This isn't really a "by hand" calculation. Not that it can't be done....

Why don't you just find your critical cross-section and work from there?

This depends on the materials, whether they are linear or not, whether the cross section is symmetric etc.

Jason McKee
proud R&D Manager of
Cross Section Analysis & Design
Software for the structural design of cross sections
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Henry,
looking at the proportions of the FEA model you showed I suspect the theory doesn't match for few possible reasons:



1, Not a slender beam. Formula σ=(M*y)/I is valid only for fairly slender beams
2, The section variation is too quick along the axis. Meaning that the transmission phase from one section to another affects the outcome more than the section "straight" section.
3, Related no 1. Section is too narrow. I understand the bending is around Y axis.

Can't tell from the picture but I take it the section profile is a rectangle (no rounds or anything that would make it a non-flat beam)
It is also difficult to say whether your verification model in ANSYS was corresponding to your hand calculation.

If you indeed need to analyze section like the one shown AND not too very frequently. I recommend sticking with FEA to save yourself a hassle. If it would be still a frequent matter, then APDL scripts might help with automation. Otherwise you need to deal with some of the problems when doing hand calculation.

I hope this helps.

Thanks for all the input.