moisture content prior to ribbing. As long as this wood fiber is capable of expanding there will be compression within the whole thickness and width of the soundboard panel. All of the panel, top middle and bottom. There may indeed be some theoretical “pressure gradient,” but it would be nominal—so slight as to probably be unmeasurable using conventional instruments. And it would all be pressure, no tension until after fiber crushing has occurred. In a compression-crowned soundboard system there must be compression in the soundboard panel to maintain crown. To relieve this compression, it would be necessary to allow it to naturally expand, but the ribs prevent this. (Well, I suppose it would be possible to relieve the compression by allowing the board to take on an obscene amount of crown, but even if the ribs didn’t break first, the strings would prevent that from happening. It would also be possible to develop tension if the moisture content of the soundboard wood were taken back below 3.5% to 4.5% moisture content, but this is not likely to happen in most parts of the U.S.) —ddf Robert W. Hohf wrote: > In any case, I believe that a change in shape represents a change in the > distribution of the stresses: the stresses in the unloaded soundboard are not > uniformly distributed, and loading the board changes the stresses into a pattern > which is less uniform and more localized. The stresses don't "go away", but > they are redistributed by the downward force applied to the bridge. I suppose it > is possible that somewhere there is a "rippled" soundboard, where the panel > is all under varying degrees of compression. No matter how distorted the soundboard surface becomes due to string loading or the later effects of climate, the soundboard panel is still under compression until the wood fiber fails under excessive compression. When this happens, the wood cells actually do become distorted and weaker. Picture a panel made up of toilet paper tubes (sorry, but that’s the best I can come up with at 5:00 am before my coffee pot delivers its morning gruel) glued edge to edge. Within certain limits you could compress this panel edge to edge and it would always return to its original shape. This panel would have some degree of resiliency until you exceeded the tube stress proportional limit. Wood is made up of “glued-together” cells that resemble hollow tubes, the walls of which are also resilient. When deformed moderately they will also restore themselves to their original size and shape when the force deforming them is removed—but again, only within certain limits. Until you compress them enough to exceed their fiber stress proportional limit. Then, like the toilet paper tube, they become permanently damaged—among other things, they loose much of their resiliency. Of course, once they loose their resiliency they no longer exert the pressure that creates the internal compression within the board. They become something like a spring that has lost it springiness. It might still look OK if it’s not under load, but its not much good as a spring any longer. —ddf Robert W. Hohf wrote: > But I think it is more likely that > this shape contains localized areas of tension. Again, cracks mean tension. > And not all cracks result from compression failure. The only way a soundboard panel can contain localized areas of tension is for the wood fiber to have failed as indicated above. (I’m assuming that the soundboard panel had a uniform moisture content throughout when the ribs were glued on. This is not always the case. Mistakes happen and repairs do get made...) Once fiber failure has occurred—during a period of high humidity—the wood cells will not expand as readily as they normally would, so as humidity decreases during the next dry period and the wood’s moisture content decreases there will indeed be areas of localized tension. When the tension becomes great enough, there will be a crack. I should add that most soundboard problems do tend to develop in localized areas. But this is primarily due to the fact that wood is a natural material. It is not perfectly uniform or consistent in its mechanical characteristics. Although the text books say that wood fiber begins to break down when it is compressed (perpendicular to grain) by more then 1.0%, in reality this means that some will probably break down at 0.5% and some may be relatively unaffected at 1.5%. The 1.0% figure is an average arrived at after testing a variety of wood samples. These figures also assume uniform drying, processing and sample consistency. In a soundboard panel, even individual boards that look the same probably come came from quite different trees that may have grown in completely different forests. Their mechanical characteristics may well be quite different. A piece of wood with very tight grain will respond differently from a piece with rather loose grain. A piece with a grain angle exactly perpendicular will not exhibit the evidence of fiber failure as early as will a piece with a grain angle that is 30° from perpendicular. The wood fiber close to a glue joint will fail sooner than wood fiber further in toward the middle of an individual board, etc., etc., etc. —ddf Robert W. Hohf wrote: > I read and enjoyed your articles. But I didn't intend to refer to a vibrating > soundboard here. I was referring to the static stresses and static shape of a > soundboard at rest. In the articles I was referring to I was also discussing the static stresses and static shapes of a soundboard assembly at rest. The dynamics of the soundboard are quite another matter entirely. Well, enough of this, I have to get back to work. (Besides, my coffee is now ready.) Regards —ddf
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