Question

In a biaxial strain system ${\epsilon }_{x}and{\epsilon }_y,$ what is the maximum engineering shearing strain?

• A. ${\epsilon }_x+{\epsilon }_y$
• B. ${\epsilon }_x-{\epsilon }_y$
• C. $\frac{{\epsilon }_x+{\epsilon }_y}{2}$
• D. $\frac{{\epsilon }_x-{\epsilon }_y}{2}$

Answer 1

The correct option is B

${\epsilon }_x-{\epsilon }_y$

$\frac{{\varphi }_{x^{\prime }{y}^{\prime }}}{2}=-\left(\frac{{\epsilon }_x-{\epsilon }_y}{2}\right)\sin 2\theta +\frac{{\varphi }_{xy}}{2}\cos 2\theta$

$For\theta =45{}^{\circ }and{\varphi }_{xy}=0$

$\Rightarrow \frac{{\varphi }_{x^{\prime }{y}^{\prime }}}{2}=-\left(\frac{{\epsilon }_x-{\epsilon }_y}{2}\right)$

$\Rightarrow {\varphi }_{x^{\prime }{y}^{\prime }}=-({\epsilon }_x-{\epsilon }_y)$

$\Rightarrow {\varphi }_{x^{\prime }{y}^{\prime }}={\epsilon }_x-{\epsilon }_y$ (magnitude)