$3\mathrm{.}32$ Testing a round steel alloy bar with a diameter of $15$ mm and a gauge length of

$250$ mm produced the stress$-$strain relationship shown in Figure P$3\mathrm{.}32.$

Determine

a$.$ the elastic modulus

b$.$ the proportional limit

c$.$ the yield strength at a strain offset of $0\mathrm{.}002$

d$.$ the tensile strength

e$.$ the magnitude of the load required to produce an increase in length of

$0\mathrm{.}38$ mm

f$.$ the final deformation, if the specimen is unloaded after being strained by

the amount specified in $($e$)$

g$.$ In designing a typical structure made of this material, would you expect

the stress applied in $($e$)$ reasonable? Why?