You are the materials engineer for a small ready$-$mix company and you are responsible for developing a proportion for a concrete mixture that has an $f^{\text{'}}$ cr of $4500l\frac{b}{i}{n}^2,$ a nominal maximum aggregate size of $\frac{3}{4}$ inch. The concrete will be placed in a column that is exposed to freezing and thawing and this column will be in contact with a soil that has a sulfate content of $0\mathrm{.}05\%.$ The cement that will be used is a general type and it has a specific gravity of $3\mathrm{.}15,$ the aggregate source contains some crushed particles. Design the concrete mix, show your calculations. Summarize your total mix design when finished. $(+45$ points$)$

Additional material properties are as follows:

Coarse aggregate:

Bulk SSD specific gravity $(S{G}_{SSD})$:$=2\mathrm{.}65$

Absorption capacity $=1\mathrm{.}5\%$

Surface moisture $=1\mathrm{.}0\%$

Dry rodded unit weight $=105l\frac{b}{f}{t}^3$

Fine aggregate:

Bulk SSD specific gravity $($SG $SGS{D}_{?}$ : $=2\mathrm{.}75$

Absorption capacity $=1\mathrm{.}0\%$

Surface moisture $=3\mathrm{.}0\%$

Fineness modulus $=2\mathrm{.}70$