$2.$ For the stress state shown in Figure $2$ answer the following questions.

a$.$ Calculate normal and shear stresses acting on plane $\backslash (\backslash$mathrm$\{$AA$\}^\{\backslash$prime$\}\backslash )$

$(10$ pts$)$

b$.$ Show the stresses calculated in part $($a$)$ on the plane $\backslash (\backslash$mathrm$\{$AA$\}^\{\backslash$prime$\}\backslash )$

$(5$ pts$)$

c$.$ Determine the major principal planes and calculate the major principal stresses acting on them

$(10$ pts$)$

d$.$ Show the major principal planes and stresses on Figure $2$

$(5$ pts$)$

e$.$ Draw a Mohr circle for the stress state shown in Figure $2,$ determine its pole and state the coordinate of pole in $\backslash (\backslash$sigma$-\backslash$tau $\backslash )$ space. You should use a compass to draw the circle in a graph paper.

$(10$ pts$)$

f$.$ Find the stress quantities in parts $($a$)$ and part $($c$)$ using the Mohr circle drawn in part e$.$

$(5$ pts$)$

Figure $2$ Stress state for use in Problem $2$