Sample Problem $9\mathrm{.}4$

Figure $($a$)$ shows a reinforced concrete T$-$beam, where the cross$-$sectional area of the steel reinforcement is $2400m{m}^2.$ Using $n=\frac{E_{st}}{E_{co}}=8$ and the working stresses of $12$MPa for concrete and $140$MPa for steel, determine the largest bending moment that the beam can carry. Use elastic analysis.