Mohr's Circle for 2-D Stress States


If you have a 2-D stress state with non-zero stress components Sxx, Syy, Sxy, the simple construction of Mohr's circle shown below can help you quickly determine the principal stress direction and value.

1) Identify point (X1,Y1)=(Sxx,Sxy) on an X-Y plot.

2) Identify a 2nd point (X2,Y2)=(Syy,-Sxy) on the plot.

3) Connect the two points, (X1,Y1) and (X2,Y2).

4) Draw the Mohr circle using the above line as a diameter.

The following applet will construct the Mohr circle for you if you fill out the boxes with Sxx, Syy, Sxy at the bottom and click "Draw".

The principal stress and the principal direction, obtainable by the shaded angle in the figure, are displayed at the lower left corner. You can double check these values by using the following fomulae:

Principal Stress = ( Sxx + Syy + Sqrt[ (Sxx-Syy)2+ 4 * Sxy2] ) / 2

Principal Angle = ( tan-1 [ 2 * Sxy / (Sxx-Syy) ] ) / 2

The filled arc spans twice the above principal angle.