Mohr’s Circle (Stress and Strain Part-5)

Mohr’s circle is a graphical representation of a general state of stress at a point.

With the help of Mohr’s Circle, we can evaluate principal stress, maximum shear stresses, also normal and tangential stress at any plane.
Many questions come in exam related to principal stress and with help of Mohr’s circle they are solved in seconds.
Let’s see the rules and sign conventions to follow to make Mohr Circle:

When drawing Mohr’s Circle, always remember

  • X-Axis shows Direct Stress

  • Y-Axis shows Shear Stress
  • Tensile stress always considered positive and will be always plotted right side to origin O.
  • Clockwise Shear considered Positive.
  • If θ is in anticlockwise direction then θ will be taken positive & radius vector will be above axis .
  • Compressive stress always considered negative and will always be plotted on left side of origin O.
  • Anti-Clockwise Shear is considered Negative.
  • If θ is in clockwise direction then θ will be taken negative & radius vector will be below axis .

Let us now move to how we should proceed when we see a problem with Mohr’s circle:

 

This is an object which on which both direct stress and sheat stress is being applied.

 

Step 1. Draw X & Y-Axis and mark both σx & σy on X-Axis. 

Step 2. Now We will mark τxy.

As in the above figure τxy at σx is trying to rotate body in anti clockwise direction, so according to our convention τxy will be downward and similarly for σy it will be upward.

Step3. Now join the lines C to D. We get a point E which interects line CD with X-Axis.

Now taking E as centre draw a circle with radius as CE=ED=r

Point F & G denotes the maximum and minimum principal stresses and half of angle CEF denotes the location of principal plane from the plane at which σx is acting.

Step4. Radius of Mohr’s represents the maximum value of shear stress.

If we observe the Mohr’s circle centre of Mohr’s Circle is given by 

Radius of Mohr’s circle can be directly obtained by following formula:

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