Theoretically you can resolve the torsion to two vertical loads. But the reality is there will also be some horizontal loads in the top and bottom HSS faces which want to try to warp the flange of your W310. Combined with the fact that a girt would often also have some horizontal loads due to wind/seismic face loading, this suggests you need some horizontal load path back to the column web rather than putting your welds into bending to transfer the loads to the column web via flange bending.
Also not quite sure how you would even get the fillet weld inside the HSS, access to weld and inspect seems very limited?
Can you cope the HSS into the web instead and FW all round? Or provide some web stiffeners to complete the horizontal load path?
Even an end plate welded across the column flanges and a stiffener(s) in the web behind with an end plate on the HSS and bolted connection may be easier to fabricate and erect? Kind of like this?
Even an end plate welded across the column flanges and a stiffener(s) in the web behind with an end plate on the HSS and bolted connection may be easier to fabricate and erect? Kind of like this? said: