Interior Platform Steel Tube Framing?
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.


Arrange for a bed and mattress that are lower so that you can simplify the platform supports by allowing for 5" or 6" beams.
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.