Mohr's Circle

• It is termed as the graphical form where transformation equations of plane stress can be signified.

• This representation is very useful since it allows you to imagine the normal and shear stress relationships acting on different inclined planes at a point in a stressed body.

• This circle is useful for the computation of principal stresses, stresses on inclined planes, and maximum shear stresses.

• This method is easy and clear approach.

Equation:

Stress transformation equations:

Here, σx1 is the stress on x1 surface, σx ,σy are the stress on x, y surface, τ xy is shear stress on x, y surface, θ is the angle, τ x1y1 is the shear stress on x1y1 surface.

Show the principal stress diagram as in Figure (1).

Show the inclined position principal stress diagram as in Figure (2).

Procedure:

• Draw a couple of coordinate axes with σx1 as positive to right and τx1y1 as positive downward.

• Place point A, indicating conditions of stress on element x face by plotting its coordinates σx1= σx and τ x1y1= τxy . A point on circle corresponds to q = 0 °.

• Situate point B, it represents stress conditions on element y face by plotting its coordinates σx1= σy and τx1y1= − τxy. B point on circle corresponds to q = 90 °.

• Plot a line from point A to B, a circle diameter passing through point c. A and B points are at diameter opposite ends.

• Draw Mohr’s circle through points A and B using circle center c. This circle radius is R and center c having coordinates of σx1=σavg and τ x1y1= 0.

Show the Mohr circle diagram as in Figure (3).

Applications:

• This technique is used in analysis of finite homogeneous strain and moment of inertia determination.

• The main benefit of this circle is that principal stresses and maximum shear stress are obtained instantly after plotting the circle.

• Values of obtained principal stress data is utilized in material failure theories to predict.