I have to derive two equations in order to get a Merit Index.
so the question is how you derive the
m=b^2*l*r , r=density
and Fy = (b^4/12 /(b/2) * sy/(m/b^2*r)
well I am in that point , Fy = failure load of a beam equation , sy=yield strees .
the final Merit index is = sy^2/3 / ρ . I am in the point Fy=b^4/12 / b/2 * σy/(m/b^2*ρ) .
So the thing is , how you get to that σy^2/3 / ρ ?
To make it a bit clearer it will be in the end Fy = b^3 *6 * m σy/2^3/ρ . So this σy/2^3/ρ will be in the final equation as it is now . without any mass or length in its function.
I hope I am clear now .