Re: kind of foundation for cast iron bathtub
Your design the load for the tub full of water. SO you need ot know the volume of the tub. A person is about the same density as water, although they could be standing up in the water ... so I'd add another 500lbs to that calculation.
SO using some rough numbers, I calculated 30 cubic feet from a 30" wid, 60" long 24" deep tub. Water weighs 62lb/cuft. SO 1800lb for the water + 320lb tun + 500lbs for people. So you're at around 2600lbs!!!
Best to double check the volume calculations... but it's probably not far off.
Tubs need MAJOR reinforcement. You should located them when possible near a load bearing wall or you will have sagging of the floor joists over time... which can crack tile floors.
On my 90 year old house, both of my tubs not surprisingly are located adjacent to the load bearing walls. Its' also a easier location to run piping to and from the basement up those walls.
1925 Two-Story Stucco Beaux Arts Neoclassical