I want to add a bathroom (with a tub) on the second floor of my house. Is it necessary to add more framing members to the first floor walls or ceiling?

Depends on how well the house was framed to begin with. Whjat size and spacing are your floor joists?

If the second floor was living space, u should have no problem.

If it was an attic space the floor beams may not be of the proper size and have to be up graded.

The wall will not be carrying any weight and should be fine.

Let us know size of floor beams.

Chuck

I agree with Chuck, if it is a re-planning an existing space you will be fine to leave floor joists like they are.
Newcomer2011.