 space is right under that toilet that's the one place it leaks then the second thing i would do is i take my foot and put it against the tub wall and push it down on the floor against because that's what happens where you have water that splashes out of the tub and lands on the floor i'm telling you this because i want you to make sure that you're getting all the areas that are rotted the first time you do this repair now in terms of that joist yes you could sifter it and what that means is to take a new beam