On May 25, 7:17*pm, (Doug White) wrote:
.....The part that always baffles
me is that the bending formulas are all in terms of the Modulus of
Elasticity, which doesn't vary much. *I expect work hardening & the like
to make a difference, but the formulas say not. * ...
Doug White

Here is a hands-on demonstration of hardness vs stiffness.

Clamp two long drywall screws upright in a vise, held by the tips.
Pluck them and adjust the length of grip until they sound the same.
Now heat one red with a torch and let it cool. Annealing removes the
hardness.

Pluck them again, they should still vibrate at the same frequency
which shows that mass and stiffness haven't changed.

Bend them with your fingers. Both show the same resistance until the
annealed one reaches its elastic limit and continues to bend with
nearly constant force.

Jim Wilkins