Thanks everyone. Tony-it is a joist. And yes, only the one joist was
damaged. My husband sistered it (on both sides) to the best of his ability
and it definitely looks a lot better. Don't worry, we didn't use nails. On
the one side we did go a couple feet beyond the damaged area, but on the
other side it was not possible to go beyond the damaged part because of
the walls. On that side there was less than 2 inches of 'good' wood to
bolt the new wood onto. I have no idea how many joists support the 2nd
floor, so I was worried about it. I'm hoping everything is ok now.