A beam with a given value of width $b,d,f_c^{\text{'}}$ and $f_y.$ Use $E_s=29000$ksi. Use the following steps to determine the steel ratio for a balanced section $({}_b).$

a$.$ Draw the strain diagram assuming ${}_c=0\mathrm{.}003$ and ${}_t={}_{ty}$

b$.$ Using similar triangles, determine the expression of $c$ in$-$terms of $d$ and ${}_{ty}.$

c$.$ In the equation in part b$,$ replace ${}_{ty}$ using $f_y$ and $E_s.$

d$.$ Using the equilibrium equation that equates compression and tension in the cross section, determine the expression for steel area for the balanced section.

e$.$ Convert the steel area to reinforcement ratio ${}_b$