If you look at the OPs post on the 06/05/2021 He clearly states the lug design is not considered here and the sketch is not accurate, in fact I certainly wouldn’t put lifting lugs in the position that’s shown on his sketch, however he was asking about stresses during the lift. Now if the lifting cables were vertical, then the small additional moment due to the 45 degree angle of the cables would disappear and the beam under self weight would sag and give tensile and compressive stresses in the normal way. My attempt to show how to calculate lifting stresses of the beam in a similar manner to that of the OP’s sketch showed that the additional bending moment was about 25% extra when compared with lifting cables being vertical for the lift. I have seen lugs welded on beams ,frames etc and then burnt off once they are in position, alternatively I have seen ropes/straps wrapped around beams and also lifted in place and so long as this is
Done in a safe manner it’s not a problem. Given that we don’t know the shape or size of the beam or it’s intended use we are both second guessing but reading between the lines of the original post I believe that the poster just wanted to know how stress the beams while it’s positioned but I could be wrong.
If the beam was going to buckle under its own weight when placed horizontal in a structure, I would of thought that it would have been considered long before it was going to be lifted by a crane.
“Do not worry about your problems with mathematics, I assure you mine are far greater.” Albert Einstein