Question

In a plane strain condition in the XY plane, the strain components associated with XY axes are ${\epsilon }_x=800\times {10}^{-6},{\epsilon }_y=100\times {10}^{-6},{\varphi }_{xy}=-800\times {10}^{-6}$. What are the principal strains for these strain values?

• A. $981\times {10}^{-6},-81\times {10}^{-6}$
• B. $891\times {10}^{-6},-81\times {10}^{-6}$
• C. $881\times {10}^{-6},-71\times {10}^{-6}$
• D. $839\times {10}^{-6},-81\times {10}^{-6}$

Answer 1

The correct option is A $981\times {10}^{-6},-81\times {10}^{-6}$

Radius of Mohr's circle of strain,

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

$=\sqrt{{\left(350\right)}^2+{\left(400\right)}^2}\times {10}^{-6}$

$=531.5\times {10}^{-6}$
The centre of Mohr's circle,

$C=\frac{{\epsilon }_x+{\epsilon }_y}{2}=450\times {10}^{-6}$
$\therefore$ Major principal strain = C + r

$=981.5\times {10}^{-6}$
Minor principal strain = C - r

$=-80.5\times {10}^{-6}$