Menu

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 $

$$q=\cfrac{a_0}{a}$$
$q=\cfrac{a_0}{a}$
Equations in LaTeX code
q=\cfrac{a_0}{a}

Dimension $ b_0 $

$$b_0=\cfrac{a_0\cdot b}{a}$$
$b_0=\cfrac{a_0\cdot b}{a}$
Equations in LaTeX code
b_0=\cfrac{a_0\cdot b}{a}

Polar moment of inertia

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

Angle of twist

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

Torsion stress

$$τ_{max}=\cfrac{2\cdot{10}^3\cdot T}{π\cdot a\cdot b^2\cdot\left(1-q^4\right)}$$
$τ_{max}=\cfrac{2\cdot{10}^3\cdot T}{π\cdot a\cdot b^2\cdot\left(1-q^4\right)}$
Equations in LaTeX code
τ_{max}=\cfrac{2\cdot{10}^3\cdot T}{π\cdot a\cdot b^2\cdot\left(1-q^4\right)}
On this page