First, let me just say "hello". I'm a practicing strucutral engineer, and TFs got me into the building side of engineering a decade ago.

Yes, FEM really works, but only if you do it right, and it's very easy to do it wrong. I've been doing this kind of work for about 15 years, first for shuttle and low eath orbit payloads, then for military/black project gear, now for buildings. Analysis ALWAYS gets followed by at least a rule-of-thumb check, and often by a supplemetal (but simplified) hand check. While there's no magic to it, the complexity with which you can model something can easily outstrip any closed form solution.

Wood is a special beast. It has the worst properties of any engineering material I can imagine, except possibly soil. The designs for wood are less "exact answers" and more "relatively safe envelopes" since the properties will vary quite a bit within grades and species.

What you may be thinking of is the theory by which FEM works - the stiffness matrix. A strucutre is broken down into degress of freedom and a stiffness matrix is generated. It is then inverted and multiplied by the force to get displacements. Derivatives are taken to get the rest of the "stuff". That's a gross oversimplification of modern solvers - but I'll take it one step further. A simple spring is governed by:

F = k * x

where F is the force, k is the stiffness, and x is the displacement. A timber beam is a spring. Push on it in the middle and it defelcts. if you know the force and measure the deflection, you can get the stiffness. So 1000lbs in the middle of an 8x10 creating a 1/4" deflection is 4000lbs/inch. Piece of cake right?

So if you can calculate the k, and you know the F, you get the x...

F / k = x

Simple! For FEM and frames, all those simple values become matrices, with thousands and thousands of terms. Those terms are interdependant (push on a knee brace and it deflects a column).

Here's the kicker - with the material stiffness within a grade possibly varying by a factor of 2 or 3 over the 5%-95% range, you introduce an effective error in your model.

It turns out that it doesn't matter too much. The averages tend to work in our favor, and the factors of safety used are conservative enough to catch most of the funny business. That, and while you can get lumber to vary wildly, you still end up with mostly the middle of the road values.

So, yeah, it's not quite like entering 6061T6 aluminum with +/-0.0005 tolerances, but it really does work.

Now if I could just figure out how to take a solid model from ADT and collapse the memebers to line elements for importing into my FEA software, I'd be dancing a jig.