Sistering wood floor joist, not along entire span, question

[StevePac]

Hello everyone,

I have an issue with a home I recently purchased - the previous owner had some plumbing work done for a 2nd story bath, and cut up a couple of joists pretty bad. One they cut about a 10" section out almost completely (save about a half inch at the bottom). The next joist over they aggressively notched. And the next joist over they drilled holes almost to code for the drain and water supply piping, but the holes are a little too close together, and not quite far enough away from the top of the joist.

The joists are 2x8's. They span almost 11', spaced 16" on center. I would like to sister a new member to these compromised joists, thinking a 2 x 8 Doug Fir from home depot. The problem is I can't sister the entire length without removing the bathtub as well as a considerable amount of sub-floor. I'm thinking of running the sister about 2' past the damage on each side, I'd prefer even shorter if it works - but I can live with 2'.

My problem is how do I prove it works? I want to bring something to the building inspector so I can talk intelligently with him about it. I am a structural engineer so I understand the basics. I can prove the member works if it was fully intact with moment, shear, and deflection, but I'm a bit confused as to how exactly things change once the sister is attached.

I have read through similar comments on this site and have not found a complete answer to my question. What I have found is advice saying as long as the existing member has the shear capacity where the sister connects to the old framing member it will be ok.

I know the shear at the end supports (assuming the beam was fully in-tact) is ~370 lb. I would assume this value is the max shear, and the shear where the sister connects would not exceed 370 lb. So wouldn't I be ok? Or does it matter that the max shear is now about 3' away from the end support? I know a 400 lb. point load 3' out affects the moment, but the overall should still be the same...I realize I'm assuming the sister basically brings the member back to being a fully in-tact beam, which practically may be true but technically is not.

I have the 3 compromised joists drawn up in CAD and can post a pic tonight when I get home if that helps.

Thanks,
Steve

 

[jayrod12]

My concern would be moment capacity across the splice. Transferring the shear through the sistered wood is not as hard and can be accomplished with the repair you're describing. Getting the moment to transfer from existing member to new and back to existing is tough. There are some shear flow calculations that you can perform. I believe if you search wood splice on this site you should come up with some stuff.