Angle of twist - Rod subjected to torque

Input(s)

E: Modulus of Elasticity (psi)

v: Poisson (dimensionless)

$\mathrm{D}_{\mathrm{o}}$: Outer Diameter $(\mathrm{ft})$

$\mathrm{D}_{\mathrm{i}}$: Inner Diameter $(\mathrm{ft})$

T: Torque (ft lbf)

L: Length of Section (ft)

Output(s)

G: Modulus of Rigidity (psi)

J: Polar Moment of Inertia $\left(\mathrm{ft}^{4}\right)$

$\theta$: Angle of Twist (rad)

Formula(s)

$$ \begin{gathered} \mathrm{G}=\frac{\mathrm{E}}{2 *(1+v)} \\ \mathrm{J}=\frac{3.142 *\left(\left(\mathrm{D}_{\mathrm{o}}\right)^{4}-\left(\mathrm{D}_{\mathrm{i}}\right)^{4}\right)}{32} \\ \theta=\frac{\mathrm{T} * \mathrm{~L}}{\mathrm{G} * \mathrm{~J}} \end{gathered} $$

Reference(s)

Samuel. E Robello. 501 Solved Problems and Calculations for Drilling Operations. Sigma Quadrant. 2015. Houston, Texas, Page: 369.