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Hollow elliptical section outer and inner boundaries similar ellipses

Hollow elliptical section, outer and inner boundaries similar ellipses 2a 0 2a 2b 0 2b
Hollow elliptical section, outer and inner boundaries similar ellipses

Values for calculation

$ T $ $ \mathrm{Nm} $
$ a $ $ \mathrm{mm} $
$ b $ $ \mathrm{mm} $
$ a_0 $ $ \mathrm{mm} $
$ L $ $ \mathrm{mm} $
$ G $ $ \mathrm{MPa} $

Calculation

Coefficient $ q $

$$q=\cfrac{a_0}{a}$$

Dimension $ b_0 $

$$b_0=\cfrac{a_0\cdot b}{a}$$

Polar moment of inertia

$$K=\cfrac{π\cdot a^3\cdot b^3}{a^2+b^2}\cdot\left(1-q^4\right)$$

Angle of twist

$$θ=\cfrac{T\cdot 10^3\cdot L}{K\cdot G}$$

Torsion stress

$$τ_{max}=\cfrac{2\cdot{10}^3\cdot T}{π\cdot a\cdot b^2\cdot\left(1-q^4\right)}$$