Problem $1$

Using the volumetric method, design a concrete mix according to the following criteria:

Design Criteria

Slab on grade in heated building in Portland, Oregon

Required strength, $f^{\text{'}c}=4000$

Standard deviation of required strength $=250$ psi $(>30$ samples$)$

Slab thickness $=12$ in

Only air entrainer allowed

Available Materials

Air entrainer dosage rate of $0\mathrm{.}15$ fl$.$ oz$./1\%$ air$/100$ lb cement

Coarse aggregate:

$\frac{3}{4}$ in$.$ nom. maximum size, river gravel $($round$)$

Bulk oven$-$dry specific gravity$=2\mathrm{.}62$

Absorption $=2\mathrm{.}6\%$

Oven$-$dry rodded density $=104\mathrm{.}1$ pcf

Moisture content $=1\mathrm{.}5\%$

Fine aggregate:

Natural sand

Bulk oven$-$dry specific gravity$=2\mathrm{.}57$

Absorption $=3\mathrm{.}5\%$

Moisture content $=4\%$

Fineness modulus $=2\mathrm{.}80$

Summarize the mix design by providing the batch ingredients $($by weight$)$ for one cubic yard of PCC$.$

Water

Portland Cement

Fine aggregate

Coarse aggregate

Admixture $($air$-$entrainer$)$