House built 1940s. The 2nd floor bathroom has an original cast iron tub. The tub is supported by 3 joists but the sill does not touch the 4th joist. There is no support at the end of the tub either - leaving No Joist support for last 20" under the tub sill. There is a 4 ft long 2x4 stringer that the back of the tub rests upon. A closet under the tub provides a wall under the sill, so the joists are really just providing vertical support and there is effectively nothing to span in order to support the tub. The plumbing under the tub and an HVAC duct complicates replacement of a full joist or placement of a buddy joist member. The tub doesn't move. There is no creaking when it is loaded. There is no cracking of the wall tile above the tub. Do I need to span that gap?