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Any thin open tube of uniform thickness

Any thin open tube of uniform thickness t
Any thin open tube of uniform thickness

Values for calculation

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

Calculation

Polar moment of inertia

$$K=\cfrac{1}{3}\cdot U\cdot t^3$$
$K=\cfrac{1}{3}\cdot U\cdot t^3$
Equations in LaTeX code
K=\cfrac{1}{3}\cdot U\cdot t^3

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

$$τ_{max}=\cfrac{10^3\cdot T\cdot\left(3\cdot U+1.8\cdot t\right)}{U^2\cdot t^2}$$
$τ_{max}=\cfrac{10^3\cdot T\cdot\left(3\cdot U+1.8\cdot t\right)}{U^2\cdot t^2}$
Equations in LaTeX code
τ_{max}=\cfrac{10^3\cdot T\cdot\left(3\cdot U+1.8\cdot t\right)}{U^2\cdot t^2}
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