Simulation study on 2x4 lumber just for practice using simulation module.....(to see how much can be applied before it breaks)

Dave Krum - what version are you running? 

Generally 2x4s are made of pine.  I think it is Ponderosa Pine, but don't quote me on that.  Also remember the fiber direction makes a huge difference in the property (wood is anisotropic, steel is isotropic).  So, make sure you choose the correct modulus.

A quick web search turned up this resource:

http://www.conradlumberco.com/pdfs/ch4-Mechanical-Properties-of-Wood.pdf

I haven't looked through it completely and verified that resource.  But, it looks pretty legit to me.

...the math formulas for the handwritten workup

... thought it would be cool to see how much weight I could apply to the center of a standard 2x4 oriented the strong way before it breaks.

What are the limitations of a linear static stress analysis?

1. The math is appropriate within the linear portion of the stress/strain curve.  (Break (fracture) might occur well past the linear portion of the curve.)

2. Istropic material properties.  (Wood is not isotropic.)

3. Relatively small displacements.  (Relative is, well, relative.)

4. More reliable if the aspect ratio between width, depth and height is not too great (another relative term).  (Take a veneer strip of that material and you can bend into a loop.  Now you do not have an aspect ratio that extreme, but you have a pretty long, skinny part.)

Use caution with your analysis.