$5-5$ Repeat $$ Problem $5-1$ by first plotting the failure loci in the ${}_A,{}_B$ plane to scale; then, for each stress

state, plot the load line and by graphical measurement estimate the factors of safety. only $($d$)$

$5-14$ An AISI $4142$ steel Q&T at $800F$ exhibits $S_{yt}=235k,S_{yc}=285k,$ and ${}_f=0\mathrm{.}07.$ For the

to given state of plane stress, $($a$)$ determine the factor of safety, $($b$)$ plot the failure locus and the load line,

$5-19$ A brittle material has the properties $S_{ut}=30k$ and $S_{uc}=90k.$ Using the brittle Coulomb$-$Mohr

and modified$-$Mohr theories, determine the fictor of safety for the following states of plane stress.

$($a$){}_x=25k,{}_y=15k$

$5-36$ 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 $T=25N*m.$

$5-38$ A $1020$ CD steel shaft is to transmit $20$ hp while rotating at $1750$ rpm $.$ Determine the minimum diameter

for the shaft to provide a minimum factor of safety of $3$ based on the maximum$-$shear$-$stress theory$\mathrm{.}5-5$ Repeat $$ Problem $5-1$ by first plotting the failure loci in the ${}_A,{}_B$ plane to scale; then, for each stress

state, plot the load line and by graphical measurement estimate the factors of safety. only $($d$)$

$5-14$ An AISI $4142$ steel Q&T at $800F$ exhibits $S_{yt}=235k,S_{yc}=285k,$ and ${}_f=0\mathrm{.}07.$ For the

to given state of plane stress, $($a$)$ determine the factor of safety, $($b$)$ plot the failure locus and the load line,

$5-19$ A brittle material has the properties $S_{ut}=30k$ and $S_{uc}=90k.$ Using the brittle Coulomb$-$Mohr

and modified$-$Mohr theories, determine the fictor of safety for the following states of plane stress.

$($a$){}_x=25k,{}_y=15k$

$5-36$ 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 $T=25N*m.$

$5-38$ A $1020$ CD steel shaft is to transmit $20$ hp while rotating at $1750$ rpm $.$ Determine the minimum diameter

for the shaft to provide a minimum factor of safety of $3$ based on the maximum$-$shear$-$stress theory.

$5-1$ 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:

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

$5-2$ Repeat Problem $5-1$ with the following principal stresses obtained from Equation $(3-13)$:

$($a$){}_A=100$MPa,${}_B=100$MPa

$($b$){}_A=100$MPa,${}_B=-100MP$

$($c$){}_A=100$MPa,${}_B=50$MPa

$($d$){}_A=100$MPa,${}_B=-50$MPa

$($e$){}_A=-50$MPa,${}_B=-100$MPa

$5-76$ The figure shows a shaft mounted in bearings at A and $D$ and having pulleys at $B$ and

$C.$ The forces shown acting on the pulley surfaces represent the belt tensions. The

shaft is to be made of AISI $1035$ CD steel. Using a conservative failure theory with a

design factor of $2,$ determine the minimum shaft diameter to avoid yielding.

$5-1$ 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:

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

$5-2$ Repeat Problem $5-1$ with the following principal stresses obtained from Equation $(3-13)$:

$($a$)$

$5-5$ Repeat Problem $5-1$ by first