Vincentpa:
As Josh suggests, the whole idea of those stiffeners is to get that concentrated load into the web. They may, but don’t have to run all the way to the other flange. Of course, their loading must be reasonably balanced or they will tend to punch through the web at their middle termination, and that would be a reason for running them (or a single stiffener) to the opposite flange. The welds are checked for bearing at the flg./stiff. joint, and for shear flow over their height vs. your loading at the web/stiff. joint. Reread Blodgett, he doesn’t suggest ignoring combined stress and the potential of a bending component, but explains why it can usually be played down. Taller stiffeners will reduce this bending component, as will running the stiff. to the opp. flg. Also, consider, most of the load is transferred in bearing immediately around the beam web/flg. fillet and near this region in bearing on the flg./stiff. welds, at fairly favorable lever arms, not out at the tip of the stiff.