U-notch in a circular shaft for elastic stress, torsion

Values for calculation

$D$ $\mathrm{mm}$
$h$ $\mathrm{mm}$
$r$ $\mathrm{mm}$

Calculation

Coefficient $C_1$

$\text{if }\ 0.25\le h/r\le 2.0$
$$C_1=1.245+0.264\cdot\sqrt{h/r}+0.491\cdot h/r$$
$\text{else}$
$$C_1=1.651+0.614\cdot\sqrt{h/r}+0.040\cdot h/r$$

Coefficient $C_2$

$\text{if }\ 0.25\le h/r\le 2.0$
$$C_2=-3.030+3.269\cdot\sqrt{h/r}-3.633\cdot h/r$$
$\text{else}$
$$C_2=-4.794-0.314\cdot\sqrt{h/r}-0.217\cdot h/r$$

Coefficient $C_3$

$\text{if }\ 0.25\le h/r\le 2.0$
$$C_3=7.199-11.286\cdot\sqrt{h/r}+8.318\cdot h/r$$
$\text{else}$
$$C_3=8.457-0.962\cdot\sqrt{h/r}+0.389\cdot h/r$$

Coefficient $C_4$

$\text{if }\ 0.25\le h/r\le 2.0$
$$C_4=-4.414+7.753\cdot\sqrt{h/r}-5.176\cdot h/r$$
$\text{else}$
$$C_4=-4.314+0.662\cdot\sqrt{h/r}-0.212\cdot h/r$$

The elastic stress concentration factor

$$K_t=C_1+C_2\cdot\left(\cfrac{2\cdot h}{D}\right)+C_3\cdot\left(\cfrac{2\cdot h}{D}\right)^2+C_4\cdot\left(\cfrac{2\cdot h}{D}\right)^3$$

Requirements

$$0.25 \le h/r \le 50$$