P$3$ Ans: $($a$)-5704\mathrm{.}11,0,8405\mathrm{.}14,($b$)6023\mathrm{.}79,-11727\mathrm{.}91,($c$)5\mathrm{.}98,4\mathrm{.}26$;$2\mathrm{.}49,($e$)-49511\mathrm{.}7,0,-6884\mathrm{.}05,$

$($f$)939\mathrm{.}33,-50451\mathrm{.}034,($g$)38\mathrm{.}32,0\mathrm{.}991$;$0\mathrm{.}966.$

A solid bar with an outside diameter $D=1\mathrm{.}25in$ is loaded as shown. It is

made of a material with an ultimate tensile strength of $36\mathrm{.}0$ ksi and an

ultimate compressive strength of $50\mathrm{.}0$ ksi $.$

$($a$)$ calculate the individual stress components in location $H$ and

superimpose them into the combined plane stress state at $H.$ Show your

combined stress results on a properly oriented plane stress element,

$($b$)$ for location $H$ calculate principal stresses,

$($c$)$ for location $H$: l$)$ determine the factors of safety predicted by the

maximum normal$-$stress theory. According to the MNST does the bar

fail? $2)$ determine the factor of safety predicted by the Mohr's failure

criterion. According to MFC does the bar fail?

$($d$)$ for location $H$ on a common or separate axis draw the stress envelopes $($failure diagram$($s$))$ for both theories indicating

all stress values as well as the load lines,

$($e$)$ calculate the individual stress components in location $K$ and superimpose them into the combined plane stress state at $K.$

Show your combined stress results on a properly oriented plane stress element,

$($f$)$ for location $K$ calculate principal stresses,

$($g$)$ for location $K$:$1)$ determine the factors of safety predicted by the maximum normal$-$stress theory. According to the MNST

does the bar fail? $2)$ determine the factor of safety predicted by the Mohr's failure criterion. According to MFC does the

bar fail?

$($h$)$ for location $K$ on a common or separate axis draw the stress envelopes $($failure diagram$($s$))$ for both theories indicating

all stress values as well as the load lines.