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 (Hartsuijker and Welleman, 2007).