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Solid circular section

Solid circular section r
Solid circular section

Values for calculation

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

Calculation

Polar moment of inertia

$$K=\cfrac{1}{2}\cdot π\cdot r^4$$
$K=\cfrac{1}{2}\cdot π\cdot r^4$
Equations in LaTeX code
K=\cfrac{1}{2}\cdot π\cdot r^4

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

$$τ_{max}=\cfrac{2\cdot 10^3\cdot T}{π\cdot r^3}$$
$τ_{max}=\cfrac{2\cdot 10^3\cdot T}{π\cdot r^3}$
Equations in LaTeX code
τ_{max}=\cfrac{2\cdot 10^3\cdot T}{π\cdot r^3}
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