Marre, you've received many different solutions, but I think your original idea is very good. 10 mm seems a bit unnecessarily thick, but with thinner sheet metal, there's a risk that the metal will "give in" and require more screws (closer together) since it is the wood that provides support for the metal. Consult with the neighboring company that has experience with steel.
Calculate the weight so that you have a manageable weight.
Placing the steel UNDER the wooden beam assumes that you can also place steel above the beam and connect these with something and screw the steel to the wooden beam so that it functions as a web is nearly impossible.
Sure, the steel works best under and above, but it must be better than two flat irons on top of each other.
If you want to be fancy, you can place a thick rod above and below connected with a thinner sheet (the web).
This does require some welding but might be easier since rods come in long lengths.
Protte
Do you think there could be problems with steel against wood in terms of moisture and stresses...they behave differently!?
Prottte is right that you need to get steel at the top and anchor it with your life, for the metal at the bottom to have any effect. Quite a lot of work to make it act like an IPE.
How can one even write that a 200x10x4500 should lie at the bottom instead of on the side? Do you usually place bearing joists on the slab?
But just screwing the metal at the ends of the rule is also nuts, how does it stiffen the rule? It's true that the metal might be weakened by too many holes, but we're talking a hell of a lot of holes in that case.
Screw the metal at cc500 with French screws of 8-10mm and it'll be fine.
Alternatively, replace with glulam (Sizing assistance available from SvenskTrä) or an IPE 200 / HEA180.
Your own alternative seems the most convenient to me.
Prottte is right that you need to get steel in the upper part and anchor this with your life for the sheet metal in the lower part to have any effect. A bit too much work to make it act like an IPE,
What does "anchor with your life" mean , maybe at the level of the existing beam?
The web is called the middle part of an IPE or HEA beam. The web contributes very little to bending resistance but is necessary to keep the upper and lower parts of the beam aligned. Without the web, it would just be two flat bars.
The proposal with steel on top and bottom assumes that the steel can be attached to the wooden beam, but this is not possible in practice, as there are very small movements and very high forces.
Thinking as you have is a waste of steel because the steel at half the height contributes nothing, but is needed as a "web."
Now it's practical to use 10 mm thick steel all the way, it costs more to deal with different thicknesses.
One would likely need to screw tightly to prevent the sheet metal at the edge from calving; I would have chosen some type of pre-made steel beam, probably a Upe160, depending on the load, which is screwed with the side against the existing wood.
Feels spontaneously like it would require tremendous stress for a 10mm steel plate that is screwed and glued to start giving way, at least theoretically
Also, this plate "only" weighs 70 kilos compared to a beam that weighs a couple of hundred kilos...
I'm starting to become a bit indecisive now, everyone says different things :O
According to the colleague and the adhesive expert at Sikabond, this should hold without any problems and be rigid, but none of them are exactly experts...
Upe160 weighs 17kg per meter. Alone it cannot support your flooring, but together with the bef it will be excellent. Set the backside (liv) against and go cc400-500 with sensible screws.
Added a picture, drew an H/I beam, but meant a Upe160 beam
I'm a bit tired and want to double-check with you first if this is what you mean!?
I looked a bit at dimensions for UPE160, it was only available in 100 mm width which fits my 90 mm, then there is a 10 mm difference next to the wooden beam... how do you solve this to make it sustainable?
Place the U beam next to the existing wood with the web against the wood.
But can't I just as well use steel plate then, or does the U make it much stronger than an ordinary flat steel plate....sorry for all the questions, but I need to be completely sure before I proceed and I've got a touch of "Tröghetius Dummus" today 😀