Question

A structural element is subjected to pure shear of 80 $N/m{m}^2$, as shown in the figure. The yield stresses both in tension and in compression are 240 $N/m{m}^2$. According to the maximum normal stress theory, the factors of safety in tension and compression are, respectively,

• A. 2 and 2
• B. 2.5 and 2.5
• C. 3 and 3
• D. 4 and 4

Answer 1

The correct option is C 3 and 3

For pure shear
${\sigma }_1=\tau =80N/m{m}^2$

${\sigma }_2=-\tau =-80N/m{m}^2$

${\sigma }_y=\pm 240N/m{m}^2$
According to maximum normal shear theory In tension,

${\sigma }_1\ge \frac{{\sigma }_y}{FOS}$

$\therefore FOS=3$
In compression,

${\sigma }_2\le -\frac{{\sigma }_y}{FOS}$

$\therefore FOS=3$