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Circular sector

Circular sector r α
Circular sector

Values for calculation

$ \{T\in\mathbb{R}\mid T>0\} $
This set includes all real numbers that are greater than zero. Therefore, it contains only positive numbers. Zero and negative numbers are not included in this set.
$ T $ $ \mathrm{Nm} $
$ \{r\in\mathbb{R}\mid r>0\} $
This set includes all real numbers that are greater than zero. Therefore, it contains only positive numbers. Zero and negative numbers are not included in this set.
$ r $ $ \mathrm{mm} $
$ \{α\in\mathbb{R}\mid α>0\} $
This set includes all real numbers that are greater than zero. Therefore, it contains only positive numbers. Zero and negative numbers are not included in this set.
$ α $ $ \mathrm{°} $
$ \{L\in\mathbb{R}\mid L>0\} $
This set includes all real numbers that are greater than zero. Therefore, it contains only positive numbers. Zero and negative numbers are not included in this set.
$ L $ $ \mathrm{mm} $
$ \{G\in\mathbb{R}\mid G>0\} $
This set includes all real numbers that are greater than zero. Therefore, it contains only positive numbers. Zero and negative numbers are not included in this set.
$ G $ $ \mathrm{MPa} $

Calculation

Coefficient $ C $

$$C=0.0034-0.0697\cdot\cfrac{α}{180}+0.5825\cdot\left(\cfrac{α}{180}\right)^2-0.295\cdot\left(\cfrac{α}{180}\right)^3-0.0874\cdot\left(\cfrac{α}{180}\right)^4-0.0111\cdot\left(\cfrac{α}{180}\right)^5$$
$C=0.0034-0.0697\cdot\cfrac{α}{180}+0.5825\cdot\left(\cfrac{α}{180}\right)^2-0.295\cdot\left(\cfrac{α}{180}\right)^3-0.0874\cdot\left(\cfrac{α}{180}\right)^4-0.0111\cdot\left(\cfrac{α}{180}\right)^5$
Equations in LaTeX code
C=0.0034-0.0697\cdot\cfrac{α}{180}+0.5825\cdot\left(\cfrac{α}{180}\right)^2-0.295\cdot\left(\cfrac{α}{180}\right)^3-0.0874\cdot\left(\cfrac{α}{180}\right)^4-0.0111\cdot\left(\cfrac{α}{180}\right)^5

Coefficient $ B $

$$B=0.0117-0.2137\cdot\cfrac{α}{180}+2.2475\cdot\left(\cfrac{α}{180}\right)^2-4.6709\cdot\left(\cfrac{α}{180}\right)^3+5.1764\cdot\left(\cfrac{α}{180}\right)^4-2.2\cdot\left(\cfrac{α}{180}\right)^5$$
$B=0.0117-0.2137\cdot\cfrac{α}{180}+2.2475\cdot\left(\cfrac{α}{180}\right)^2-4.6709\cdot\left(\cfrac{α}{180}\right)^3+5.1764\cdot\left(\cfrac{α}{180}\right)^4-2.2\cdot\left(\cfrac{α}{180}\right)^5$
Equations in LaTeX code
B=0.0117-0.2137\cdot\cfrac{α}{180}+2.2475\cdot\left(\cfrac{α}{180}\right)^2-4.6709\cdot\left(\cfrac{α}{180}\right)^3+5.1764\cdot\left(\cfrac{α}{180}\right)^4-2.2\cdot\left(\cfrac{α}{180}\right)^5

Polar moment of inertia

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

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

Requirements

$$ 0.1 \le\cfrac{α}{180}\le1 $$
$0.1 \le\cfrac{α}{180}\le1$
Equations in LaTeX code
0.1 \le\cfrac{α}{180}\le1
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