Problem $5$

Consider an infinite plate subjected to loading stresses such that the stress state

${}_{ij}$ is given in MPa by the following stress tensor:

$\left[\begin{array}{ccc}-400& 100& 0\\ 100& -300& 0\\ 0& 0& 0\end{array}\right]$

If the yield stress of this material is ${}_y=500$MPa, answer the following

questions:

$($a$)$ Draw Mohr's circle and find the principal stresses for the given stress

state.

$($b$)$ What are the principal axes?

$($c$)$ Using Tresca and von$-$Mises criteria, determine whether the material will

yield. Which is more conservative?

$($d$)$ A small hole is punctured in the infinite plate, will the material yield now?