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Circular segmental section

Circular_segmental_section
Circular segmental section

Values for calculation

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

Calculation

Height of the segment

$$h=r\cdot\left(1-\cos(α)\right)$$

Coefficient $ C $

$$C=0.7854-0.0333\cdot\cfrac{h}{r}-2.6183\cdot\left(\cfrac{h}{r}\right)^2+4.1595\cdot\left(\cfrac{h}{r}\right)^3-3.0769\cdot\left(\cfrac{h}{r}\right)^4+0.9299\cdot\left(\cfrac{h}{r}\right)^5$$

Coefficient $ B $

$$B=0.6366+1.7598\cdot\cfrac{h}{r}-5.4897\cdot\left(\cfrac{h}{r}\right)^2+14.062\cdot\left(\cfrac{h}{r}\right)^3-14.51\cdot\left(\cfrac{h}{r}\right)^4+6.434\cdot\left(\cfrac{h}{r}\right)^5$$

Polar moment of inertia

$$K=2\cdot C\cdot r^4$$

Angle of twist

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

Torsion stress

$$τ_{max}=\cfrac{T\cdot10^3\cdot B}{r^3}$$

Requirements

$$0\le\cfrac{h}{r}\le1$$