# Torsion Constant for Ellipse Cross-section

Written by Jerry Ratzlaff on . Posted in Classical Mechanics

## Torsion Constant for Ellipse Cross-section formula

 $$\large{ J = \frac{\pi\;a^3\;b^3}{a^2\;+\;b^2} }$$

### Where:

 Units English Metric $$\large{ J }$$  (Greek symbol alpha) = torsion constant $$\large{\frac{lbf-ft}{rad}}$$ $$\large{\frac{N-m}{rad}}$$ $$\large{ a }$$ = semi-major axis of an ellipse $$\large{in}$$ $$\large{m}$$ $$\large{ b }$$ = semi-minor axis of an ellipse $$\large{in}$$ $$\large{m}$$ $$\large{ \pi }$$ = Pi $$\large{3.141 592 653 ...}$$