Solve by using hand writing only.

Q$1.$ A specimen of steel having an initial diameter of $12\mathrm{.}8$ mm was tested in tension using a gauge length of $50$ mm $.$ The following data were obtained for the elastic and plastic states:

Elastic State Plastic State Load P$($kN$)$ Elongation $($mm$)$ Load P$($kN$)$ Area A$\_($i$)($mm$^(2))4\mathrm{.}50\mathrm{.}0139\mathrm{.}61289\mathrm{.}00\mathrm{.}01541\mathrm{.}412713\mathrm{.}50\mathrm{.}02541\mathrm{.}012618\mathrm{.}00\mathrm{.}032559\mathrm{.}412431\mathrm{.}50\mathrm{.}057568\mathrm{.}412137\mathrm{.}80\mathrm{.}0776\mathrm{.}510139\mathrm{.}60\mathrm{.}0973\mathrm{.}88441\mathrm{.}40\mathrm{.}222566\mathrm{.}670$

Please note that there is some overlap in the data.

$($a$)$ Plot the engineering or nominal stress$-$strain diagram using two scales for the unit strain, one scale from zero to about $0\mathrm{.}002$mm$//$mm and the other scale from zero to the maximum strain.

$($b$)$ From the diagrams completed under $($a$),$ find the modulus of elasticity and the ultimate strength of the material. Also, find the percent reduction in the area of the specimen.

$($c$)$ Characterize the material as ductile or brittle. Explain your reasoning.

$($d$)$ Identify a material specification from Table A$-20($Shigley$\text{'}$s book$)$ that has a reasonable match to the data.