Question

The radius of Mohr's circle is zero when the state of stress is such that

• A. Shear stress is zero
• B. There is pure shear
• C. There is no shear stress but identical direct stresses in two mutually perpendicular directions.
• D. There is no shear stress but equal direct stresses, opposite in nature, in two mutually perpendicular directions.

Answer 1

The correct option is C There is no shear stress but identical direct stresses in two mutually perpendicular directions.

$R=\sqrt{{\left(\frac{{\sigma }_1-{\sigma }_2}{2}\right)}^2+{\tau }^2}$
If R is zero

${\tau }^2=0$
$\tau =0$

$and\left(\frac{{\sigma }_1-{\sigma }_2}{2}\right)=0$

${\sigma }_1={\sigma }_2$