Chapter $6$ problems:

A specimen of copper having a rectangular cross section $.)$ is pulled in tension with $44,500N(10,000lbl{b}_f)$ force, producing only elastic deformation. Calculate the resulting strain.

A cylindrical specimen of a metal alloy $10$ mm $(0\mathrm{.}4$ in $.)$ in diameter is stressed elastically in tension. A force of $15,000N(3,370l{b}_f)$ produces a reduction in specimen diameter of $7{10}^{-3}.).$ Compute Poisson's ratio for this material if its elastic modulus is $100$ GPa $(14\mathrm{.}5{10}^6).$

A cylindrical specimen of stainless steel having a diameter of $12\mathrm{.}8$ mm $(0\mathrm{.}505$ in $.)$ and a gauge length of $50\mathrm{.}800$ mm $(2\mathrm{.}000$ in $.)$ is pulled in tension. Use the load$-$elongation characteristics shown in the following table to complete parts $($a$)$ through $($e$).$

$\backslash$table$[[$Load$,$Length$],[$N$,,$mm$,$in$.],[0,0,50\mathrm{.}800,2\mathrm{.}000],[12,700,2,850,50\mathrm{.}825,2\mathrm{.}001],[25,400,5,710,50\mathrm{.}851,2\mathrm{.}002],[38,100,8,560,50\mathrm{.}876,2\mathrm{.}003],[50,800,11,400,50\mathrm{.}902,2\mathrm{.}004],[76,200,17,100,50\mathrm{.}952,2\mathrm{.}006],[89,100,20,000,51\mathrm{.}003,2\mathrm{.}008],[92,700,20,800,51\mathrm{.}054,2\mathrm{.}010],[102,500,23,000,51\mathrm{.}181,2\mathrm{.}015],[107,800,24,200,51\mathrm{.}308,2\mathrm{.}020],[119,400,26,800,51\mathrm{.}562,2\mathrm{.}030],[128,300,28,800,51\mathrm{.}816,2\mathrm{.}040],[149,700,33,650,52\mathrm{.}832,2\mathrm{.}080],[159,000,35,750,53\mathrm{.}848,2\mathrm{.}120],[160,400,36,000,54\mathrm{.}356,2\mathrm{.}140],[159,500,35,850,54\mathrm{.}864,2\mathrm{.}160],[151,500,34,050,55\mathrm{.}880,2\mathrm{.}200],[124,700,28,000,56\mathrm{.}642,2\mathrm{.}230],[,,,]]$

$($a$)$ Plot the data as engineering stress versus engineering strain.

$($b$)$ Compute the modulus of elasticity.

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

$($d$)$ Determine the tensile strength of this alloy.

$($e$)$ What is the approximate ductility, in percent elongation?