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Was looking at your pics closeup. Is that particle board or wood chips?
Also do you have a hvac unit separate from the rest of the house in the basement? I find it hard to believe that there was some hvac work that was done, hence the holes in the engineered I-beam, since we are in two separate parts of the world with the same idiotic issue with the I-beams. Also like you, when I look across the i-beams that support the entire main floor, they all have these gigantic holes in them. Some I-beams, especially those long ones, have multiple holes
Was looking at your pics closeup. Is that particle board or wood chips?
That's called engineered I-beam, which is typically made out of osb for the webbing if I'm not wrong
http://www.fireengineering.com/articles/2007/04/silent-floors-silent-killers.html
Some info about holes on these things
Won't let me read it without signing up, are you able to copy and paste the text?
I have not read through the entire thread. I am a structural engineer, professional licensed PE and SE (not to show off, only to lend credibility). Those are I-joists you have there, and as I'm sure you've heard, those holes are no good. While they may have been working to date, they absolutely need fixing. Holes are not allowed near the end of the joists, and they are certainly not allowed to be the whole depth of the web (plywood part). The plywood takes all the shear load in the joist, your joists have essentially no shear capacity at this point. Absolutely do not place any large tank on any joists that have those holes present. Small holes of diameter that is less than 1/3 the height of the joist and within the middle 1/3 of the span of the joists are acceptable.
Note, simply placing some plywood and screwing it to the hole may not be an effective solution. The screws and nails that are used to attach the new plywood to the existing joists must be properly sized, spaced, and calculated to take the loads being applied to your floor.
Sorry to be a bummer. I really really very much absolutely super duper recommend you get that checked out by a local structural engineer. Not a framer, not a contractor, but someone that can come out, take measurements, and provide you a code compliant repair that will ensure you and your family are safe.

