$3\mathrm{.}1-3\mathrm{.}5$ A tensile test specimen having a diameter of $10$ mm and a gage length of $50$ mm was tested to fracture. The stress$-$strain curve from the tension test is shown in Figure P$3\mathrm{.}3.$ The lower plot is the expanded region OAB and associated with the strain values given on the lower scale. Solve Problems $3\mathrm{.}1$ through $3\mathrm{.}5.$

$3\mathrm{.}1$ Determine $($a$)$ the ultimate stress; $($b$)$ the fracture stress; $($c$)$ the modulus of elasticity; $($d$)$ the proportional limit; $($e$)$ the offset yield stress at $\backslash (0\mathrm{.}2\backslash \%\backslash )$; $($f$)$ the tangent modulus at stress level of $420$ MPa ; $($g$)$ the secant modulus at stress level of $420$ MPa $.$

$3\mathrm{.}2$ Determine the axial force acting on the specimen when it is extended by $($a$)0\mathrm{.}2$ mm ; $($b$)4\mathrm{.}0$ mm $.$

$3\mathrm{.}3$ Determine the extension of the specimen when the axial force on the specimen is $33$ kN $.$