Mohr’s Circle for Plane Stress and Plane Strain Notes for Civil Engineering Exams

By Mallesham Devasane|Updated : December 30th, 2016

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, variations of normal stress and shear stress are studied with the help of Mohr's circle.

s2 are Principal Stress then normal and shear stress on the lane which is inclined at angle ‘θ’ from major principal plane, then

Normal stress:

Shear stress:

General State of Stress at an Element:

If s5 are normal stress on vertical and horizontal plane respectively and this plane is accompanied by shear stress then normal stress and shear stress on plane, which is inclined at an angle θ from plane of



Let s5 be two normal stresses(both tensile) and s10 be shear stress then,

  • Maximum and Minimum Principal Stresses are:


  • Radius of Mohr’s circle:


Strength of Materials

Observations from Mohr's Circle

The following are the observations of Mohr's circle as

* At point M on circle σn is maximum and shear stress is zero.

∴ Maximum principal stress ≡ coordinate of M

* At point N on circle σn is minimum and shear stress τ is zero.

∴ minimum principal stress ≡ coordinate of N

* At point P on Circle τ is maximum.

Maximum shear stress ≡ ordinate of P(i.e. radius of circle)

Also, normal stress on plane of maximum shear stress

Where, σn ≡ Average stress

* Mohr's circle becomes zero at a point if radius of circle has the following consideration.

Radius of circle

* If σx = σy, then radius of Mohr's circle is zero and τxy = 0

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Mallesham DevasaneMallesham DevasaneMember since Oct 2015
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Amit kumar

Amit kumarSep 5, 2016

Very nice.. short and simple
Jagannath Palo
Very easy to clear the concept
Avinash Panda
There r some mistakes is formula
Aftab Khan

Aftab KhanDec 31, 2016

Very nice

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