Mohr's Circle

Mohr's circle, named after Christian Otto Mohr, is a two-dimensional graphical representation of the state of stress at a point. The abscissa, and ordinate, of each point on the circle are the normal stress and shear stress components, respectively, acting on a particular cut plane with a unit vector with components . In other words, the circumference of the circle is the locus of points that represent the state of stress on individual planes at all their orientations,where the axes represent the principal axes of the stress element.

Karl Culmann was the first to conceive a graphical representation for stresses while considering longitudinal and vertical stresses in horizontal beams during bending. Mohr's contribution extended the use of this representation for both two- and three-dimensional stresses and developed a failure criterion based on the stress circle.

There is also a similar Mohr's circle for strain where x-axis depicts strain and the y-axis represents half of shear strain which can be found out by Generalised Hooke's Law.

Other graphical methods for the representation of the stress state at a point include the Lame's stress ellipsoid and Cauchy's stress quadric.