Question

In a strained material, the principal stresses in the x and y directions are 100 $N/m{m}^2$ (tensile) and 60 $N/m{m}^2$ (compressive). On an inclined plane, the normal to which makes an angle 30° to the x-axis, what is the tangential stress in $N/m{m}^2$?

• A. $30\sqrt{3}$
• B. $40\sqrt{3}$
• C. 60
• D. 40

Answer 1

The correct option is B $40\sqrt{3}$

The magnitude of tangential stress is given by

${\tau }_{x^{\prime }{y}^{\prime }}=\frac{({\sigma }_1-{\sigma }_2)}{2}\sin 2\theta$

$=\frac{(100+60)}{2}\sin 60{}^{\circ }=40\sqrt{3}$