Static Analysis of a short beam

Hi guys and gals,

I have a short simple question. To put it simply I'm making a seesaw. Now the pivot or the teeter bar (seesaw bar) is a short piece (12") of 1.25" solid bar. The bar goes through the center of the teeter bear and each end of it its secured in pillow block bearings.

I've done the FEA for the beam so far and have gotten my results however, I'd like to to some sort of hand calculations to verify if the result of the FEA is as I predicted.

Does anyone know what sort of stress theory I'd have to use to do the hand calculations for this?

I've added some images to explain the case.

Thank you,

David

TOP VIEW

FEA SETUP

THE POINTS WHERE THE TEETER BEAM IS WELDED TO THE SHORT BAR

SolidworksSimulation