Question

An element of a certain material in plane strain has
${\epsilon }_x=800\times {10}^{-6}$

${\epsilon }_y=400\times {10}^{-6}$

${\gamma }_{xy}=300\times {10}^{-6}$
What is the maximum shearing strain?

• A. $150\times {10}^{-6}$
• B. $355\times {10}^{-6}$
• C. $250\times {10}^{-6}$
• D. $500\times {10}^{-6}$

Answer 1

The correct option is D $500\times {10}^{-6}$

${\epsilon }_x=800\times {10}^{-6}$

${\epsilon }_y=400\times {10}^{-6}$

${\varphi }_{xy}=300\times {10}^{-6}$

Maximum shear strain

$\frac{{\varphi }_{max}}{2}=\sqrt{{\left(\frac{{\epsilon }_x-{\epsilon }_y}{2}\right)}^2+{\left(\frac{{\gamma }_{xy}}{2}\right)}^2}=250\times {10}^{-6}$

$\Rightarrow {\gamma }_{max}=500\times {10}^{-6}$