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Af flexural reinforcement -corbels

Af flexural reinforcement -corbels

(OP)
Hi there. for corbel flexural reinforcement Af (moment) the PCI code example uses the following formula to find it

Af = [ Vu*av + Nuc*(h-d)] ÷ [ Φ fy d ]

and this is the formula I have been using ever since. But I recently bought a practice book online that states that Af is actually derived???? He writes the formula is :

Af = 0.85 bw d fc' (1- square root ( 1 - M / 0.319 b d^2 fc )) / fy

As can be seen this is a much more longer formula and if it is derived which means I can't just use it on any corbel?? He also states he got this from ACI Section 10.2 but I have been reading and re-reading this section all day as well as 10.3 and I cannot find this. So I'm not sure where he got this. All sources I've used say to use flexural theory but none has a specific formula. If I use flexural theory can't I just use that first formula (the PCI one) ? I had posted a similar thread about Af discrepancy not long ago but the discrepancy was not this huge dazed. So I am back at square one - in uncertainty of this formula.

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