# Stepped tension bar of circular cross section with shoulder fillet

## Values for calculation

$P$ $\mathrm{N}$
$D$ $\mathrm{mm}$
$d$ $\mathrm{mm}$
$r$ $\mathrm{mm}$

## Calculation

### Depth of groove, notch

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

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

### Coefficient $C_1$

$\text{if }\ 0.1\le t/r\le 2.0$
$$C_1=0.926+1.157\cdot\sqrt{t/r}-0.099\cdot t/r$$
$\text{else}$
$$C_1=1.200+0.860\cdot\sqrt{t/r}-0.022\cdot t/r$$

### Coefficient $C_2$

$\text{if }\ 0.1\le t/r\le 2.0$
$$C_2=0.012-3.036\cdot\sqrt{t/r}+0.961\cdot t/r$$
$\text{else}$
$$C_2=-1.805-0.346\cdot\sqrt{t/r}-0.038\cdot t/r$$

### Coefficient $C_3$

$\text{if }\ 0.1\le t/r\le 2.0$
$$C_3=-0.302+3.977\cdot\sqrt{t/r}-1.744\cdot t/r$$
$\text{else}$
$$C_3=2.198-0.486\cdot\sqrt{t/r}+0.165\cdot t/r$$

### Coefficient $C_4$

$\text{if }\ 0.1\le t/r\le 2.0$
$$C_4=0.365-2.098\cdot\sqrt{t/r}+0.878\cdot t/r$$
$\text{else}$
$$C_4=-0.593-0.028\cdot\sqrt{t/r}-0.106\cdot t/r$$

### 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

$$σ_{nom}=\cfrac{4\cdot P}{π\cdot d^2}$$

### Maximum normal stress

$$σ_{max}=K_t\cdot σ_{nom}$$