calculating lbs per sq ft. to support soaker tub
The 40 psf live load for a typical floor is assumed to be a distributed load. When computing the stress on a joist, you perform the calculations based on the live load plus the dead load, which is also a distributed load, typically about 10 psf, and includes the weight of the flooring and self weight of the joists.
A tub such as you described is typically modelled as a point load. The stress on the joists is computed based on the combination of live load (distributed), dead load (distributed), and the point load of the tub. Describing the mathematics of computing combined dead, live and point loads is a bit too much for this post, but you may be able to get a lumber yard or perhaps the supplier of the tub to perform the computations.
In general, you compute the maximum stress on the joists, compare that against the allowable stress on the joists, and that tells you whether you are OK for strength. Similarly, you compute the deflection of the joists caused by the combination of loads, and use the computed deflection to computed the l/D ratio, which tells you if the flooring is likely to crack (this is mostly a problem with stone or tile). Computing deflection is more complex than computing strength, and is normally done using computer software.