calculation c.g. for composite section
 

calculation c.g. for composite section
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)