how do you support a sawn off loft beam?

I assume you've cut it to fit a loft ladder!
Two ways 1. Get some timber the same or near the same dimensions as the ceiling joist you've cut. cut two lengths to fit accross the gap neatly against the full joists each side and against the joist you've cut. Nail in place with cut nails any DIY shop has got them..
2. The other method is instead of nailing fix four joist brackets/hangers in position and drop the new cut lengths in then just nail them through at the cut joists point . If you are boarding the loft in then the boards will act as ADDED support if you screw the boards down on to the joist . I cut mine out to fit an American style loft ladder. More than twice the length of the standard loft opening and it ain't moved.

Bob the builder

B.t.b
January 2005