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Circular segmental section

Circular segmental section r α
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

$$h=r\cdot\left(1-\cos{α}\right)$$
$h=r\cdot\left(1-\cos{α}\right)$
Equations in LaTeX code
h=r\cdot\left(1-\cos{α}\right)

Coefficient $ C $

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

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

$$K=2\cdot C\cdot r^4$$
$K=2\cdot C\cdot r^4$
Equations in LaTeX code
K=2\cdot C\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

$$τ_{max}=\cfrac{T\cdot10^3\cdot B}{r^3}$$
$τ_{max}=\cfrac{T\cdot10^3\cdot B}{r^3}$
Equations in LaTeX code
τ_{max}=\cfrac{T\cdot10^3\cdot B}{r^3}

Requirements

$$0\le\cfrac{h}{r}\le1$$
$0\le\cfrac{h}{r}\le1$
Equations in LaTeX code
0\le\cfrac{h}{r}\le1
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