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Thin circular open tube of uniform thickness

Thin_circular_open_tube_of_uniform_thickness
Thin circular open tube of uniform thickness

Values for calculation

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

Calculation

Polar moment of inertia

$$K=\cfrac{2}{3}\cdot π\cdot r\cdot t^3$$

Angle of twist

$$θ=\cfrac{T\cdot 10^3\cdot L}{K\cdot G}$$

Torsion stress

$$τ_{max}=\cfrac{10^3\cdot T\cdot\left(6\cdotπ\cdot r+1.8\cdot t\right)}{4\cdot π^2\cdot r^2\cdot t^2}$$