# Bending of a stepped bar of circular cross section with a shoulder fillet

## Values for calculation

$M$ $\mathrm{Nm}$
$D$ $\mathrm{mm}$
$d$ $\mathrm{mm}$
$r$ $\mathrm{mm}$

## Calculation

### Depth of groove, notch

$$t=\cfrac{D-d}{2}$$

$$0.1\le t/r\le 20$$

### Coefficient $C_1$

$\text{if }\ 0.1\le t/r\le 2.0$
$$C_1=0.947+1.206\cdot\sqrt{t/r}-0.131\cdot t/r$$
$\text{else}$
$$C_1=1.232+0.832\cdot\sqrt{t/r}-0.008\cdot t/r$$

### Coefficient $C_2$

$\text{if }\ 0.1\le t/r\le 2.0$
$$C_2=0.022-3.405\cdot\sqrt{t/r}+0.915\cdot t/r$$
$\text{else}$
$$C_2=-3.813+0.968\cdot\sqrt{t/r}-0.260\cdot t/r$$

### Coefficient $C_3$

$\text{if }\ 0.1\le t/r\le 2.0$
$$C_3=0.869+1.777\cdot\sqrt{t/r}-0.555\cdot t/r$$
$\text{else}$
$$C_3=7.423-4.868\cdot\sqrt{t/r}+0.869\cdot t/r$$

### Coefficient $C_4$

$\text{if }\ 0.1\le t/r\le 2.0$
$$C_4=-0.810+0.422\cdot\sqrt{t/r}-0.260\cdot t/r$$
$\text{else}$
$$C_4=-3.839+3.070\cdot\sqrt{t/r}-0.600\cdot t/r$$

### Stress concentration factor

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

### Nominal or reference normal stress

$$σ_{nom}=\cfrac{32\cdot M\cdot 10^3}{π\cdot d^3}$$

### Maximum normal stress

$$σ_{max}=K_t\cdot σ_{nom}$$