Is it OK to run a 3" drain through a jois reinforcement (pictures attached) ?

[MiniMe4Eng]

If you need to understand why I am doing this here is why: I am trying to conceal a drain and a vent pipe in the wall of my basement (this is the outer wall of my basement)
For more info see this thread

https://www.eng-tips.com/viewthread.cfm?qid=472249

This is the current situation

And this is what I need as final result.

 

[bridgebuster]

Off the top of my head, the International Residential Code says the hole diameter cannot exceed d/3 and the edge of the hole most be at least 2" from the top and bottom of the joist. Based on your sketch it looks like you're cutting a slot, I would say no. However, could you add elbows to eliminate the slot?

 

[MiniMe4Eng]

I am not sure how much that piece counts in that exact position as it is at the end of the joists, toward the exterior wall in the basement
I think it is meant to keep together the double joists that are on each side of the pipes and there is already a double piece like that before
It is attached using hangers ...here is a detail
I could probably take it out, rotate that elbow in position under the upstairs toilet so that it connects back to the position of the new drain pipe
and then put the piece of wood and the stringers back

 

[bridgebuster]

You should put it back. Take a look at the attached publication. There is some guidance about floor framing for tubs and openings.

 

[MiniMe4Eng]

thanks for the link
The author of this video has a couple of videos that deal with this issue

https://www.youtube.com/watch?v=73_vpD-lLyY

also some details here

https://www.youtube.com/watch?v=74pk6faF58A

 

[dauwerda]

If it were my house I would have zero issues with removing it. You may need to add some other framing back in to make sure the subfloor is supported adequately, but those would not need to be full depth members.

 

[MiniMe4Eng]

I just realized that it is there for the only purpose that it supports the toilet. it reinforces the area under it which might cave in if not supported from underneath
real life picture below
I will slightly relocate it