Question

Given that for an element in a body of homogeneous isotropic material subjected to plane stresses, Ex, ${\epsilon }_x,{\epsilon }_y$ and ${\epsilon }_z$ are normal strains in x, y and z direction respectively and μ is the Poisson's ratio, the magnitude of unit volume change of the element is given by

• A. ${\epsilon }_x+{\epsilon }_y+{\epsilon }_z$
• B. ${\epsilon }_x+\mu ({\epsilon }_y+{\epsilon }_z)$
• C. $\mu ({\epsilon }_x+{\epsilon }_y+{\epsilon }_z)$
• D. $\frac{1}{{\epsilon }_x}+\frac{1}{{\epsilon }_y}+\frac{1}{{\epsilon }_z}$

Answer 1

The correct option is A ${\epsilon }_x+{\epsilon }_y+{\epsilon }_z$

$\frac{\Delta V}{V}=\frac{\text{Final volume - Initial volume}}{\text{Initial volume}}$

$={\epsilon }_x+{\epsilon }_y+{\epsilon }_z$