Mohrs Circle

  • Draw and interpret the Mohr’s circle of stress, for any prescribed stress state.

Mohr's Circle

  1. Draw normal and shear axes with positive axes.

  2. Mark normal stress values with sign convention, tensile stress is positive and compression stress is negative.

  3. Draw shear stress values starting from already marked normal stress points.

  4. Connect end of shear stress lines

  5. Draw Mohr’s circle assuming the connection line as diameter of the circle .

  6. Stress Analysis on Mohr’s circle - To get normal and shear stress values at any plane theta, take angle two times \(\theta\) in Mohr’s circle starting from diagonal of the circle and locate a peripheral point. Shear stress value will be Y axis value and normal stress value will be X axis value.

Solved Examples

Solved Example:

40-3-01

The state of the point under plane stress condition is: $\sigma_{xx} = 40, \sigma_{yy} =100, \tau = 40$. The radius of Mohr's circle representing the given state of stress is: (ESE Mech 2014- Paper 2)

Correct Answer: B

Solved Example:

40-3-02

The state of stress at a point in a component is represented by a Mohr's circle of radius 100 MPa centered at 200 MPa on the normal stress axis. On a plane passing through the same point, the normal stress is 260 MPa. The magnitude of the shear stress on the same plane at the same point, in MPa, is: (GATE ME 2019- Shift II)

Solution:

40-3-02

\[\tau = \sqrt{100^2 - 60^2} = 80\ \mathrm{MPa}\]

Correct Answer: B