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Solid elliptical section

Solid elliptical section 2b 2a
Solid elliptical section

Values for calculation

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

Calculation

Polar moment of inertia

$$K=\cfrac{π\cdot a^3\cdot b^3}{a^2+b^2}$$
$K=\cfrac{π\cdot a^3\cdot b^3}{a^2+b^2}$
Equations in LaTeX code
K=\cfrac{π\cdot a^3\cdot b^3}{a^2+b^2}

Angle of twist

$$θ=\cfrac{T\cdot 10^3\cdot L}{K\cdot G}$$
$θ=\cfrac{T\cdot 10^3\cdot L}{K\cdot G}$
Equations in LaTeX code
θ=\cfrac{T\cdot 10^3\cdot L}{K\cdot G}

Torsion stress

$$τ_{max}=\cfrac{2\cdot 10^3\cdot T}{π\cdot a\cdot b^2}$$
$τ_{max}=\cfrac{2\cdot 10^3\cdot T}{π\cdot a\cdot b^2}$
Equations in LaTeX code
τ_{max}=\cfrac{2\cdot 10^3\cdot T}{π\cdot a\cdot b^2}
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