framingjoists
Does adding a sister that is smaller than the original joist actually increase strength at all? If so, does it need to be sistered at the bottom (so both beams touch the sill) or does it still add strength if sistered to be flush on the top?
To extend the question, does a sistered joist that doesn't go the full span add strength?
The reason that joists are sistered using the same height of wood is simply space; generally there's no extra room. If you've got nothing below and there's space then there's no reason you can't use a taller piece of wood. Things to keep in mind:
My answer is to cut your two inch hole as close to your drywall as possible. In the picture you went right down the middle and barely hit the joist. Methinks that you could drill right along the side and have to barely notch out the joist below. Might not even have to notch all the way through it. No reason for vac lines to have to be centered in your wall. Use the notch guidelines I found to help further.
Below is a helpful chart that provides actual notch and hole size limitations for 2x4, 2x6, 2x8, 2x10 and 2x12 joists. It should be noted that limitations on the allowable notching and boring of wood joist are meant to retain the structural and functional integrity of the member.
Best Answer
Yes. They will both bear the load.
As long as the joists are attached together with sufficient strength, the force will be carried by both joists through the entire length of the span, but the larger joist will transfer all of the load to the sill. That will work.
Now if the joists are the same size, the attachment from joist to joist is not so critical - they can share the load from the floor without transferring part of that load from one to the other.
Yes, it will add some strength, although calculating just how much strength it will add may be difficult.