I recently was forced to replace a basement bath fan. My basement is
fully finished with drywall ceilings and walls. To my surprise I
discovered that the original fan was never vented outside, simply just
dumping inbetween the joists.

I would like to vent this outside, but my only logical options are to
follow the joists with the vent pipe and go through the sill plate on
top of the concrete basement wall and a 2 x 10 joist for my deck, or
go a shorter distance through several joists a 2 x 10 and through the
sill plate. I am not sure how this can be done easily without
destroying the integrity of the exterior walls, as standard vent
piping is 3 or 4 inches in diameter.

Anyone have any unique suggestions that would still provide good
venting, such as using PVC/other piping with a smaller diameter. Or
some type of reinforcement for the sill plate since there are already
2x10s for the deck? Maybe simply adding some screws in the area to
fasten the sill to the deck joist more securely?

Thanks, Tom R.