On 12-Aug-2003, Tom Watson wrote:

I should have referenced this formula in my original post. It comes
from the AWI spec book and they got the formula and the field testing
from the University of West Virginia wood sciences people.

That's interesting - the formula is identical to the one previously posted
but with the constants multiplied/divided out ( 5*12/384 = 0.15625) and
the variables factored into something simpler. Hence it's the plain old
elastic theory solution - no correction for the specific properties/behavior
of wood. It may still be reasonable if applied correctly (something that
really is a beam), but I'm fairly certain that a wide, thin sheet of ply
supported at four corners isn't quite right.

To use this reliably, I'd expect the short sides of the plywood to be
fairly well supported so they don't flex much. Four legs bolted on won't
do that.

Consider a really thin sheet (one extreme of behavior). It will act as
a membrane and it will sag like a "bowl" and the legs would collapse
At the other extreme is an infinitely rigid board. The original poster's
plywood table is somewhere in between, probably closer to the
membrane. Hence the beam formula is probably not reliable.

The real deflection formula would be a fourth order, second degree
differential equation (or is that second order, fourth degree?) and you
don't want to go there.

The problem with those handbooks is that they don't always tell you
the limits of applicability.

I haven't heard anyone say "This is a good idea" so I think that the
smart money is on making a stiffer table.

Mike