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Hollow this-walled section of uniform thickness

Hollow, this-walled section of uniform thickness 2a 2b t
Hollow, this-walled section of uniform thickness

Values for calculation

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

Calculation

Length of median boundary

$$U=π\cdot\left(a+b-t\right)\cdot\left[1+0.258\cdot\cfrac{\left(a-b\right)^2}{\left(a+b-t\right)^2}\right]$$
$U=π\cdot\left(a+b-t\right)\cdot\left[1+0.258\cdot\cfrac{\left(a-b\right)^2}{\left(a+b-t\right)^2}\right]$
Equations in LaTeX code
U=π\cdot\left(a+b-t\right)\cdot\left[1+0.258\cdot\cfrac{\left(a-b\right)^2}{\left(a+b-t\right)^2}\right]

Polar moment of inertia

$$K=\cfrac{4\cdot π^2\cdot t\cdot\left[\left(a-\cfrac{1}{2}\cdot t\right)^2\cdot\left(b-\cfrac{1}{2}\cdot t\right)^2\right]}{U}$$
$K=\cfrac{4\cdot π^2\cdot t\cdot\left[\left(a-\cfrac{1}{2}\cdot t\right)^2\cdot\left(b-\cfrac{1}{2}\cdot t\right)^2\right]}{U}$
Equations in LaTeX code
K=\cfrac{4\cdot π^2\cdot t\cdot\left[\left(a-\cfrac{1}{2}\cdot t\right)^2\cdot\left(b-\cfrac{1}{2}\cdot t\right)^2\right]}{U}

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 (average)

$$τ_{average}=\cfrac{10^3\cdot T}{2\cdot π\cdot t\cdot\left(a-\cfrac{1}{2}\cdot t\right)\cdot\left(b-\cfrac{1}{2}\cdot t\right)}$$
$τ_{average}=\cfrac{10^3\cdot T}{2\cdot π\cdot t\cdot\left(a-\cfrac{1}{2}\cdot t\right)\cdot\left(b-\cfrac{1}{2}\cdot t\right)}$
Equations in LaTeX code
τ_{average}=\cfrac{10^3\cdot T}{2\cdot π\cdot t\cdot\left(a-\cfrac{1}{2}\cdot t\right)\cdot\left(b-\cfrac{1}{2}\cdot t\right)}
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