A large shear box tests $($Sample $\backslash (300\backslash$times $300\backslash$times $50\backslash$mathrm$\{$~mm$\}\backslash )$ high$)$ was carried out on a sample of sand and gravel from the site for a proposed new hospital.

The results are given below.

Note: a negative vertical movement number means the box is moving upwards.

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

$\backslash$hline Shear stress $($kPa$)$ & Horizontal movement $($mm$)$ & Vertical movement $($mm$)\backslash \backslash$

$\backslash$hline $0$ & $0$ & $0\mathrm{.}00\backslash \backslash$

$\backslash$hline $28\mathrm{.}82$ & $0\mathrm{.}50$ & $0\mathrm{.}00\backslash \backslash$

$\backslash$hline $61\mathrm{.}97$ & $1\mathrm{.}00$ & $-0\mathrm{.}01\backslash \backslash$

$\backslash$hline $98\mathrm{.}57$ & $1\mathrm{.}50$ & $-0\mathrm{.}03\backslash \backslash$

$\backslash$hline $130\mathrm{.}28$ & $2\mathrm{.}00$ & $-0\mathrm{.}13\backslash \backslash$

$\backslash$hline $141\mathrm{.}81$ & $2\mathrm{.}50$ & $-0\mathrm{.}23\backslash \backslash$

$\backslash$hline $153\mathrm{.}33$ & $3\mathrm{.}00$ & $-0\mathrm{.}35\backslash \backslash$

$\backslash$hline $159\mathrm{.}10$ & $3\mathrm{.}50$ & $-0\mathrm{.}46\backslash \backslash$

$\backslash$hline $163\mathrm{.}42$ & $4\mathrm{.}00$ & $-0\mathrm{.}64\backslash \backslash$

$\backslash$hline $162\mathrm{.}27$ & $4\mathrm{.}50$ & $-0\mathrm{.}79\backslash \backslash$

$\backslash$hline $158\mathrm{.}52$ & $5\mathrm{.}00$ & $-1\mathrm{.}00\backslash \backslash$

$\backslash$hline $152\mathrm{.}47$ & $5\mathrm{.}50$ & $-1\mathrm{.}16\backslash \backslash$

$\backslash$hline $149\mathrm{.}01$ & $6\mathrm{.}00$ & $-1\mathrm{.}31\backslash \backslash$

$\backslash$hline $145\mathrm{.}26$ & $7\mathrm{.}00$ & $-1\mathrm{.}46\backslash \backslash$

$\backslash$hline

$\backslash$end$\{$tabular$\}($i$)$ Plot the data in a manner appropriate for engineering analysis. Note you do not need to plot all the data $-$ just enough to demonstrate clearly the pattern of behaviour of the material

$($ii$)$ Comment on the behaviour of the material under test

$($iii$)$ Plot the shear stiffness $($or modulus$)$ versus shear strain and comment on the resulting curve

$($iv$)$ On the same plot indicate what the shear stiffness $-$ shear strain curve for a steel piece might look like

$($v$)$ For the point of maximum shear stiffness determine Young's Modulus and the Bulk Modulus if Poisson's Ratio $\backslash (($v$)=0\mathrm{.}25\backslash ).$