>Ric B wrote: >>>Its a >>>question of degrees... and as somebody (I wont get into who... >>>grin) pointed >>>out a couple years back in another soundboard discussion, with >>>something about >>>a mosquito colliding with a Concord.... relative to what deflects what.... >>>every little bit counts... Ron N wrote: >>An aircraft carrier, not the Concord, and if you want relativity, >>pay attention this time and I'll try again. These figures are >>approximate, and I'm not interested in all the details of what >>might happen on the molecular level. Just in case. >> >>A rib of 800mm (35.5"), crowned at 18M (59') radius, is 0.069mm >>(0.0027") longer over the "arch" than the straight shot of the rib >>length. The crown height is 4.44mm (0.175"). The outward "thrust" >>of an arch of these proportions should be roughly proportional to >>the leverage arms of half the span divided by the arch height, or >>90.09:1, so every pound or Kilo of bearing put on the bridge in the >>middle of the arch would put 90 pounds on the edge of the >>soundboard. My quick calcs yield half this number. >> Ten pounds of load would put 900 pounds on the soundboard edge. A >>rib half that long will produce over twice that thrust ratio. > I think you have this backwards. Half the span with the same crown height would yield half the thrust. Also, my understanding is that rib crowners tend to put more crown height on the shorter ribs, which would further reduce the thrust. >>A piano with an overall bearing load of 700lbs will be putting >>considerably more (since most of the ribs are shorter than 800mm) >>than 63000 pounds of outward thrust on the rim. A considerable >>portion of this thrust will be on the less substantial belly rail. >>The panel that was dried down to 4%MC for assembly and re-hydrated >>to 8%MC has already been compressed 5.5mm (0.2") or so, and is >>already under considerable PSI load. It will take a lot less than >>the additional string bearing load to compress the panel another >>0.066mm (less than half that on a rib half that long). So the >>physical compliance of the material is considerably higher under >>the loads imposed than would make it possible for a soundboard to >>work as a buttressed arch. Even if the rim was infinitely stiff, >>the soundboard material would not make it possible. The centripetal >>tension resonator does not, and can not in any way support and >>maintain crown for any length of time and to any degree. The >>compressibility of the panel material just won't allow it. >> >>Arguably, and I know that if it is, you will, the "resonator" might >>just actually help to support the soundboard crown until enough >>strings are installed for the bearing to overpower the >>compressibility of the wood, but it's all over long before it's >>chipped up to pitch. >> >>Ron N This argument is convincing if you insist that if the soundboard acts as an arch, then all the string loading must be taken as an arch. All the load doesn't have to be (and won't be) reacted this way. The panel has bending stiffness, as do the ribs, as does the combination of the two. Also, the ribs tend to get ignored in these arch discussions. If the ribs are glued to the rim then they have an arch load path along the grain (their strong direction). The load will divide itself among the load paths according to their relative stiffness. If the rim is flexible and the cross grain stiffness of the panel is low and the compressive stiffness of the ribs is low then this path will be soft relative to the bending path. That doesn't mean it's nonexistent. Perhaps 10% of the load could be taken by the arch and 90% by bending. If this were the case then the compressive stresses in the board might be well below the allowables. And the rim (or tension resonator, or whatever) could be said to be helping to support the crown. I don't know what is actually happening. But I would like to see something other than argument or calculation before accepting the dictum that the rim and frame do nothing to support crown. A proposed experiment: Take a crowned section of panel with a rib attached. Glue one end to a rigid support. Glue the other end to a block which is guided by bushings or rollers, so that the block support will resist vertical load and rotation of the edge of the board (as in a piano) but will not offer any restraint for outward movement of the edge (in other words will not permit an arch effect). Put on load of your choice at the midpoint and measure the deflection. Next take the same setup but rigidly fix the block to a support, so that it can't move (in other words it will permit a thrust load or allow an arch effect if there is one). Put the same load on the same spot and measure the deflection. If I understand you correctly, your contention is that the deflection will be the same in both cases. My belief is that the case in which the block is rigidly supported will have a lower deflection. If it does, this indicates to me that the framing can help support crown at least temporarily. If there is a difference in deflection, then you could work backwards, using the original setup and putting a thrust load on the guided block to see how much load was required to cause a rise in the middle of the panel equal to the difference in deflection. This would be the amount of thrust load or arch load that is being supported by the frame. Dividing this load by the cross sectional area of the end of the panel (ignoring for the moment that the rib is stiffer and would pick up a proportionately higher percentage of the load) would give the compressive stress due to the arch effect. If this stress is substantially below the allowable stress for the material then this support should not be temporary. If this stress is a high percentage of the material allowable then this 'support' would only be temporary. Phil Ford
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