Mohr's Circle For Plane Stress & Plane Strain.

Mohr’s circle is the locus of points representing magnitude of normal andshear stress at various plane in a given stress element.Graphically, variation of normal stress and shear stress are studied with the help of Mohr's circle.

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

Normal stress:

Shear stress:

General State of Stress at an Element:

If   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

then,

Let  be two normal stresses(both tensile) and  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 σ_n is maximum and shear stress is zero.

∴ Maximum principal stress ≡coordinate of M

* At point N on circle σ_n 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, σ_n ≡ Average stress

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

Radius of circle

* If σ_x = σ_y, then radius of Mohr's circle is zero and τ_xy = 0

Mechanism Of Solid Mohr's Circle

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