Installed new floor joists with glued routed uponor chipboard in the house a few years ago. Then I loaded everything quite heavily with, among other things, grips and other building materials. The joists sagged a bit, which I realized after a while and remedied with a whole bunch of props in the basement. Now I plan to install an HEA or HEB beam underneath so that I don't have to worry about it anymore. The joists are 45x195. 3.4 m at the fastenings and 7.6 m long. They should be C24 but I'll leave that unsaid. I was thinking of placing a support at 4.7 on the steel beam. Now the room is basically not much wider than what it should be with those dimensions, but my concern is if I go down in size on the steel beam, it might sag more in the middle than the wooden joists do. I can't find any information on the sagging or what would be a good dimension. I'm considering a 160 mm beam but I have absolutely no idea how much it might sag over a span of 4.7m.
Your floor structure consists of 45x195 mm, strength class unclear. The span is 3.4 meters. Under these beams, you want to place a steel beam in the middle, with the largest span of 4.7 meters. Is this a correct description? If this is correct, the wooden beams are too weak for that span, even if they have a C 24 class. If you cannot reinforce them, a beam underneath seems like a reasonable measure provided it is not too much in the way. In that case, I would opt for an HEA 180.
That's correct. Maybe I can move the support/pole to 4.15 m instead of 4.7 m so that it's more in the middle. As I said, my biggest concern is how much the beam will sag in the middle. If it sags 1 cm, then the wooden beams will also sink by that amount. I haven't considered any floor weights, only the weight of the beam itself. The question might be wrong.
You are onto something important, that the support line/steel beam should not deflect more (measured in mm) than what is acceptable for the floor joists. HEA 180 should meet that requirement.