For a construction that is exposed to both XF$4$ and XS$2$ environmental conditions. concrete has

been ordered and should be designed. In the aggregate mix. $36\%$ natural sand. and $12\%$ natural crushed

sand. $52\%$ natural crushed stone are to be used. Sieve analysis for aggregates is given in Table $2.$ CEMI$-$

$52\mathrm{.}5R$ is to be used. According to earlier productions. ready mix plant has a standard deviation value of

$5\mathrm{.}2.$ Concrete is going to be cast in an inclined formwork. In your calculations. you should assume an air

void ratio of $2\%.$ After casting trial mix. actual concrete unit weight was measured to be $3\mathrm{.}7\%$ lower than

the theoretical values.

a$)$ Find theoretical mixture values using Graf formula.

b$)$ Find the actual mixture values.

c$)$ Find the actual air void ratio.