The International Building Code has language stating the maximum size and spacing for drilled holes in wall studs. The maximum hole size being 60% of the stud width. If the holes are from 40-60% of the stud width, then the stud is supposed to be doubled (and not more than 2 such bored studs in succession). With an exception for using "approved" stud shoes.
That said, a 3.5" stud (2x4) could handle having a 2" hole..... but the hole saw is usually larger O.D. As long as the hole saw O.D is smaller than 2.1" you should be fine.
There are some other exceptions listed here in NC, so you may want to verify with your local jurisdictions in Ohio. For example, if the studs have a minimum 1/2" plywood (or equivalent) attached you can increase the size of the hole to 65%.
I just realized you mentioned joists, so use that info as you will.
As long as you stay in the middle third of the depth of the joists, and OUT of the middle third of the length of the joist and also Not under any bearing points, you are fine