Question

A plate in equilibrium is subjected to uniform stresses along its edges with magnitude ${\sigma }_{xx}=30MPa$ and ${\sigma }_{yy}=50MPa$ as shown in figure.

The Young's modulus of the material is $2\times {10}^{11}N/m^2$ and the Poisson's ratio is $0.3$. If ${\sigma }_{zz}$ is negligibly small and assumed to be zero, then the strain ${ϵ}_{zz}$ is

• A. $-120\times {10}^{-6}$
• B. $-60\times {10}^{-6}$
• C. $0.0$
• D. $120\times {10}^{-6}$

Answer 1

The correct option is A $-120\times {10}^{-6}$

${\sigma }_{xx}=30MPa,{\sigma }_{yy}=50MPa$
$E=2\times {10}^{11}N/m^2=2\times {10}^{5}N/m{m}^2$
$=2\times {10}^{5}MPa$
Poisson ratio, $\mu =0.3$
${\sigma }_{zz}=0$
$\therefore {ϵ}_{zz}=\frac{{\sigma }_{zz}}{E}-\frac{\mu ({\sigma }_{xx}+{\sigma }_{yy})}{E}$
$=-\frac{0.3(30+50)}{2\times {10}^5}$
$=-120\times {10}^{-6}$