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Minimum Reinforcement ACI-318 10.5

Minimum Reinforcement ACI-318 10.5

Minimum Reinforcement ACI-318 10.5

(OP)
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.

RE: Minimum Reinforcement ACI-318 10.5

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

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