Question

The radius of Mohr’s circle is zero when the state of stress is such that
1. Shear stress is zero
2. There is pure shear
3. There is not shear stress but identical direct stresses in two mutually perpendicular directions
4. There is no shear stress but equal direct stresses, opposite in nature, in two mutually perpendicular directions

Answer 1

Correct Answer - Option 3 : There is not shear stress but identical direct stresses in two mutually perpendicular directions

Concept:

The radius of mohr’s circle is, \({\tau _{max}} = \sqrt {{{\left( {\frac{{{\sigma _x} - {\sigma _y}}}{2}} \right)}^2} + {{\left( {{\tau _{xy}}} \right)}^2}} \)

Calculation:

Given that,

Radius of mohr circle is zero, \({\tau _{max}} = 0\;\) when and only when

1. \({\sigma _x} = {\sigma _y}\)​
2. \({\tau _{xy}} = 0\)

Putting above values in below equation,

\({\tau _{max}} = \sqrt {{{\left( {\frac{{{\sigma _x} - {\sigma _y}}}{2}} \right)}^2} + {{\left( {{\tau _{xy}}} \right)}^2}} = 0\)

So, there is no shear stress but identical direct stresses in two mutually perpendicular directions.