There's a reason why no one has done what being proposed in your sketch - it's a more difficult, more expensive, and less predictable way to do a reinforced concrete slab. Why not just use reinforcing bars?
Design-wise it would be basically the same as a conventionally reinforced concrete slab, with the exception of figuring out how much, and to what extent, the web of the tee section is to be included as tension reinforcement. As you move towards the top of the slab, it will take much more tension strain at the bottom of the section (and therefore increasingly large deflections) in order to produce substantial strain and stress in the upper portion of the web.
There's also the not small matter of ensuring the WT section remains locked into the concrete and doesn't 'slip'. Reinforcing bars have deformations to provide a positive mechanical connection to the concrete. Unless you add something, such as shear studs, channels, lugs, etc. to the WT, you'll be relying on the bond strength between the steel and concrete to ensure composite action (thus the "less predictable" part I mentioned earlier).
Rod Smith, P.E., The artist formerly known as HotRod10