We have done this many times. The issues to watch out for:
1. Understand that the web members may not all have the same capacity across the span (including the weld connection to the chords). Thus, you should first establish a shear/moment load capacity diagram across the span of the existing joist. The shear capacity would be the normal "bow tie" shear diagram...but one that doesn't go to zero at the midspan. SJI requires joist manufacturers to design webs for a minimum of 25% of the maximum end reaction. This gives you a shear capacity across your original, full span.
2. The same goes for the bending, although by observation, you can field verify whether the top and bottom chords have the same cross section along the full length of the original span. If so, your moment diagram of the original joist gives you a rough, conservative moment capacity curve.
3. Now that you have the capacity envelope diagrams across your original span, generate the new, anticipated shear/moment diagrams for the shorter span and super-impose this on your original shear/moment diagrams. With the shorter span, most of the time you should be OK. In some instances, though, your shear at the cut end may exceed the original shear capacity and you must add additional diagonal web members (usually small angles welded to the outsides of the chords, paralleling the existing diagonals.
If you have any moment capacity problems, many joist manufacturers will weld rods to the inside "elbow" of the chord members to add area, and thus, moment strength.