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Isosceles triangle

Isosceles triangle a b α
Isosceles triangle

Values for calculation

$T$ $\mathrm{Nm}$
$a$ $\mathrm{mm}$
$b$ $\mathrm{mm}$
$L$ $\mathrm{mm}$
$G$ $\mathrm{MPa}$

Calculation

Angle

$$α=2\cdot\tan{\cfrac{a}{2\cdot b}}\cdot\cfrac{180}{π}$$
$α=2\cdot\tan{\cfrac{a}{2\cdot b}}\cdot\cfrac{180}{π}$
Equations in LaTeX code
α=2\cdot\tan{\cfrac{a}{2\cdot b}}\cdot\cfrac{180}{π}

Polar moment of inertia

$\text{if }\ \cfrac{2}{3} < a/b < 2\cdot\sqrt{3}$
$\text{if }\ \cfrac{2}{3} < a/b < 2\cdot\sqrt{3}$
Equations in LaTeX code
\text{if }\ \cfrac{2}{3} < a/b < 2\cdot\sqrt{3}
$$K=\cfrac{a^3\cdot b^3}{15\cdot a^2+20\cdot b^2}$$
$K=\cfrac{a^3\cdot b^3}{15\cdot a^2+20\cdot b^2}$
Equations in LaTeX code
K=\cfrac{a^3\cdot b^3}{15\cdot a^2+20\cdot b^2}
$\text{else}$
$\text{else}$
Equations in LaTeX code
\text{else}
$$K=0.0915\cdot b^4\cdot\left(\cfrac{a}{b}-0.8592\right)$$
$K=0.0915\cdot b^4\cdot\left(\cfrac{a}{b}-0.8592\right)$
Equations in LaTeX code
K=0.0915\cdot b^4\cdot\left(\cfrac{a}{b}-0.8592\right)

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

$$τ_{max}=\cfrac{T\cdot{10}^3\cdot b\cdot\left[0.2+0.309\cdot a/b-0.0418\cdot\left(a/b\right)^2\right]}{K}$$
$τ_{max}=\cfrac{T\cdot{10}^3\cdot b\cdot\left[0.2+0.309\cdot a/b-0.0418\cdot\left(a/b\right)^2\right]}{K}$
Equations in LaTeX code
τ_{max}=\cfrac{T\cdot{10}^3\cdot b\cdot\left[0.2+0.309\cdot a/b-0.0418\cdot\left(a/b\right)^2\right]}{K}

Requirements

$$\cfrac{2}{3} < a/b < 2\cdot\sqrt3$$
$\cfrac{2}{3} < a/b < 2\cdot\sqrt3$
Equations in LaTeX code
\cfrac{2}{3} < a/b < 2\cdot\sqrt3
$$39 < α < 120$$
$39 < α < 120$
Equations in LaTeX code
39 < α < 120
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