Example 01: Required Steel Area of Reinforced Concrete Beam

$M = \frac{1}{2}f_c bx(d - \frac{1}{3}x)$

$80(1000^2) = \frac{1}{2}(5)(300x)(600 - \frac{1}{3}x)$

$250x^2 - 450\,000x + 80\,000\,000$

$x = 1600 \, \text{ and } \, 200$
 

Use $x = 200 ~ \text{mm}$           answer

$300x(\frac{1}{2}x) = nA_s(d - x)$

$150x^2 = nA_s(d - x)$

$150(200^2) = 9A_s(600 - 200)$

$A_s = 1666.67 ~ \text{mm}^2$           answer

$\dfrac{f_s/9}{600 - 200} = \dfrac{5}{200}$

$f_s = 90 ~ \text{MPa}$           answer