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

                                         τ_m =16T / πb²  h

Figure: Ellipse

The angle of twist per unit length is

θ= 4π² T J / A² G