Torsion for Rectangular Sections

For a member with a rectangular cross-sectional area $b\times c$, the shear stress is given as:

$${\tau }_{\text{max}}=\frac{T}{\alpha b{c}^2}\approx \frac{T}{b{c}^2}\left(3+\frac{1.8}{b/c}\right)$$

where:

• $b$ is the width (longer side)
• $c$ is the thickness (shorter side)
• $\alpha$ is a factor that is a function of the ratio $b/c$

The angle of twist is given by:

$$\theta =\frac{Tl}{\beta b{c}^{3}G}$$

where $\beta$ is also a factor that is a function of the ratio $b/c$.

$\alpha$ and $\beta$ can usually be found in tables: