```{index} Torsional moment of inertia
```

# Torsional moment of inertia thin-walled tubes

$$I_t = \cfrac{{4A_m^2}}{{\oint {\cfrac{1}{t}{{d}}m} }}$$

For a thin-walled strip this reduces to:

$$I_t = \cfrac{1}{3}ht^3$$

For thin-walled open cross-section this leads to:

$$I_t = \sum_i\cfrac{1}{3}h_it_i^3$$

This is treated in chapter 6.3.1 and 6.3.2 of the book Engineering Mechanics Volume 2 {cite:p}`Hartsuijker2007`.