Question

A square element is subjected to principal stresses in $N/m{m}^2$ as shown in figure below. The intensity of normal stress ${\sigma }_n$ on plane BD is

• A. $200\sqrt{2}$
• B. 100
• C. 200
• D. 0

Answer 1

The correct option is D 0

For the square clement, $\theta =45°$

$\therefore {\sigma }_n=\frac{{\sigma }_1+{\sigma }_2}{2}+\left(\frac{{\sigma }_1-{\sigma }_2}{2}\right)\times \cos 2\theta$

$=\frac{200-200}{2}+\left(\frac{200-(-200)}{2}\right)\times \cos (2\times 45{}^{\circ })$
= 0