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Trapezoid

Trapezoid m b n
Trapezoid

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} $
$ \{m\in\mathbb{R}\mid m>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.
$ m $ $ \mathrm{mm} $
$ \{n\in\mathbb{R}\mid n>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.
$ n $ $ \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} $
$ \{D\in\mathbb{R}\mid D>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.
$ D $ $ \mathrm{mm} $
$ \{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} $
$ \{φ\in\mathbb{R}\mid φ\geq0\} $
This set includes all real numbers that are greater than or equal to zero. Therefore, it contains all positive numbers and zero, but no negative numbers.
$ φ $ $ \mathrm{rad} $
$ \{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

Profile area

$$A=\cfrac{m+n}{2}\cdot b$$
$A=\cfrac{m+n}{2}\cdot b$
Equations in LaTeX code
A=\cfrac{m+n}{2}\cdot b

Coefficient $ s $

$$s=\cfrac{m-n}{b}$$
$s=\cfrac{m-n}{b}$
Equations in LaTeX code
s=\cfrac{m-n}{b}

Coefficient $ V_L $

$$V_L=0.10504-0.1\cdot s+0.0848\cdot s^2-0.06746\cdot s^3+0.0515\cdot s^4$$
$V_L=0.10504-0.1\cdot s+0.0848\cdot s^2-0.06746\cdot s^3+0.0515\cdot s^4$
Equations in LaTeX code
V_L=0.10504-0.1\cdot s+0.0848\cdot s^2-0.06746\cdot s^3+0.0515\cdot s^4

Coefficient $ V_s $

$$V_s=0.10504+0.1\cdot s+0.0848\cdot s^2+0.06746\cdot s^3+0.0515\cdot s^4$$
$V_s=0.10504+0.1\cdot s+0.0848\cdot s^2+0.06746\cdot s^3+0.0515\cdot s^4$
Equations in LaTeX code
V_s=0.10504+0.1\cdot s+0.0848\cdot s^2+0.06746\cdot s^3+0.0515\cdot s^4

Coefficient $ C $

$$C=\cfrac{D}{1+\cfrac{π^2\cdot D^4}{16\cdot A^2}}\cdot\left[1+\left[0.118\cdot\ln{\left(1+\cfrac{D}{2\cdot r}\right)+0.238\cdot\cfrac{D}{2\cdot r}}\right]\cdot\tanh\left(\cfrac{2\cdotφ}{π}\right)\right]$$
$C=\cfrac{D}{1+\cfrac{π^2\cdot D^4}{16\cdot A^2}}\cdot\left[1+\left[0.118\cdot\ln{\left(1+\cfrac{D}{2\cdot r}\right)+0.238\cdot\cfrac{D}{2\cdot r}}\right]\cdot\tanh\left(\cfrac{2\cdotφ}{π}\right)\right]$
Equations in LaTeX code
C=\cfrac{D}{1+\cfrac{π^2\cdot D^4}{16\cdot A^2}}\cdot\left[1+\left[0.118\cdot\ln{\left(1+\cfrac{D}{2\cdot r}\right)+0.238\cdot\cfrac{D}{2\cdot r}}\right]\cdot\tanh\left(\cfrac{2\cdotφ}{π}\right)\right]

Polar moment of inertia

$$K=\cfrac{1}{12}\cdot b\cdot\left(m+n\right)\cdot\left(m^2+n^2\right)-V_L\cdot m^4-V_s\cdot n^4$$
$K=\cfrac{1}{12}\cdot b\cdot\left(m+n\right)\cdot\left(m^2+n^2\right)-V_L\cdot m^4-V_s\cdot n^4$
Equations in LaTeX code
K=\cfrac{1}{12}\cdot b\cdot\left(m+n\right)\cdot\left(m^2+n^2\right)-V_L\cdot m^4-V_s\cdot n^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

$$τ_{max}=\cfrac{10^3\cdot T}{K}\cdot C$$
$τ_{max}=\cfrac{10^3\cdot T}{K}\cdot C$
Equations in LaTeX code
τ_{max}=\cfrac{10^3\cdot T}{K}\cdot C
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