Compression in Soundboards

[Robin Hufford]

Hello Richard,
     I have not had the time to study all of the RC vs CC posts to
follow the line of thought there but the question of compressive stress
in soundboards and the deleterious, ubiquitous effects so direly
lamented and commented upon in articles by Fandrich in the Journal and
defended vociferously here on the list by Nossman are predicated on
very questionable assumptions, number one and, number two don't appear
to be as generalized a fault as is frequently claimed.  Some of the
reasons for these discrepancies, I would suggest, lie in certain
erroneous assumptions made in their analyses which I have intimated
before.
     The tests used by  labs to develop testing data for mechanical
properties in wood are based upon simple, clear specimens, a point noted
in cautionary commentary  made by Hoadley and in other references which
are frequently referred to here by this school of thought even though
the general cautions and limitations of these tests themselves appear to
have been disregarded, or misunderstood.   The tests themselves are
uniaxial, that is the compressive force or tensile force, as the case
may be, is applied in one dimension; for example the determination of
the fiber stress at proportional limit in perpendicular to grain
compression which is so often used to assert that soundboards experience
disabling damage.
     Uniaxial stresses in wood in situations such as the testing for
mechanical properties normally quoted are greatly different from  stress
distributions occuring  in soundboards.  Such distributions preclude the
kind of simplied approach taken in extending such things, for example,
simply calculating that cross grain compression will reach such and such
a value, and that a soundboard has, in fact, been damaged in such a
case.  This is practically a case of admiring the Emperor's new clothes
in my mind.  This may or may not have happened and, in fact, it is
unlikely that stresses will have reached damaging levels due to the fact
that the interactive stresses in actual, real soundboards, invalidate
applying, without at least some discretion, simple unaxial moduli.
     In a real soundboard  the stresses encountered would be more
accurately characterized as tri-axial due to the loading of the strings,
the bridges, crown, etc.  This is an absolutely critical point.
Triaxial stress in wood is not as well studied and, where such studies
have been undertaken they demonstrate that it is entirely unwarranted to
make generalizations about complicated structures and stress
distributions proceeding from the results of simple uniaxial tests.
Elastic moduli change depending upon the complexities of the stress
distribution itself.  To disregard, or be unawares of such things and
proceed to develop a complicated rationale for failure without taking
them into account is produce nothing but questionable generalizations as
I have maintained for several years now.
     Take a look at:
              http://www.ndt.net/article/v04n11/mascia/mascia.htm#5 for
one such study.
     The uniaxial tests themselves are made under certain simplifying
assumptions which are also questionable.  Again, this is part of the
rationale, in my opinion, for the cautions found here and there in such
references.
     A second, also highly important point of criticism concerns the
assumptions made for the uniaxial tests of mechanical properties
themselves which assume isosotropy and the applicability of Saint
Venant's principle which asserts that the intermediary cross section
must have the same distribution as the end cross section.  Such
assumptions limit their applicability to a complicated composite
structure such as a soundboard in which it is necessary to take into
account the effect of numerous boundary conditions such as bridges, the
rim, the ribs, soundboard buttons and holes,  not to mention alien
stresses such as the downbearing load, having been forced down on the
rim in certain areas during installation, the effect of the bridge and
crown itself.  etc.  Another useful site on this point:
             http://www.nd.edu/~ame/announcements/Horgan.html

     I include part of the abstract of the site given just above for
emphasis:

     "A proper assessment of end or edge effects in composite structures
is of fundamental technological importance.
      The extent to which local stresses can penetrate structural
elements must be understood by the designer. Thus a
       distinction must be made between global domains (where Strentgh
of Materials or other approximate theories
      may be used) and local domains which require more detailed (and
more costly) analyses based on exact elasticity.
       The neglect of end effects is usually justified by appeals to
some form of Saint-Venant's principle and years of
        experience with homogenous isotropic elastic structures has
served to establish this standard procedure.
        Saint-Venant's principle also is the fundamental basis for
static mechanical tests of material properties. Thus
     property measurements are made in a suitable gage section where
uniform stress and strain states are induced and
      local effects due to clamping of the specimen are neglected on
invoking Saint-Venant's principle. Such traditional
        applications of Saint-Venant's principle require major
modifications when strongly anisotropic and composite
      materials are of concern. For such materials, local stress effects
persist over distances far greater than is typical
       for isotropic materials. In this lecture, we provide a survey of
situations in linear elasticity where anisotropy and
      material inhomogeneity induce such extended Saint-Venant end
zones. The implications for the analysis and design
                        of structures using advanced composite materials
are addressed."

     It should be easy, although I don't know why it would require my
posts to make them aware of it, for a certain school of thought which
frequently condemns soundboards based upon what can be seen to be
questionable calculations, to see the utility of caution  for those that
claim to have fully understood soundboard behavior when making sweeping
generalizations about such a "strongly anisotropic and composite
material" such as a soundboard most eminently is.  Yet, no such caution
appears to be evident.
Regards, Robin Hufford

Richard Brekne wrote:

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