Example $4\mathrm{.}7$

Design a rectangular beam for a $10-m$ simple span to support a dead load of $20k\frac{N}{m}($not including beam weight$)$ and a live load of $30k\frac{N}{m}.$ Use $=0\mathrm{.}5{}_b,f_c^{\text{'}}=28$MPa, and $f_y=420$MPa, and concrete weight is $23\mathrm{.}5k\frac{N}{m^3}.$ Do not use the ACl thickness limitation$.$