Q$1$: A cylindrical metal specimen having an initial diameter of $0\mathrm{.}503$ in was tested in tension using a gauge length of $2$ in $.$ The following data were obtained until the fracture.

$($a$)$ Calculate stress and strain values corresponding to load and gauge length. $(15$ points$)$

$($b$)$ Plot the engineering stress$-$strain curve using data from $($a$).$ Use Excel or any other plotting software. $(15$ points$)$

$($c$)$ Calculate Young's modulus, yield strength $($at $0\mathrm{.}2\%$ strain$),$ and ultimate tensile strength from the stress$-$strain curve. $(20$ points$)$

$\backslash$table$[[$Load $($Lb$),$Gauge Length $($in$)],[318,2\mathrm{.}0004],[633,2\mathrm{.}0006],[950,2\mathrm{.}001],[1265,2\mathrm{.}0013],[2215,2\mathrm{.}0023],[2700,2\mathrm{.}0026],[2800,2\mathrm{.}0036],[3525,2\mathrm{.}02446],[4200,2\mathrm{.}06548],[4425,2\mathrm{.}08],[4750,2\mathrm{.}11946],[4800,2\mathrm{.}14],[5020,2\mathrm{.}20278],[5225,2\mathrm{.}3],[5430,2\mathrm{.}44],[5480,2\mathrm{.}54254],[5220,3\mathrm{.}04056],[4700,3\mathrm{.}68988]]$Q$1$: A cylindrical metal specimen having an initial diameter of $0\mathrm{.}503$ in was tested in tension using a gauge length of $2$ in $.$ The following data were obtained until the fracture.

$($a$)$ Calculate stress and strain values corresponding to load and gauge length. $(15$ points$)$

$($b$)$ Plot the engineering stress$-$strain curve using data from $($a$).$ Use Excel or any other plotting software. $(15$ points$)$

$($c$)$ Calculate Young's modulus, yield strength $($at $0\mathrm{.}2\%$ strain$),$ and ultimate tensile strength from the stress$-$strain curve. $(20$ points$)$

$\backslash$table$[[$Load $($Lb$),$Gauge Length $($in$)],[318,2\mathrm{.}0004],[633,2\mathrm{.}0006],[950,2\mathrm{.}001],[1265,2\mathrm{.}0013],[2215,2\mathrm{.}0023],[2700,2\mathrm{.}0026],[2800,2\mathrm{.}0036],[3525,2\mathrm{.}02446],[4200,2\mathrm{.}06548],[4425,2\mathrm{.}08],[4750,2\mathrm{.}11946],[4800,2\mathrm{.}14],[5020,2\mathrm{.}20278],[5225,2\mathrm{.}3],[5430,2\mathrm{.}44],[5480,2\mathrm{.}54254],[5220,3\mathrm{.}04056],[4700,3\mathrm{.}68988]]$