Question

In a plane strain problem in XY plane, the shear strain = $12\times {10}^{-6}$, and the normal strain in X and Y direction = 0. For this state of strain, what is the diameter of the Mohr's circle of strain?

• A. $6\times {10}^{-6}$
• B. $8\times {10}^{-6}$
• C. $12\times {10}^{-6}$
• D. $24\times {10}^{-6}$

Answer 1

The correct option is C $12\times {10}^{-6}$

Radius of Mohr's circle in plane strain condition

$R=\sqrt{{\left(\frac{{\epsilon }_x-{\epsilon }_y}{2}\right)}^2+{\left(\frac{{\varphi }_{xy}}{2}\right)}^2}$

$=\sqrt{{\left(\frac{0}{2}\right)}^2+{\left(\frac{12\times {10}^{-6}}{2}\right)}^2}$

$R=6\times {10}^{-6}$

$Diameter=2R=12\times {10}^{-6}$