Q$\mathrm{.}2.$ An element in plane stress in subjected to stresses ${}_x,{}_y$ and ${}_{xy}($see the figure$).$

Using Mohr's circle,

a$)$ Determine the principle stresses. $(10\%)$

b$)$ Determine the maximum shear stresses and associated normal stresses. $(10\%)$

c$)$ Determine the stresses acting on an element oriented clockwise at an angle $=50$ from the $x-$axis. $(15\%)$

d$)$ Draw the Mohr Circle $(15\%)$

e$)$ Show the principle and maximum shear stresses on sketch. $(10\%)$