Problem # $2(50$pts$)$

A $2-$inch diameter manganese bronze test specimen was subjected to a trial tensile load, and the following data was obtained.

$\backslash$table$[[,,,,,,,,,,],[\backslash$table$[[$Gauge$],[$Length$],[($inch$)]],10,,,,,,,,,],[\backslash$table$[[$Final Gauge$],[$Length$],[($inch$)]],11\mathrm{.}25,,,,,,,,,],[\backslash$table$[[$Load at$],[$proportional$],[($Ib$)]],19,500,,,,,,,,,],[\backslash$table$[[$Elongation$],[$at$]],0\mathrm{.}016,,,,,,,,,],[\backslash$table$[[$Proportional$],[$Limit $($inch$)]],,,,,,,,,,],[\backslash$table$[[$Maximum$],[$Load $($lb$)]],50,000,,,,,,,,,],[\backslash$table$[[$Load at$],[$rapture $(($b$)]],42,000,,,,,,,,,],[\backslash$table$[[$Diameter at$],[$rapture$],[($inch$)]],1\mathrm{.}445,,,,,,,,,]]$

$*$Find:

$($a$)$ the proportional limit$,$

$($b$)$ modulus of elasticity,

$($c$)$ ultimate strength,

$($d$)$ percent elongation,

$($e$)$ percent reduction in area,

$($f$)$ indicated rupture strength, and

$($g$)$ true rupture strength.

NB: sample problem in textbook page $309(5\mathrm{.}11)$

Sample problem in textbook page $281(5\mathrm{.}11)$