$($a$)$ For problem $3\mathrm{.}72$ of the textbook, principal stress values are mentioned below which are built upon the results of the original problem. Determine the minimum factor of safety for yielding using both the maximum$-$shear$-$stress theory and the distortion$-$energy theory, and compare the results. The material is $1018$ CD steel. Use the relevant table from the textbook to find the yield strength and other properties of the material.

${}_1=36\mathrm{.}7K$

${}_2=-1\mathrm{.}47K$

${}_{\text{m}\text{a}\text{x}}=19\mathrm{.}1K$

$($b$)$ If the material is ASTM grade $30$ cast iron, can we use the same failure theories mentioned in part $($a$)?$ If not, determine the minimum factor of safety.

$=?MMS$

Part a Sy$=54$ kpsi

I got the answers

n von mises $=1\mathrm{.}44$

n MMS $=1\mathrm{.}41$

For part b

Sut$=31$ kpsi $,$ Suc $=109$ kpsi

I got n $=0\mathrm{.}835$

Please check these answers if true or not and if not tell me the true