[[Torsion]] of non-circular shafts is usually approached empirically. Typically torsion of non-circular shafts are based on the analysis of an equivalent rectangular shaft. The width, $a$, and thickness, $b$, of a rectangular shaft are used to determine the maximum shear stress and angle of twist in a non-circular shaft. $\tau_{max}=\dfrac{T}{c_1ab^2}$ $\psi=\dfrac{TL}{c_2ab^3G}$ The constants, $c_1$ and $c_2$, are dependent on geometric dimensions $a$ and $b$ and calculated empirically. An accurate formula exists for $\dfrac{a}{b}\ge 5$. $c_1=c_2=\dfrac{1}{3}\left(1−0.63\dfrac{b}{a}\right)$ Further information on the stress distribution requires the use of the so-called membrane analogy if so desired. ![[noncircular.png]]