Closed Thin-Walled Tubes

In closed thin-walled tubes, where $t\ll r$, shear stress is given by:

$$\tau =\frac{T}{2A_{m}t}$$

The angular twist (radians) per unit of length of the tube is given by:

$$\theta =\frac{T{L}_m}{4G{A}_m^{2}t}$$

where:

• $T$ is torque
• $t$ is thickness
• $\tau$ is shear stress
• $G$ is modulus of rigidity
• $L_m$ is the length of section median line
• $A_m$ is the area enclosed by the section median line
• $\theta$ is the angle of twist per unit length of the tube