Problem $5$:

An air$-$entrained concrete mix is to be proportioned for a reinforced concrete structure that would be placed under seaw$$ter$.$ A required compressive strength, $f_{cr}^{\text{'}},$ of $4\mathrm{.}5$ksi is specified. Placement conditions allow for concrete with a slump of $3$ to $4in.$ The coarse aggregate is satisfactorily graded from No$.4$ to $1\mathrm{.}5-$in $($nominal max size of $1\mathrm{.}5-$in$)$ in accordance with ASTM C$33$ and has a dry$-$rodded weight density of $110l\frac{b}{f}{t}^3.$ The coarse aggregates will be gravel with crushed particles. Determine the weight of proportions needed in a $1$ cubic yard of concrete using the absolute volume method. What is the weight of ingredients needed for a laboratory trial batch of $0\mathrm{.}01y{d}^3?$ Material characteristics of the cement and aggregates are detailed in the table below.

$\backslash$table$[[$Material characteristics,Cement,Fine aggregates,Coarse aggregates$],[$Bulk specific gravity,$3\mathrm{.}17,2\mathrm{.}3,2\mathrm{.}61],[$Fineness modulus,$-,2\mathrm{.}5,],[$Absorption $(\%),-,2\mathrm{.}1,3\mathrm{.}3],[$Moisture content $(\%),-,1\mathrm{.}6,41],[\backslash$table$[[$Dry$-$rodded unit weight$],[(l\frac{b}{f}{t}^3)$