# V-notch in a circular shaft for elastic stress, torsion

## Values for calculation

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

## 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 for a U-notch

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

### The elastic stress concentration factor

$$K_t=\min\left\{K_{tu}, 1.065\cdot K_{tu}-\left[0.022+0.137\cdot\left(\cfrac{θ}{135}\right)^2\right]\cdot\left(K_{tu}-1\right)\cdot K_{tu}\right\}$$

## Requirements

$$\cfrac{r}{D-2\cdot h} \le 0.01$$$$θ \le 135$$