Oh my bad... At the back of my head I always thought that rho_max should be greater than rho_balance when in fact, it should not be. I get these things mixed up in my head. Thank you for your reply. Is 0.015 not too small for an upper bound?
I have this computation for singly reinforced rectangular beam and found that
rho_max = (3/7) * 0.85 * f'c * beta_1 / fy
That is based on ACI 318 strain of tension steel of 0.004 and concrete of 0.003.
The same formula actually was posted by user JAE (Structural) in this thread...
