WARNING – LONG NOTE
I'm an engineer and have recently gone through these calcs for a friend planning to install a new system. Please take this as information only and not as professional advice or recommendations. (Insert the "I probably don't know what I'm talking about any way" clause in here)
Determining if the wall the tank is up against is load bearing would be very good info because if the wall is a load wall then you shouldn't have any problems what so ever. However, in the absence of that info, you must assume that the wall is not and that the closest load wall is the nearest outside wall perpendicular to the direction of the joists.
What is the distance to the nearest outside wall perpendicular to the joists?? I do have the point loading specs for typical floor joists and I could calc the moment based on the distance if you have that.
Also, I noticed that your builder used 'fingered' 2x4's for the floor joists in the shot of the storage room. That's not good news as fingered wood, although having similar strength characteristics to whole wood, does have a tendency to deform or permanently flex more easily under load.
In any case, assuming that you are some distance from a load wall, you will likely get permanent deformation of your floor joists. Saying that, your floor will likely NOT fail catastrophically. (Insert another liability disclaimer here!) However, in a bad situation, your ceiling in the developed room under the tank could show 'parting' lines in the dry wall seams.
If you are unable to determine whether the wall is load bearing, you could significantly mitigate the stress on the joist by placing a large board under you tank that would have a span that would overlap the joists on both sides. I would suggest a minimum 1” bored made of a very hard wood. It appears you only have 6” on the right hand side and 2” on the left to ensure overlap to the next joists. This would mean the difference of each joist bearing 1000lbs each with 3 joists compared to 600lbs with 5 joists.
(Well it’s actually not quite that simple as there will be preferentially loading under the weight point; however, many hardwoods have almost no flex at all and can distribute a significant amount of weight. I have seen this done before and it looked very nice as a base for the tank and stand.)
If you want to go the structural engineer route, I may have contacts that could help you out for a more reasonable price (PM me if you want). Don’t forget, the joists used in houses are not specifically designed for high loads in small area’s for long periods of time. Wooden joists can take a significant point load for a short period of time without fail, however long term point loading will cause deformation. (i.e. a 300 pound man jumping up and down on 1 leg in high heels can produce a point load well in excess of 1500 psi, and that would be fine as the wood will flex and restore to original shape
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To get an engineer to stamp a structural drawing for you will likely involve some modifications to your house. Structural engineers don’t like the words “Likely won’t & Shouldn’t fail” and in the face of uncertainty they will over engineer until you could park your car on your roof!!