# Square shoulder with fillet in circular shaft for elastic stress, bending

## Values for calculation

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

## Calculation

### Coefficient $C_1$

$\text{if }\ 0.25\le h/r\le 2.0$
$$C_1=0.927+1.149\cdot\sqrt{h/r}-0.086\cdot h/r$$
$\text{else}$
$$C_1=1.225+0.831\cdot\sqrt{h/r}-0.010\cdot h/r$$

### Coefficient $C_2$

$\text{if }\ 0.25\le h/r\le 2.0$
$$C_2=0.015-3.281\cdot\sqrt{h/r}+0.837\cdot h/r$$
$\text{else}$
$$C_2=-3.790+0.958\cdot\sqrt{h/r}-0.257\cdot h/r$$

### Coefficient $C_3$

$\text{if }\ 0.25\le h/r\le 2.0$
$$C_3=0.847+1.716\cdot\sqrt{h/r}-0.506\cdot h/r$$
$\text{else}$
$$C_3=7.374-4.834\cdot\sqrt{h/r}+0.862\cdot h/r$$

### Coefficient $C_4$

$\text{if }\ 0.25\le h/r\le 2.0$
$$C_4=-0.790+0.417\cdot\sqrt{h/r}-0.246\cdot h/r$$
$\text{else}$
$$C_4=-3.809+3.046\cdot\sqrt{h/r}-0.595\cdot h/r$$

### 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

$$0.25 \le h/r \le 20$$