Are there span tables published for repairing a cut roof joist?

Question

A roofing company mistakenly cut a 2 foot section out of a roof joist, on my home. I'm seeking a reference to what would constitute a proper repair, preferably a prescriptive code or a load table. I am aware of the American Wood Council tables, but that's for uncut modern lumber and at this point I have neither.

This rafter spanned 14 feet with a mid span support. The roof is flat, with 2x4 rafters at 24 inch on center, topped with 1x6 boards, all nailed. This is all true dimension rough cut Douglas Fir: good solid stuff.

One end of the cut rafter buts against a brick chimney. The house was built in 1938 and is in an earthquake zone (Hayward Fault).

The roofer said nothing but screwed some plywood on top to cover the gap.

Update 1: The roofer added a patch. The gap is almost at the center beam. The patch overlap is 9 inches on the right side, and about 4 inches on the left. On the left both new and patched rafters straddle the center beam.

The only access is through a 14 inch hole below.

Update 2:

After consulting with a structural engineer (who wanted 12+ inches of overlap), we ended up compromising a bit. A filler piece will take compressive load when the chimney slams into the house in a quake:

Answer 1

There is no mention where the cut out is but this should take care of it in any respect, as long as the mid span support is a series of posts and not a purlin... Can you get a 2X6 in there that will give close to a full span? if the material is clean or can be scraped clean, a healthy bead of construction adhesive zig-zagged on the face of the old 2X and screw the 2X6 starting 4 inches from the ends with a pair of screws and 12+/- inches apart in the remainder in pairs also. Use 3 inch drywall screws or 2 3/4 inch SDS screws through the 2X6 into the 2X4. Make sure the screws draw tight the material, pilot if needed with a 3/16" bit.

If you have a mid span support that goes to good bearing through to the foundation, you can use a shorter repair joist, but a single joist that goes over multiple spans is stronger than a single span joist.

FWIW, it looks like a 2X4 will suffice from what I seen the table at page 396 of the 2012 building code (table R802.5.1).

Answer 2

After asking here, on the Journal of Light Construction, and consulting with a structural engineer, I was unable to find an answer to the question. Everyone just guesses when it comes to wood repair, there are no published tables for joints or splices. If you have a better answer please post it.