# Filleted bars in bending

## Values for calculation

$M$ $\mathrm{Nm}$
$H$ $\mathrm{mm}$
$h$ $\mathrm{mm}$
$d$ $\mathrm{mm}$
$r$ $\mathrm{mm}$
$L$ $\mathrm{mm}$

## Calculation

### Depth of groove, notch

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

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

### Coefficient $C_1$

$\text{if }\ 0.1\le t/r\le 2.0$
$$C_1=1.006+0.967\cdot\sqrt{t/r}+0.013\cdot t/r$$
$\text{else}$
$$C_1=1.058+1.002\cdot\sqrt{t/r}-0.038\cdot t/r$$

### Coefficient $C_2$

$\text{if }\ 0.1\le t/r\le 2.0$
$$C_2=-0.270-2.372\cdot\sqrt{t/r}+0.708\cdot t/r$$
$\text{else}$
$$C_2=-3.652+1.639\cdot\sqrt{t/r}-0.436\cdot t/r$$

### Coefficient $C_3$

$\text{if }\ 0.1\le t/r\le 2.0$
$$C_3=0.662+1.157\cdot\sqrt{t/r}-0.908\cdot t/r$$
$\text{else}$
$$C_3=6.170-5.687\cdot\sqrt{t/r}+1.175\cdot t/r$$

### Coefficient $C_4$

$\text{if }\ 0.1\le t/r\le 2.0$
$$C_4=-0.405+0.249\cdot\sqrt{t/r}-0.200\cdot t/r$$
$\text{else}$
$$C_4=-2.558+3.046\cdot\sqrt{t/r}-0.701\cdot t/r$$

### Stress concentration factor

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

### Nominal or reference normal stress

$$σ_{nom}=\cfrac{6\cdot M\cdot 10^3}{h\cdot d^2}$$

### Maximum normal stress

$$σ_{max}=K_t\cdot σ_{nom}$$