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Hollow concentric circular section

Hollow concentric circular section r o r i
Hollow concentric circular section

Values for calculation

$T$ $\mathrm{Nm}$
$r_o$ $\mathrm{mm}$
$r_i$ $\mathrm{mm}$
$L$ $\mathrm{mm}$
$G$ $\mathrm{MPa}$

Calculation

Polar moment of inertia

$$K=\cfrac{1}{2}\cdot π\cdot\left(r_o^4-r_i^4\right)$$
$K=\cfrac{1}{2}\cdot π\cdot\left(r_o^4-r_i^4\right)$
Equations in LaTeX code
K=\cfrac{1}{2}\cdot π\cdot\left(r_o^4-r_i^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

$$τ_{max}=\cfrac{2\cdot{10}^3\cdot T\cdot r_o}{π\cdot\left(r_o^4-r_i^4\right)}$$
$τ_{max}=\cfrac{2\cdot{10}^3\cdot T\cdot r_o}{π\cdot\left(r_o^4-r_i^4\right)}$
Equations in LaTeX code
τ_{max}=\cfrac{2\cdot{10}^3\cdot T\cdot r_o}{π\cdot\left(r_o^4-r_i^4\right)}
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