have a bathroom with cc 600 between the beams and 2500 in span. On top, there is floor chipboard, floor gypsum, 10mm leveling compound, and finally tiles. I plan to install a corner bath against the outer wall. The tub holds 400 liters. Will the beam structure hold, or do I need to reinforce from underneath? If so, what's the simplest way to proceed?
 
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The beam structure should hold, as well as the particle board flooring. I believe that Byggelit regulation flooring (particle board) can handle a point load of 150 kg / surface load over 1 m2 of 300 kg, provided it is installed according to the manufacturer's instructions.

The question is how much sagging occurs between the beams due to the weight.

On how many feet will the weight be distributed?
 
Yes, the joist is guaranteed to hold, but it is questionable if it is rigid enough. The bathtub will weigh somewhere around half a ton when filled, and when the joists are on 60 c/c there can be enough deflection for tiles to detach or crack. But it depends partly on how many legs the bathtub has, and partly on where the legs land. If the legs land over a joist, the risk is smaller than if they land in the middle between two joists.
 
The bathtub has five legs, most of them end up right over a joist.
 
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