PowersPE80 :
As second and third ‘asides,’ that’s an awful detail and the angle extension will cause the whole beam be loaded torsionally. The angle’s carrying cap’y. is biased toward its vert. leg, so it will tend to twist the beam, or else its shear center should be centered over the web of the W4. I would pick a 3" S shape for the extension, and center it on the W4. Then, your welds are out near the flg. tips, so flg. bending, strain and deflection should be considered, as they relate to prying at the roots of your longitudinal fillet welds. Finally the end terminations of your welds are particularly sensitive to stress concentrations by the nature of the weld process, and your arrangement essentially has the potential of infinite weld load or stresses at these weld terminations. They will just unzip from one end or the other. You might increase the lap length to something greater than 6" to improve this situation, but in its simplest form your moment is resisted by a weld load couple with a lever arm of about 5". I would increase the lap length, and put cross welds from flg. to flg. at both ends. These welds would/could only be about 2" long, but they would be centered over the webs of the two members and be much less susceptible to high stresses (unzipping stresses) at weld end terminations. I would leave the light longitudinal welds, just terminate all the welds short of an edge or corner. Do not weld all around, and over a corner, or you just create another notch.