In general, I can start by asking if you see any issues with the setup so far?
Dimensions: 2 supports, 45x220 C30 (Span approximately 4.5m) with CC 300mm
All according to the sizing help on byggbeskrivningar.se.
The problem is addressing the open area you can see in the images.
I can't manage the spans. If possible, I would continue with construction timber over the section of 5970mm (6m) according to the current construction. Unfortunately, it might be too weak.
Is it as "simple" as adding a steel beam? What do you think?
Laying a steel beam is straightforward. A freely supported beam of 6m can have significant dimensions mainly due to deflection. The beam will likely be taller than the wooden joists, making it difficult to conceal it within the floor structure. In that case, one might choose taller kertobalks with a wider spacing and hide the beam within the floor structure. Of course, there are naturally more solutions for fixing the floor structure. As a guideline, it can be simply stated that the span of the floor structure should be longer than that of the beams to achieve reasonable proportions in the structure.
It also seems that there is 45 mm glulam that can handle the span, but then the entire floor structure becomes thicker. According to the supplier's specifications, you end up with 45x315 at a 6m span and cc 600.
I think it's time for some lateral thinking in this case. One option is to insert a primary frame of glulam with perhaps 2400 mm c/c and then hang the secondary support between the glulam beams in the longitudinal direction of the house. This way you can use reasonable qualities, dimensions, and c/c distances. This hodgepodge of closely spaced beams is never good. Then a plumber comes and starts cutting into them... What does C 30 timber cost? You have added nearly 5 cubic meters. Kerto beams are otherwise an underrated product. An important question is what you want to achieve (besides ensuring it holds)? Glulam beams can be exposed and provide qualities beyond just the static.
