Question

The tangential or shear stress on an oblique plane at an angle $\theta$ to the cross-section of a body which is subjected to a direct tensile stress $\left(\sigma \right)$ is equal to

• A. $\frac{\sigma }{2}$ sin 2$\theta$
• B. $\sigma$ cos $\theta$
• C. $\sigma co{s}^2\theta$
• D. $\sigma si{n}^2\theta$

Answer 1

The correct option is A $\frac{\sigma }{2}$ sin 2$\theta$

We have $\sigma =\frac{F}{A}$
For an oblique plane we have
$\frac{Fcos\theta }{A/cos\theta }=\frac{\sigma }{2}sin2\theta$