I am in the process of renovating my bathroom. Two floor joists (2"x8") under the tub were notched to accommodate the plumbing. One joist runs parallel to the length of the tub is notched out by 80%. There is only an inch and a half of wood left. The other joist is beside the other is notched 50%. However, the floor in the bathroom is level. I want to put a bigger soaker tub in. Both of these joists are under the tub. I definitely do not want to sister in new joists over the whole span because I would have a lot of electrical work moving the wires going through the joists. I want to sister in 4 foot 2x8 joists by laminating with construction glue and securing with 4 to 8 carriage bolts. I am also considering using a steel plate on the other side of the damaged joist and tie the carriage bolts through the steel also.
Answer:
A 4' scab is not going to be enough. Each end of the scab should go at least four feet past the notch or be sitting on a support (concrete wall?). If you cannot do that, you have a lot of wiring to re-do.