Re: leaf spring energy

[David Dockstader <DRDOCK00@UKCC.UKY.EDU>]

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.

On Tue, 14 Apr 1998 23:32:46 -0700 (PDT) James Mclean said:
> Why did I expect this?  Say a force F on a 10cm spring gives angular
> deflection phi.  Now, for the same force on a 20cm spring, consider the
> outer 10cm of it.  That outer half is static, so the total force on it is
> zero.  This implies that the force of the inner half on the outer half is
> -F, and (for small phi) is almost entirely a *shear* force.  By N3, the
> inner half of the long spring is exactly the same as the entire shorter
> spring, so it has deflection phi.  Of course, the outer half also bends.
> So for constant force, a double length spring will have double the angular
> deflection.  This argument only really makes any sense for small phi, which
> is why I was so surprised that my experiment worked so well.
>
> (An aside:  it took me quite some thinking to realize the existence of this
> shear force.  Perhaps this is one for the misconception list?  A leaf
> spring does *not* support/push things by compression/tension along the
> spring.  That's incompatible with N3.)
>
> Besides the fact that I found the angular deflection 'phi' easier to think
> about in the above argument, there's actually another reason to consider it
> instead of the distance deflection 'x'.  My guess as to the important local
> property of a bent leaf spring is the curvature, which is given by the
> derivative (d phi)/(d d).  (I've been trapped by my notation, but I hope
> that's clear.)
>
> --
> --James McLean
> jmclean@chem.ucsd.edu
> post doc
> UC San Diego, Chemistry