Problem $3($Answer at bottom$)$

The critical point in a beam is in a state of plane$-$stress given as

${}_x=150$MPa,${}_y=80$MPa,${}_{xy}=50$MPa,${}_z=0$MPa

The beam is made up of AISI $1020$ hot$-$rolled steel. Use table A$-20$ to get the necessary material

parameters.

$($a$)$ Determine the factors of safety according to MSS and DE theories.

$($b$)$ Plot or sketch the MSS and DE yield surfaces on the ${}_A-{}_B$ plane.

$($c$)$ Plot or sketch the load point and load line

Answer: nmss$=1\mathrm{.}19,$ nde $=1\mathrm{.}34$