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Hollow rectangle thin-walled

Hollow rectangle, thin-walled a b t 1 t 1 t t
Hollow rectangle, thin-walled

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} $
$ \{a\in\mathbb{R}\mid a>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.
$ a $ $ \mathrm{mm} $
$ \{b\in\mathbb{R}\mid b>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.
$ b $ $ \mathrm{mm} $
$ \{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{mm} $
$ \{t_1\in\mathbb{R}\mid t_1>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_1 $ $ \mathrm{mm} $
$ \{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

Polar moment of inertia

$$K=\cfrac{2\cdot t\cdot t_1\cdot\left(a-t\right)^2\cdot\left(b-t_1\right)^2}{a\cdot t+b\cdot t_1-t^2-t_1^2}$$
$K=\cfrac{2\cdot t\cdot t_1\cdot\left(a-t\right)^2\cdot\left(b-t_1\right)^2}{a\cdot t+b\cdot t_1-t^2-t_1^2}$
Equations in LaTeX code
K=\cfrac{2\cdot t\cdot t_1\cdot\left(a-t\right)^2\cdot\left(b-t_1\right)^2}{a\cdot t+b\cdot t_1-t^2-t_1^2}

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 (average) dimension $ a $

$$τ_{average-a}=\cfrac{10^3\cdot T}{2\cdot t\cdot\left(a-t\right)\cdot\left(b-t_1\right)}$$
$τ_{average-a}=\cfrac{10^3\cdot T}{2\cdot t\cdot\left(a-t\right)\cdot\left(b-t_1\right)}$
Equations in LaTeX code
τ_{average-a}=\cfrac{10^3\cdot T}{2\cdot t\cdot\left(a-t\right)\cdot\left(b-t_1\right)}

Torsion stress (average) dimension $ b $

$$τ_{average-b}=\cfrac{10^3\cdot T}{2\cdot t_1\cdot\left(a-t\right)\cdot\left(b-t_1\right)}$$
$τ_{average-b}=\cfrac{10^3\cdot T}{2\cdot t_1\cdot\left(a-t\right)\cdot\left(b-t_1\right)}$
Equations in LaTeX code
τ_{average-b}=\cfrac{10^3\cdot T}{2\cdot t_1\cdot\left(a-t\right)\cdot\left(b-t_1\right)}
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