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Calculation C.G. for composite section

Calculation C.G. for composite section

Calculation C.G. for composite section

(OP)
Using Limit State Design (or other) how doe you arrive the quadratic equation to determine the exact location og the N.A. (ie center of gravity) for a typical 100mm (4") concrete overlying on a C10x3½x0.105 (12Ga) purlin?  

bc(x2)/2 = n As (tc + ds - x)

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