I recently bought a cape cod style house built in 1938 with 2×10 joists on the first floor with a span of 16 feet on one side of the main beam that has a noticeable sag of about an inch and a half. There are no signs of damage to the joists themselves(very solid, no rot at all) but there was some minor water damage to parts of the surface flooring so I don't have a problem ripping it up if need be. I was wondering if I should just sister new 2x10s to the old joists making the tops of the new ones level and putting a new subfloor on that when I go to replace the surface flooring or would it be better to build temporary supports underneath the existing joists, cut them, then install a laminated beam with joist hangers, jack it level then put in some lolly columns(with footers of course)?
Boy that is a hard one. Both have their merits and drawbacks. Installing sisters would be the hardest way of going and will do the most damage to the existing floor if its in good shape and most likely the most expensive material and labor wise. However cutting and lifting the center will lower ceiling height in basement and not completely correct the arch of the floor joists. As once its lifted up in middle to be level to ends, the arc of the floor joists will be at both sides of the new support beam.
I would, using a string line, and starting from the middle of the floor and running it to the wall edge, see if the curve of this half of the floor is acceptable to you. Do this on both sides of where the bean would be located below. If you do not like the amount of curve that remains, then the sister route is the way you will only be happy, However if you can tolerate the curve of each half of the floor, then go the beam method.