QUESTION $2$

Three strain gauges are fixed at a point on the free surface of a machine component as in Figure Q$2.$ Strain gauge ${}_3$ has reading of $500,{}_b$ has reading of $-200$ while ${}_c$ has reading of $100.$

Let $E=208$GPa and $v=0\mathrm{.}32$

a$)$ Find the values and draw the strain element in the a$-$b direction.

b$)$ Find the values and draw the strain element in the $x-y$ direction.

c$)$ Find the values and draw the principal strains element.

d$)$ Find the values and draw the maximum shear strain element.

e$)$ Find the values and draw the principal stresses element.