# U-notch in a circular shaft for elastic stress, bending

## Values for calculation

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

## Calculation

### Coefficient $C_1$

$\text{if }\ 0.25\le h/r\le 2.0$
$$C_1=0.455+3.354\cdot\sqrt{h/r}-0.769\cdot h/r$$
$\text{else}$
$$C_1=0.935+1.922\cdot\sqrt{h/r}+0.004\cdot h/r$$

### Coefficient $C_2$

$\text{if }\ 0.25\le h/r\le 2.0$
$$C_2=0.891-12.721\cdot\sqrt{h/r}+4.593\cdot h/r$$
$\text{else}$
$$C_2=-0.552-5.327\cdot\sqrt{h/r}+0.086\cdot h/r$$

### Coefficient $C_3$

$\text{if }\ 0.25\le h/r\le 2.0$
$$C_3=0.286+15.481\cdot\sqrt{h/r}-6.392\cdot h/r$$
$\text{else}$
$$C_3=0.754+6.281\cdot\sqrt{h/r}-0.121\cdot h/r$$

### Coefficient $C_4$

$\text{if }\ 0.25\le h/r\le 2.0$
$$C_4=-0.632-6.115\cdot\sqrt{h/r}+2.568\cdot h/r$$
$\text{else}$
$$C_4=-0.138-2.876\cdot\sqrt{h/r}+0.031\cdot h/r$$

### 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

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