If I am picturing that correctly then the strut will be in pure tension in flight & compression on the ground, with no bending moment.
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Pure bending in flight only when under positive g, but you must allow for the negative g limit loads causing column buckling, which as pointed out is usually the critical factor for a wing strut.
Note that the buckling load is independent of the tube's tensile strength, it's a factor of geometry and the elastic modulus... i.e. a 4130 tube will be no stronger in buckling than a 1018 tube.
How I understood his description the ends would be free to rotate so there would be no bending moment, but I would need to see drawings & do some calculations (and get paid) before I would put my PE stamp on anything. On long members buckling loads are usually the problem.
Does that 1928 strut include a jury strut in the middle? I hope it does, it would be weak in buckling if no jury strut.
I have seen several Piper Cubs that had collapsed rear struts from wind coming from behind (while tied down outside).
Cub owners will duct tape 2x4's to the rear strut to prevent this collapse on high wind days.