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.