To use the steel effectively as a flitch beam it would have to be sandwiched between wood members. Strength in constricted spaces seems to be the main advantage of using them.

When I renoed century homes, this DIY butchery wasn't uncommon. (What did these people think held up the house?)

I've always just sistered with wood joists. Be sure to check the floor level first. There's likely sagging that can be corrected.

(I recently saw one of those home reno shows where the ceiling had been opened up, revealing a whole missing support wall. In place of the wall, some hack had put in a couple of steel fence posts to "support" the joists.)

Here is a link that might be useful: Guide to Flitch Beams

Flitch plates are normally used between wood members (and through bolted repeatedly) to provide the plate with buckling resistance.
The metal is normally relatively thin compared to its height.
By trapping it between wood members you prevent buckling, but it needs enough fasteners to not exceed the crush rating of the wood in two planes.
The structural load is vertical (parallel to the height of the beam) and the buckling load horizontal (perpendicular to the face of the beam).
You could use thicker metal but it would be far more effective to either use u-channel or angle iron across the damaged area.
I would use either U or angle on both sides with though fasteners.
The leg of the angle perpendicular to the side of the beam acts to prevent buckling and the metal on each side distributes the load across the face of the beam and prevents crushing under the fasteners.

Oh, that sounds too familiar

State of our LR ceiling/BR floor

Corrected by 5 new LVL's I believe

Good luck - no fun correcting others' errors!

thanks for the info--here's pics for clarification.

After deciding we couldn't alter the angle iron to sit on the "sill" to bear weight, we're back to the idea of using wood 2x6 so we can notch it out to do so--possibly adding some steel plate for strength. Our handyman suggested 1/2 bolts for fastening, and using 2x6 on both sides. He thought the 2x4's in the pic aren't doing much supporting--I don't believe they extend to the sill. They're sitting on a corner unit built in to hide the plumbing--not sure how strong that is.

Here is a link that might be useful: joist pics

How many adjacent joists were V-notched like that? I can't tell from the pics.

Only one was v notched (the one under the toilet).

the one next to it, towards the outer wall, has a very large irregular hole. the one next to, towards the center of the ceiling, has a smaller hole large enough to accomodate the 2 copper & one drain pipe. Still largish.

Upon peeking through that joist (and worrying that they butchered them down the line, all the way to the sink at the other wall)--the next joist had 2 small, perfectly round holes for copper, and one round just large enough for the 2 inch pvc. Hopefully that's what the rest look like.

I've been looking at a small inspection camera at the local hardware store with a 3' foot cable that would be great to peek inside walls & ceilings--I'm trying to convince my husband that we need one ;-)

The 2x4 is likely to be doing a decent job if it is fastened well enough to the old joist.
The bottom of a joist is in tension, and as long as there are enough fasteners to not crush the wood fibers the 2x4 will take the tension.
It would have been better to pout 2x4s on both sides of the old joist and through bolt with 3/8 fasteners (bigger does no good due to crushing of the wood fiber for most softwood joists).
You should be able to easily use 2 inch steel angle iron on each side of the old joist to replace all the 2x4s.
The load rating of a pair of 2 inch angles (use the 1/4 inch thick stuff) is way over the missing wood.
All you need is enough fasteners to adequately transfer the load between the wood and steel.

Thanks!

Brickeyee, do you mean 3/8 bolts?

So, 2 pieces of angle iron, one on either side, right? Could you give any more information as to number & placement of bolts?

thanks if you spare a bit more info!

"Brickeyee, do you mean 3/8 bolts?"

3/8 bolts are fine. Anything larger almost always exceeds the crush rating of 2x softwood lumber.
The fastener schedule depends on the wood species.
The span of the steel depends on the loads, the location in the joist, and the wood species.

A few $$ to a local engineer will provide a fix that will be acceptable to an AHJ.
This is the type of thing that can only be designed after a examining the actual installation.