The columns for the building in Question #$1$ are to be made of concrete with the following specifications:

Design compressive strength: $4100$ psi, based on $25$ tests of samples having a standard deviation of $550.$

Non$-$air$-$entrained, and clear space between rebar: $2$ inches

Fine aggregate: $G=2\mathrm{.}38,FM=2\mathrm{.}4$

Coarse aggregate: ${?}_O=2\mathrm{.}57$

Determine the following:

i$.$ w$/$c ratio, largest nominal max. coarse aggregate size, $\%$ coarse aggregate, $\%$ air $(2$ pts$.)$

ii$.$ weight of water, weight of cement, and weight of coarse aggregate to be used per cubic yard of concrete $(1$ pt$.)$

iii. weights and volumes of water, cement, air, coarse aggregate, and fine aggregate needed to mix a $12-$yard batch of this mix $(3$ pts$.)$

Also:

Why we might create a composite of this concrete poured into a PVC $($polyvinyl chloride$)$ sleeve for these columns? $($Give specific reasons based on the characteristics of the individual materials.$)(2$ pts$.)$