$7\mathrm{.}27$ Three $\backslash (100\backslash$mathrm$\{$~mm$\}\backslash$times $200\backslash$mathrm$\{$~mm$\}\backslash )$ concrete cylinders with water to cement ratlos of $\backslash (0\mathrm{.}50,0\mathrm{.}55\backslash ),$ and $0\mathrm{.}60,$ respectively. After curing for $7$ days, the specimens were subjected to increments of compressive loads. The load versus deformation results were as shown in Table P$7\mathrm{.}27.$

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Chapter $7$ Portland Cement Concrete

TABLE P$7.27$

$\backslash$begin$\{$tabular$\}\{|$c$|$c$|$c$|$c$|$c$|$c$|$c$|\}$

$\backslash$hline Specimen No$.$ & $\backslash$begin$\{$tabular$\}\{$l$\}$

w$/$c $\backslash \backslash$

Ratio

$\backslash$end$\{$tabular$\}$ & Load $($kN$)$ & Deformation $($mm$)$ & $\backslash$begin$\{$tabular$\}\{$l$\}$

Stress $\backslash \backslash$

$($MPa$)$

$\backslash$end$\{$tabular$\}$ & Strain $(\backslash (\backslash$mathrm$\{$m$\}/\backslash$mathrm$\{$m$\}\backslash ))$ & Secant Modulus $($MPa$)\backslash \backslash$

$\backslash$hline $\backslash$multirow$\{5\}\{*\}\{1\}$ & $\backslash$multirow$\{5\}\{*\}\{0\mathrm{.}50\}$ & $0$ & $0$ & & & $\backslash \backslash$

$\backslash$hline & & $25$ & $0\mathrm{.}0007$ & & & $\backslash \backslash$

$\backslash$hline & & $50$ & $0\mathrm{.}0014$ & & & $\backslash \backslash$

$\backslash$hline & & $75$ & $0\mathrm{.}0021$ & & & $\backslash \backslash$

$\backslash$hline & & $100$ & $0\mathrm{.}0029$ & & & $\backslash \backslash$

$\backslash$hline $\backslash$multirow$\{5\}\{*\}\{2\}$ & $\backslash$multirow$\{5\}\{*\}\{0\mathrm{.}55\}$ & $0$ & $0$ & & & $\backslash \backslash$

$\backslash$hline & & $25$ & $0\mathrm{.}0008$ & & & $\backslash \backslash$

$\backslash$hline & & $50$ & $0\mathrm{.}0016$ & & & $\backslash \backslash$

$\backslash$hline & & $75$ & $0\mathrm{.}0025$ & & & $\backslash \backslash$

$\backslash$hline & & $100$ & $0\mathrm{.}0036$ & & & $\backslash \backslash$

$\backslash$hline $\backslash$multirow$\{5\}\{*\}\{3\}$ & $\backslash$multirow$\{5\}\{*\}\{0\mathrm{.}60\}$ & $0$ & $0$ & & & $\backslash \backslash$

$\backslash$hline & & $25$ & $0\mathrm{.}001$ & & & $\backslash \backslash$

$\backslash$hline & & $50$ & $0\mathrm{.}0021$ & & & $\backslash \backslash$

$\backslash$hline & & $75$ & $0\mathrm{.}0034$ & & & $\backslash \backslash$

$\backslash$hline & & $100$ & $0\mathrm{.}0051$ & & & $\backslash \backslash$

$\backslash$hline

$\backslash$end$\{$tabular$\}$

Assuming that the gauge length is the whole specimen height, determine the following:

a$.$ The compressive stresses and strains for each specimen at each load increment.

b$.$ Plot stresses versus strains for each specimen on one graph.

c$.$ If the ultimate stress is $30,25$ and $20$ MPa at $\backslash (0\mathrm{.}50,0\mathrm{.}55\backslash )$ and $0\mathrm{.}60,$ respectively, determine modulus of elasticity as the secant modulus at $\backslash (40\backslash \%\backslash )$ of the ultimate stress at each water$-$cement ratio.

d$.$ Comment on the effect of increasing the water$-$cement ratio on the