Problem $2(6$ points$)$

A round AISI $4140$ steel dogbone sample is loaded in tension. The dogbone only undergoes elastic deformation until a maximum load of $1800$ lbf is reached. Given the parameters below, calculate the maximum stress, maximum longitudinal strain, modulus of elasticity, maximum lateral strain, and Poisson's ratio for the sample. If the sample is unloaded to zero force, what will the final strain be$?$

Sample diameter: $0\mathrm{.}200$ inches

Gage length: $6\mathrm{.}00$ inches

Longitudinal deformation: $0\mathrm{.}012$ inches

Transverse deformation: $0\mathrm{.}0006$ inches