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Any elongated section with axis of symmetry 0X

Any elongated section with axis of symmetry OX U 0 X
Any elongated section with axis of symmetry 0X

Values for calculation

$T$ $\mathrm{Nm}$
$U$ $\mathrm{mm}$
$A$ $\mathrm{mm^2}$
$I_x$ $\mathrm{mm^4}$
$D$ $\mathrm{mm}$
$r$ $\mathrm{mm}$
$L$ $\mathrm{mm}$
$G$ $\mathrm{MPa}$

Calculation

Coefficient $ C $

$$C=\cfrac{D}{1+\cfrac{π^2\cdot D^4}{16\cdot A^2}}\cdot\left[1+0.15\cdot \left(\cfrac{π^2\cdot D^4}{16\cdot A^2}-\cfrac{D}{2\cdot r}\right)\right]$$
$C=\cfrac{D}{1+\cfrac{π^2\cdot D^4}{16\cdot A^2}}\cdot\left[1+0.15\cdot \left(\cfrac{π^2\cdot D^4}{16\cdot A^2}-\cfrac{D}{2\cdot r}\right)\right]$
Equations in LaTeX code
C=\cfrac{D}{1+\cfrac{π^2\cdot D^4}{16\cdot A^2}}\cdot\left[1+0.15\cdot \left(\cfrac{π^2\cdot D^4}{16\cdot A^2}-\cfrac{D}{2\cdot r}\right)\right]

Polar moment of inertia

$$K=\cfrac{4\cdot I_x}{1+16\cdot I_x/(A\cdot U^2)}$$
$K=\cfrac{4\cdot I_x}{1+16\cdot I_x/(A\cdot U^2)}$
Equations in LaTeX code
K=\cfrac{4\cdot I_x}{1+16\cdot I_x/(A\cdot U^2)}

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

$$τ_{max}=\cfrac{10^3\cdot T}{K}\cdot C$$
$τ_{max}=\cfrac{10^3\cdot T}{K}\cdot C$
Equations in LaTeX code
τ_{max}=\cfrac{10^3\cdot T}{K}\cdot C
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