### Material Subjected to Combined Direct & Shear Stress

• Combining the theory with the basic equations of torsion in a cylindrical shaft, find maximum shear stress in shafts.

Direct stress on a plane located at an angle $\theta$ $\sigma_\theta = \frac{\sigma_x + \sigma_y}{2} + \frac{\sigma_x\ - \sigma_y}{2} \cos 2\theta + \tau_{xy} sin 2\theta$

Shear stress on a plane located at an angle $\theta$ $\tau_\theta = \frac{\sigma_x - \sigma_y}{2} \sin 2\theta - \tau_{xy} cos 2\theta$ For $\tau_\theta$ to be maximum or minimum, $\tan 2\theta = \frac{2\tau_{xy}}{(\sigma_x - \sigma_y)}$

### Solved Example:

#### 46-1-01

The equation for maximum shear stress for a body subjected to Combined Direct & Shear Stress is: