Tub P-Trap in 6" floor joist?

Is there any possible way to fit a tub drain and p-trap into a 6" (5.5") floor joist?

This bath is on a second floor and the joists are only 5.5"s deep. I'd rather not have to fir down the ceiling in order to fit the plumbing in. I measured a 1.5" p-trap and it was 6" deep just by itself.

I guess my other option is to elevate the tub, which would probably be easier.

Is there any solution to this that I'm overlooking?

If you use an above floor rough bathtub, and a street sanitary tee, that should put the hub of the Ptrap up into the subfloor.

So like this? The main drain is actually back behind the tub, so it will span the distance of the floor joist.

I can use 1.5" for this right? Or do I have to use 2"?

1 1/2 is all you need. But use a glued trap in place of the slip joint trap.

Thanks John, will do. Just copied and pasted that one, but yes I will use a glued trap.