I will assume you are referring to the inside rolled cope of the beam where the flange and web come together. Other than access to achieve a good quality weld, no. The weld profile will be odd for two reasons...you are likely to leave inclusions on the back side of the plate unless you miter the plate to its back side, leaving no land. The opposite edge of the weld would be made against the coped surface, making the weld section tapered in thickness. I doubt that this profile would be pre-qualified, so to meet US code, you would have to qualify a welding procedure specification for this.
I don't because you can introduce a triaxial stress state that can crecipitate a crack. With older steels this was a bigger problem. It is not a good idea.
A shear plate to a girder web is typically clipped in the corners. Although the residual stresses in the corner will be minimal in a shear only condition, this is still not recommended. The clips also allow the plate to fit properly to the web and flanges. Otherwise gaps are created.
I went to an AISC welding class a couple years ago. They reccomended against it as this area will have higher residual stresses due to differential cooling after rolling. There is specific guidance as to the distance away from the area to weld. I would reccomend that you look at AISC design guide 21.
I quickly went through my desk in hopes of providing a more detailed response, but to no avail. I will have to dig into the filing cabinet.
Paraphrase from my AISC connection class handbook...
Cracking has been reported in the k-area (web/flange juncture) of rotary straightened wide flange shapes (AISC 1997). Most of the cracks occurred at highly restrained joints (like at column doubler plates) indicating that weld shrinkage stresses contributed to the cracking. Rotary straitening involves cold working of the k-area resulting in a reduction in toughness and ductility. Larger sections are currently straightened by other means that do not result in as much loss of toughness in the k-area. FEMA 350 (2000) recommends that it is prudent to assume that all rolled sections are rotary straightened.
In some cases CVN toughness was below 5 ft-lb absorbed energy at +70 degrees F and the ductility was less than half that in the other parts of the cross section. (Tide 1977).
To avoid k-area welds the manual recommends larger columns, corner clips, fillet welds rather than groove welds for doubler plates, increase preheat and minimize weld volume, and consider magnetic particle or dye penetrant inspection for welds near the k-area in highly restrained connections.
