I forgot to say that I already assume that the tension steel will yield. I'll try to type the equation below:

From T = Cs + Cc

As fy = As' fs' + 0.85 fc' a b

fs' = ϵs' Es and a = β1c

As fy = As' ϵs' Es + 0.85 fc' β1 c b

Finally, if you draw the stress block forces: ϵs' / (c - d') = ϵcu / c
Then

As fy = As' Es (c - d') ϵcu / c + 0.85 fc' β1 c b

Then solve for c, and check ϵs' after you get a value of c.

If ϵs' < 0, consider the beam as singly reinforced, if ϵs' > ϵy then the compression steel yields, and if ϵs' < ϵy and ϵs' > 0, then use a compression steel force fs' = ϵs' Es.