Elliptic Section:
The polar moment of inertia of elliptic section is
J = (π/64 ) (b h3 + b3 h)
and area of section is
A = πbh / 4
where 2h is semi-minor axis and 2b is semi-major axis. The maximum shearing stress occurs at the ends of semi-minor axis that means at points on and in
τm =16T / πb2 h
Figure: Ellipse
The angle of twist per unit length is
θ= 4π2 T J / A2 G