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like this but with a hidden metal frame, I hope

I'm building a platform 22.5-23.5" high in a space 88" by 62-64", supports on three side but one free span side for a bed to slide out - the long side, of course. Because of height/width restrictions, space is at a premium, and wood just takes up too much room. I'm looking to save inches and weight wherever possible, but still end up with a platform that is structurally sound with minimal deflection (i.e. 50+psf live load, less than 1/3" deflection across long span).

Various online calculators go back and forth on whether I can use 2x2 steel or need 2x3 steel at 1/4" thick, or whether aluminum at 2x3, 1/4" would suffice. Will 2x2 steel work or 2x3 aluminum? Or stick with steel 2x3, with the long side vertical?

For either steel or aluminum: do I just use another length of same dimensions at sides for beam, and what kind of posts? For welding, as long as it is in the same plane, I don't 'pay' (in height or width, the most restrictive measurements) for extra lateral or bracing support on the platform top; besides corner triangular braces, should I add short lengths between metal joists for more support?

And, finally, how do I attach a plywood subfloor to the top of this frame? Are there brackets that go around 2x3 (or 2x2) that would work?

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I would probably still use wood for the beam across the bed opening because it is so much easier to work with. The picture you posted shows a good 6 to 7 inches of space from the platform surface down to the top of the bed opening. This should be more than enough room for beams that can carry the weight.

If your current plan is only allowing for a 3" beam dimension then you should consider the following options.

  1. Arrange for a bed and mattress that are lower so that you can simplify the platform supports by allowing for 5" or 6" beams.
  2. Try trussing the narrow beams along their length similar to the picture below. Trussing like this would be similar to the way that wooden step ladder treads are trussed.

enter image description here

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