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Waqas Haider

ETABS beam design formulas from verification manual

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Assalam o alaikum,

I was reading ETABS concrete frame design manual ACI 318-08. In beam design section, it gives two formulae which I am unable to find in books. One formula for stress block depth and one formula for negative steel calculation. I have highlighted the formulae in below images. The manual design using these formulae and conventional formulae gives the same result. But kindly guide me from where I can get derivation of these formulae or theory behind this.  

Beam image 1.png

beam image 2.png

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Waqas, just reverse calculate;

In books you will find for singly reinforced;

a = Asfy/0.85f'cb

and Phi Mn = 0.9Asfy(d-a/2)

re-arrange, and you will find your answer.

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