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Hollow elliptical section outer and inner boundaries similar ellipses

Hollow_elliptical_section,_outer_and_inner_boundaries_similar_ellipses
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

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