Question

In a rectangular element subjected to like principal tensile stresses '${\rho }_1^{\prime }and{}^{\prime }{\rho }_2$' in two mutually perpendicular directions X and Y, the maximum shear would occur along the

• A. plane normal to X-axis
• B. plane normal to Y-axis
• C. plane at 45° to Y-direction
• D. plane at 45° and 135° to the Y-direction

Answer 1

The correct option is D plane at 45° and 135° to the Y-direction

The shear stress $\tau =-\left(\frac{{\sigma }_1-{\sigma }_2}{2}\right)\sin 2\theta$

where, $\theta$ is the angle of inclination of the plane of major principal stress.

$\sin 2\theta =1$

$\therefore \theta =45{}^{\circ }and135{}^{\circ }$
with y-direction $\left(planeof{p}_1\right)$