This might not be a problem, but I don't like the wood studs the black drain pipe passes through. First, the horizontal 2x8 isn't supported. Treat it like a window header and install jack studs under it (one on each side). The hanging sink can be heavy.
What I've done with the 2x8 is screwed in 2x2s to the studs in behind it with 3 inch s/s screws. Then I was going to attach the 2x8 to the 2x2s with more 3 inch s/s screws. The sink that will be hanging there is small and weighs 25 lbs. Would my method be acceptable for that weight?
1. Someone leaning on the sink can add to the weight...
2. 2x2s are bad in general, unless they're a nailer for drywall. You need 2x4 in order to put in TWO large screws/nails. While I like screws, their sheer strength is a lot less than larger nails. I always use more screws than I would nails when any loading is involved.
3. I really can't say (without doing calculations) if your scheme is sufficient. Follow the weight. Sink puts weight on 2x8 levering it (rotating it) as well as pulling it down. Your framing needs to consider this twisting.
I'd get as strong a connection at the corners of the header as possible, using doubled wood to give more surface area for connecting the header to the studs. I'd also double the studs to control their deflection as the header twists.
Don't forget to fasten side by side studs together to unify them into a single piece, ditto for the header and its backing.
Note: I'm a DIY with common code knowledge, plus a few civil engineering courses from my college days. What I don't often know is what solutions are used in the field, i.e. were engineered way back in time and passed down as "works fine". If I can't find a specific example, I often just overbuild it rather than take a lot of time doing the calculations.
Second, the old notch at the bottom of the doubled stud isn't sister-ed well. The break in the right hand stud is too close to the notch. This problem may be fixed by adding the jack stud if the wall is non-bearing.
The wall is non-bearing. The stud on the left isn't actually the stud that goes to the top plate. It's the one on the right which, when we opened up the wall, was missing the entire bottom piece. So, I cut a piece that fits in there snugly and was going to screw it to the stud on the left (which is what was holding up the framing for the old medicine cabinet.
missing the entire bottom piece!!!!! It wasn't doing any work as a stud, i.e. carrying the compressive load from the wall top plate down to the joists!
I'd like to think that sistering it on the right (left doesn't count because of notch) would help, but I don't know that the sister would extend far enough past the break without running into the drain pipe. Bottom line is probably "no problem" until the tornado comes or tree falls through the roof.
Finally, any remaining notches, like the one in the left hand stud, must not remove more than than 25% of the 2x4 (.25 x 3.5"=7/8" ) for a bearing wall, and not more than 40% (1 3/8") of a non-bearing wall. Measure to see if you need to fix them. Also, I'd treat that stud as bearing because it's supporting the header for the sink.
I was going to add another piece of wood to fill that squared notch on the stud on the left.
(Old) holes are centered and 40% max in a bearing wall, 60% non-bearing; all seems OK there, nothing to fix. Doubling the stud allows the hole for the drain pipe to be larger than the hole size allowed in a single stud.
So, can I screw in the piece of stud I added at the bottom of the one that's cut out and add the third stud to the right of it but only up to the new pipe or do I have to sister it all the way up to the top plate because there's wiring I can't move and I'd have to notch it out at that point?
The more I thing about things, the more I'd go with adding in a bit of steel to fix the notches and breaks, instead of wood sistering.
Stud Shoes are made for these situations.
Compression and Tension Straps may also be just what you need in place of sistering. See also
this link.
USP is just as good as Simpson StrongTie.
Again, thanks a lot. This is a first time project and I'd like to get it done properly even if I have to backtrack a little.
Best Wishes, and remember my disclaimer