# Trapezoid

## Values for calculation

## Calculation

### Profile area

### Coefficient $ s $

### Coefficient $ V_L $

### Coefficient $ V_s $

### Coefficient $ C $

### Polar moment of inertia

### Angle of twist

### Torsion stress

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$$A=\cfrac{m+n}{2}\cdot b$$

$$s=\cfrac{m-n}{b}$$

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

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

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

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

$$θ=\cfrac{T\cdot 10^3\cdot L}{K\cdot G}$$

$$τ_{max}=\cfrac{10^3\cdot T}{K}\cdot C$$