Question $3$

A $2m$ concrete beam with rectangular cross$-$section of $150mm$ wide and $300mm$ depth is to be

fabricated. The strength of the beam is targeted to be $50$MPa. Determine the mass of cement $($C$),$

water $($W$),$ sand $($S$),$ and coarse aggregate $($CA$)$ required based on the following information:

$C$:$S=1\mathrm{.}5$

$S$:$CA=0\mathrm{.}6$

Assume the density of concrete is $2400k\frac{g}{m^3}$ and the variation of concrete strength follows the Abram's

law. Take the value of $K_1$ and $K_2$ in Abram's equation as $96\frac{N}{m}{m}^2$ and $7$ respectively.