Using USD or ultimate strength design method, design a simply supported reinforced concrete beam $0\mathrm{.}20m$ wide and $4\mathrm{.}50m$ long, carrying only a wall load of $8\mathrm{.}27k\frac{N}{m}$ including its own weight. Keep the steel ratio within $1\%$ and use $16mm$ dia. Reinforcing bars. Use fy$=413\mathrm{.}17$ MPa and fc$\text{'}27\mathrm{.}6$MPa and a min. concrete cover of $63\mathrm{.}5mm.$