I recently opened up the ceiling below my bathroom and was surprised by what I found. The floor joists are 2 1/2" x 8" x 15.5' and 16" on center. This seems way too small for the span. Also, some of the joists have been cut to accommodate drain pipes. I'm going to be re-doing the bathroom, adding concrete board and tile, and I want to make sure the load, along with the load of the tub, can be properly supported. I'm contemplating sistering the existing joists with 2 x 8 x 16' joists. Will this be sufficient to handle the load? The bathtub is about 5 feet in from one wall. To complicate things, the house is balloon framed, so I will have to attach a ribbon or ledger to the 2 x 4s to support the new beams, but I'm concerned about what kind of fasteners to use (the sheer strength of the fasteners). Any info would be great.

Thanks