$[2].$ Consider the stresses at the periphery of an elliptical hole in a large plate. Two cases are to be considered, $($a$)$ uniaxial loading along the $y$ axis, and $($b$)$ biaxial loading along the x and y axes. The major axis of the elliptical hole is along the x axis as shown in the two sketches below. For the biaxial case, the stress along the x and y axes are different from each other. Consider $4$ locations $a,b,c,d$ along the edge of the hole in your analysis. Assume that tangential stress at locations $b$ and $d,$ for the uniaxial case arising from far$-$field loading applied along the y axis, are given by $-($compressive$)$ and at location a and $c$ are given by $[1+2(\frac{r_2}{r_1})]($tensile$).$ Determine the expressions for the stress concentration factors for the two load cases and for each of the $4$ locations $a,b,c,$ d$.|$~$2$ marks ~$|$