Minimum Reinforcement ACI-318 10.5

[igdelimb]

As you all know, we need to provide minimum reinforcement to prevent sudden failure of concrete sections. This amount is determined on ACI 318-02 on section 10.5 with equation 10-3. I was wondering how this equation is derived and simplified to this form. I can imagine that this equation is dependent on cracking moment. I came up with something like this:
As = Mcr / (fy*j*d) where Mcr = 7.5*fc'^0.5 * b*h^2 / 6.
Does anybody know, how ACI came up with that equation?

Thanks.

 

[UcfSE]

The minimum ratio is derived by equating the cracking moment to flexural strength and solving for A_s in that equation, using f_r=7.5(f'_c)^1/2.