... If "H" is a tension "doubler", not otherwise part of the beam "Second Moment of Area", then just fillets at the ends would do? Maybe small fillets along sides, out to edges of the "C" (channel) sections?
---------------------- As a separate element H is only a little stronger than the lower channel flange, because it has slightly more area and is further from the neutral axis, but as part of V it more than doubles the second moment. I think shear causes the difference.
I couldn't accurately measure these channels until a few days ago when I sawed off the end plates (they were pallet rack shelves) and removed the rust.