YOu know, FEA is really sensitive to element type and mesh resolution so I would do a mesh sensitivity test before reaching any conclusions. Also for that big span (high aspect ratio) would be more suited beam elements rather than 3D solid elements, so basically you have to calibrate your FEA simulation by the hand calculations.
Also, with the 10x length, your theory is showing a 1000x displacement. I wonder if you shouldn't be doing a non-linear at that point anyway.
The hand calculations are working under beam assumptions, so we should really run the study with beams to compare them.
I just ran them in beams and the results are better matched to the hand calcs. I've attached the file for you to review.
I think the issue is the restraints, with beams we have rotational degrees of freedom in the nodes whereas the solid elements you were using do not have these, so we have to be careful with the restraints we apply when comparing beam hand calculations with solid meshes.
Span TEST.SLDPRT.zip 395.8 KB