I have come to a standstill of sorts in my bath remodel, hoping the picture helps to explain the situation. We have decided on a bathroom fan for our project, now the problem is how to run it to the outside. This is a 2 story house, going up won't work, there is a bathroom right above. I thought about doing a wall fan, but not quite what we want. We would like to position the fan in the center of the room, and the shortest run to the outside would be across the ceiling joists. Would it be possible to header these joists off where the red lines are, to the rim joist with joist hangers. I am concerned about weakening the floor because there is already a header put in for the upstairs shower. Would this be chopping up the framing too much, or would it be strong enough? I thought of another option; running the ducting with the floor joists thru the ceiling of another room (suspended ceiling, so not too much of a problem). Its about a 20 foot run, and terminates at the deck ledger board on the second floor. (The duct would then be right under the deck) Is this kosher do you think?