Question

The state of stress on an element is as shown in the figure. If $E=2\times {10}^{5}N/m{m}^2$ and Poisson's ratio $=0.3$, the magnitude of the stress $\sigma$ for no strain in $BC$ is

• A. $84N/m{m}^2$
• B. $64N/m{m}^2$
• C. $34N/m{m}^2$
• D. $24N/m{m}^2$

Answer 1

The correct option is D $24N/m{m}^2$


Strain in BC,

${ϵ}_y=\frac{{\sigma }_y}{E}-\mu \frac{{\sigma }_x}{E}$
$0=\frac{\sigma }{E}-\frac{0.3\times 80}{E}$
$\therefore \sigma =24N/m{m}^2$