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First of all, thank you dlooman for your perseverance!
I'm pretty sure there is a linear distribution of normal stress in beam axis direction. I haven't found a nice figure for my example (rectangular pipe), but for standard rectangle und T-shape cross section I found nice figures here Spura 2019Â (very nice book by the way).
And even if we neglect the linear distribution. We just can calculate the max normal stress located on the top (or bottom) edge sig_y,max. Continuums mechanics (without any FEM) gives us 94,1 MPa (see fig. 2). And by summing up the constant normal stress and normal stress resulting from bending (see fig. 3), we should get 94.1 MPa. Superposition is definitly allowed, as shown here: