Problem $3(30$ points$)$

The critical state of strain in the supporting pylon of a segmental box girder bridge is given below in tensor form $($units of microstrain$).$

$[{}_{xyz}]=\left[\begin{array}{ccc}810& -657& 101\\ -657& 1205& 443\\ 101& 443& -730\end{array}\right]$

$($a$.)$ Calculate the corresponding stresses given the following material properties: $E=29,000$ksi, $v=0\mathrm{.}3,$ and $G=11,150$ksi. Provide the values in units of ksi $.$

$($b$.)$ Determine the minimum uniaxial yield strain $($tension or compression$)$ to prevent the pylon from failing by using an analogous approach for strain as that used for stress in the Tresca yield criterion and Von Mises yield criterion.