CLASS 4: MOHRS CIRCLE

Mohrs Circle-    developed by Otto Mohr (1835-1918).

a convenient graphical means to depict states of stress; 

A force applied to an area (stress) may be resolved into a

normal force (Fn) perpendicular to a plane and a

shear force (Fs) , parallel to a plane in questions.

1    Sigma 1- Maximum Compressive Stress  

2     Sigma 2- Intermediae Compressive Stress         

 3    Sigma 3- Minimum Compressive Stress

Stress is a vector quantity that can be considered as:

n    Normal Stress-

                oriented perpendicular to a plane                                

s     Shear Stress-

                oriented parallel to a plane in question

    Theta- angle formed by an inclined plane with the maximum and minimum compressive stress directions, and measured from the minimum stress position.

Important Normal Stress and Shear Stress Equations:

s_n= (s₁+s₃) + (s₁-s₃) cos 2q

        2                2

s_s= (s₁-s₃) sin 2q

        2               

Importance of Mohrs Diagram:

1.For any value of maximum compressive stress value and minimum compressive stress value, one can determine the normal and shear stress for any planes that lie at an angle theta 

2.Depicts the attitude of planes along which shear stress is the greatest for a given stress state

3. The most important aspect of Mohrs diagram is that it facilitates a quick, graphical determination of stresses on planes of any orientation.

4.Mohr diagrams are excellent for visualizing the state of stress but difficult for calculating stress. Stress tensors are used to calculate stress.

PLOTTING MOHR'S CIRCLE:

Mohr's circle is  plotted on two perpendicular axes: The vertical axis

 (ordinate) depicts shear  stress and the horizontal axis (abscissa) depicts

 normal stress.

By convention compressive  stress is positive (+) and

 tensile stress is negative (-).