Re: leaf spring energy

[jmclean@chem.ucsd.edu (James Mclean)]

David Dockstader says:
> At any given point the stress in a material may be described by an ellipsoid.
> If one examines the stress on planes of different orientation one finds planes
> where the shear stresses disappear and one has only normal stresses to contend
> with.  These are known as principal planes and the stresses are the principle
> stresses.  However at other orientations there will be shear stresses and
> somewhere there will be a plane where the stresses reduce to a hydrostatic
> normal stress plus a shear stress.  Thus, your visualization of the shear
> stress is not incompatible with the notions of compression and tension in a
> bending beam.  They are just different manifistations of the same stress.
If I understand this correctly, you are saying that the stress tensor can
always be diagonalized.  Is that correct?

Please elaborate on the ellipsoid visualization.  I'm not seeing how
rotating a diagonal matrix can be so represented.  Do you mean a genuine
ellipsoid, or just an oval-oid like shape?

I think that in these terms, my 'misconception' could be restated as:
In a bent leaf spring, the principle stress planes are never perpendicular
to the surfaces of the spring.

-- 
--James McLean
jmclean@chem.ucsd.edu
post doc
UC San Diego, Chemistry