[[Torsion]] causes two types of measurable deformation. First is the angle of twist, $\phi$, which is a measure of how much the shaft face has rotated. The second deformation measure is the helix angle, $\gamma$, drawn on the axial face of the shaft between the shaft axis helix caused by deformation. There is a geometric relationship between these two measurements, detailed in the figure below. ![[torsion_geo.png|center|500]] $\phi r =\gamma L$In fact the helix angle is the exact same measurement as [[Engineering Shear Strain|shearing strain]]. The relationship between shearing stress and strain makes it clear that the [[Shear Stress|shear stress]] distribution is purely a function of shaft radius and can be expressed using the following formula: $\tau (r)=\tau_{max}\dfrac{r}{r_{max}}$ $\tau_{max}=G\dfrac{\phi r_{max}}{L}$ It should be noted that this expression only holds in the [[Elastic|elastic]] region of the material ($\tau<\tau_y$​).