Mohr’s Circle Principle

Mohr’s circle principle is named after Christian Otto Mohr in 1882, it is the 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, and also acting on a particular cut plane with a unit vector with components. To say 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. To construct the Mohr’s circle for a general three dimensional case of stresses at a point, the values of the principal stresses and their principle directions must be evaluated first.

Mohr’s circle was considered to be the leading tool used for visualizing the relationship between the normal and shear stresses, and to estimate the maximum stresses, before the hand held calculators became popular. Even today Mohr’s circle principle is still widely used lot of engineer all over the world.

The person who was first to create a graphical representation for the stresses, while considering longitudinal and vertical stresses in the horizontal beams during bending was Karl Culmann. Mohr’s contribution had made the extended use of this representation for both two and three dimensional stresses and also developed a failure criterion based on the stress circle. Lames’ stress ellipsoid and the Cauchy’s stress quadric are the other graphical methods for the representation of the stress state at a point.

Mohr’s circle for two dimensional stress states

The Mohr’s circle principles for two dimensional stress states,

• Tensile stresses (positive) are to be right.
• Compressive stresses (negative) are to be left
• Plot the clock wise shear stresses upward
• Counter clock wise shear stresses are plotted downward.

Importance of Mohr’s diagram

• One can determine the normal and shear stress for any planes that lie at an angle theta, for any value of maximum compressive stress value and the minimum compressive stress value.
• Illustrate the attitude of planes along which the shear stress is the greatest for a given stress state.
• It will facilitate a quick, graphical determination of stresses on the planes of any orientation; it is the most important aspect of the Mohr’s diagram.
• Stress tensors are used to calculate the stress. Mohr’s diagrams are very excellent for visualizing the state of stress but at the same time it is difficult for calculating stress.

Questions:

• What is Mohr's circle?
• Explain the importance of Mohr’s diagram?