Mohr's circle

Mohr's circle

Mohr's circle is a graphical representation of any 2-D stress state proposed in 1892 by Christian Otto Mohr. It can be applied to many engineering quantities such as stresses, strains, and moments of area.


Consider the state of stress at a point in a body. The Mohr's circle may be constructed as follows.

  1. Draw two perpendicular axes with the horizontal axis representing normal stress, while the vertical axis the shear stress.
  2. Plot the state of stress on the x-plane as the point A, whose abscissa (x value) is the magnitude of the normal stress, σx (tension is positive), and whose ordinate (y value) is the shear stress (clockwise shear is positive).
  3. Mark the magnitude of the normal stress σy on the horizontal axis (tension being positive).
  4. Mark the midpoint of the two normal stresses, O (Figure 1).
  5. Draw the circle with radius OA, centered at O (Figure 2).
  6. A point on the Mohr's circle represents the state of stresses on a particular plane at the point P. Of special interest are the points where the circle crosses the horizontal axis, for they represent the magnitudes of the principal stresses (Figure 3).

Mohr's circle may also be applied to three-dimensional stress. In this case, the diagram has three circles, two within a third.

You can use Mohr's circle to find the planes of maximum normal, principle and shear stresses, as well as the stresses on known weak planes. For example, if the material is brittle, the engineer might use Mohr's circle to find the maximum component of normal stress (tension or compression); and for ductile materials, the engineer might look for the maximum shear stress.

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