[TRE Cup]

Needing some engineering advice on a center spine single story staircase for new inside construction.
Each tread will be made of oak 2 inches thick, 11 deep , and 38 wide.
The treads fasten to a steel structure. So, there will be full width fastener locations to p and bottom.
We want to have a clear span from bottom to top. ( floor to ceiling windows behind it)
So how thick should each tread steel platform should be? How wide and deep should the sawtooth steel center spine be?of course hand rails need to be installed
We want it rigid enough so there isn't the vibrations that come from thinner structures

Thanks