## Mohr's Circle

From the stress transformations, an equation in the form of a circle can be derived as follows: $$ [\sigma _ \theta - \frac{\sigma _x + \sigma _y}{2}]^2 + \tau _ \theta ^2 = ( \frac {\sigma _x - \sigma _y}{2}) + \tau _{xy} ^2 $$ Where the centre of the circle is \( ( \frac{ \sigma _x