I have a tube with a circular cross-section, this tube protrudes from the ground vertically for a section, then arcs over to one side. At the end of the tube, a flat plate is mounted to the end of it. The arc is of a constant radius but is not necessarily a 90 degree bend. (i.e. the angle of the flat plate to the ground plane is not necessarily 90 degrees). How would you go about calculating, by hand, how much load the flat plate could hold before the tube bends beyond it's yield point.
Assuming all geometries are known and the material properties are known and constant.
I've been working on a solution using a combination of formulas from Roarks book. But, I'd like to see how others would approach this problem. "Solve using FEA" is not an answer i'm looking for, but rather a reasonably accurate hand calculation approach.
Edit: -dimensions and loading direction added
Approximate tube dimensions:
Vertical straight section: 1m
'Bent' section arc radius: 125mm
Flat end, 10 degrees to floor
Tube OD - 25mm
Tube ID - 23mm
Loading direction will be in the negative z-axis i.e. gravitational loading only.