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Hollow rectangle thin-walled

Hollow_rectangle,_thin-walled
Hollow rectangle, thin-walled

Values for calculation

$T$ $\mathrm{Nm}$
$a$ $\mathrm{mm}$
$b$ $\mathrm{mm}$
$t$ $\mathrm{mm}$
$t_1$ $\mathrm{mm}$
$L$ $\mathrm{mm}$
$G$ $\mathrm{MPa}$

Calculation

Polar moment of inertia

$$K=\cfrac{2\cdot t\cdot t_1\cdot\left(a-t\right)^2\cdot\left(b-t_1\right)^2}{a\cdot t+b\cdot t_1-t^2-t_1^2}$$

Angle of twist

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

Torsion stress (average) dimension $ a $

$$τ_{average-a}=\cfrac{10^3\cdot T}{2\cdot t\cdot\left(a-t\right)\cdot\left(b-t_1\right)}$$

Torsion stress (average) dimension $ b $

$$τ_{average-b}=\cfrac{10^3\cdot T}{2\cdot t_1\cdot\left(a-t\right)\cdot\left(b-t_1\right)}$$