Do the marked problems

$5-1($a$),($c$),($e$)/5-7,5-9,5-11/5-36$:

$5-1$ A ductile hot$-$rolled steel bar has a minimum yield strength in tension and compression of $350$ MPa $.$

Using the distortion$-$energy and maximum$-$shear$-$stress theories determine the factors of safety

for the following plane stress states:

$($a$){}_x=100$MPa,${}_y=100$MPa

$($b$){}_x=100$MPa,${}_y=50$MPa

$($c$){}_x=100$MPa,${}_{xy}=-75$MPa

$($d$){}_x=-50$MPa,${}_y=-75$MPa,${}_{xy}=-50$MPa

$($e$){}_x=100$MPa,${}_y=20$MPa,${}_{xy}=-20$MPa

$5-7$ to

An AISI $1018$ steel has a yield strength, $S_y=295$MPa. Using the distortion$-$energy theory for

$5-11$ the given state of plane stress, $($a$)$ determine the factor of safety, $($b$)$ plot the failure locus, the

load line, and estimate the factor of safety by graphical measurement.

$5-36$ This problem illustrates that the factor of safety for a machine element depends on the particular

point selected for analysis. Here you are to compute factors of safety, based upon the distortion$-$

energy theory, for stress elements at A and $B$ of the member shown in the figure. This bar is

made of AISI $1006$ cold$-$drawn steel and is loaded by the forces $F=0\mathrm{.}55kN,P=4\mathrm{.}0kN,$ and

$T=25N*m.$