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elinah34 There really aren't any relevant hand calculation formulas for a short beam. The closest you're going to get is something akin to stress on a gear tooth, and even this likely won't give you reasonable results for hand calcs. FYI, this is all reviewable in Roark's Formulas for Stress...

I think the reason you're seeing such a discrepancy between your hand calculations and the FEA results are because you're using σ = M*y/ I to determine bending stress. Beam bending is only really valid when the span/depth ratio is around 8 (according to Roark)... It appears you have a...