Mohr’s circle is the locus of points representing the magnitude of normal and shear stress at the various plane in a given stress element. Graphically, a variation of normal stress and shear stress are studied with the help of Mohr's circle.
σ_{1} and σ_{2} are Principal Stresses, then normal and shear stress on lane which is inclined at angle ‘θ’ from major principal plane, then
Different Stress Diagram
Mohr's circle for plane Stress and StrainNormal Stress
Shear Stress
If σx and σy are normal stress on vertical and horizontal plane respectively and this plane is accompanied by shear stress then normal stress and shear stress on the plane, which is inclined at an angle θ from the plane of
then,
Let σ_{x}, σ_{y} be two normal stresses(both tensile) and τ_{xy} be shear stress then:
Maximum and Minimum Principal Stresses are:
The radius of Mohr’s circle:
Strength of Materials
Mohr's circle for plane stressed
Observations from Mohr's Circle
The following are the observations of Mohr's circle as:
Strain analysis
Principle Strain
∈_{θ }+ ∈_{θ + 90º} = ∈_{x} + ∈_{y}
Relation between Principle strain and stress
Strain Rosetts
∈_{x} = ∈_{0º}, ∈_{y} = ∈_{90º} and Ф = 2∈_{45º}  (∈_{x} + ∈_{y})
∈_{θ}_{º = }∈_{x}
37 videos39 docs45 tests

1. What is Mohr's circle and how is it used to analyze plane stress and plane strain? 
2. What is the difference between plane stress and plane strain? 
3. How can Mohr's circle be used to determine the principal stresses? 
4. How is the maximum shear stress determined using Mohr's circle? 
5. What are the applications of Mohr's circle in mechanical engineering? 

Explore Courses for Mechanical Engineering exam
