Jumbo:
There shouldn’t be any problem in doing that, just check the beam stresses at each of the transition points. And, the end connection design will change a little as a function of the shallower beam at the end. Pay some attention to detailing and welding details as these relate to any fatigue issues. The bending stresses are pretty low at that location in the beam span, although the shear stresses are somewhat higher. Talk with a couple fabricators about how they would prefer to do this in their shop. You could also taper the flange on both sides to a somewhat smaller width if you wished. There are basically two ways to do this:
Out at about 5' you saw cut the bot. flg. You want a gradual transition slope. Then you cut the web to the desired coped shape with the deeper transition starting at the flg. cut, and the upper transition, with a nice radius, at about 3'-8" and up about 6". You bend a new bot. flg. and weld it to the existing bot. flg. and then to the web. This bot. flg. weld is the critical detail, it should probably be full pen. and the two flgs. blended together in thickness and width. You might want to provide a web cut-out (see AISC typical details for beam flg. moment connections at heavy columns) so you can back gouge the top of the flg. weld and reweld it, under the web. Also, at the upper transition, note that the flange forces tend to pull the flange away from the web, so for 6" or so on either side of this transition increase the size of the web to flg. fillet welds a bit. One way to do this is to provide web bevels in this transition region, then fill the bevels and do the normal web/flg. fillet welds over the bevels.
Alternatively, cut the coped shape out of the web and just above the flg., and clean up the existing flg. in the area of the web/flg. radii. Then over bend (slightly) the upper transition into the flg., and finally bend the flg. up at the lower transition to match the web shape. This bending is usually done by heating the flg. at each bend area, and using typical fab shop bending equipment. Finally, make the web to flg. fillet welds, starting at the lower transition and working to the end of the beam. Note that these web/flg. fillet welds will seldom have to be as large as the radii in the rolled shape.
