# Bending of a flat beam with opposite U notches

## Values for calculation

$M$ $\mathrm{Nm}$
$r$ $\mathrm{mm}$
$t$ $\mathrm{mm}$
$H$ $\mathrm{mm}$
$h$ $\mathrm{mm}$

## Calculation

### Coefficient $C_1$

$\text{if }\ 0.1\le t/r\le 2.0$
$$C_1=1.024+2.092\cdot\sqrt{t/r}-0.051\cdot t/r$$
$\text{else}$
$$C_1=1.113+1.957\cdot\sqrt{t/r}$$

### Coefficient $C_2$

$\text{if }\ 0.1\le t/r\le 2.0$
$$C_2=-0.630-7.194\cdot\sqrt{t/r}+1.288\cdot t/r$$
$\text{else}$
$$C_2=-2.579-4.017\cdot\sqrt{t/r}-0.013\cdot t/r$$

### Coefficient $C_3$

$\text{if }\ 0.1\le t/r\le 2.0$
$$C_3=2.117+8.574\cdot\sqrt{t/r}-2.160\cdot t/r$$
$\text{else}$
$$C_3=4.100+3.922\cdot\sqrt{t/r}+0.083\cdot t/r$$

### Coefficient $C_4$

$\text{if }\ 0.1\le t/r\le 2.0$
$$C_4=-1.420-3.494\cdot\sqrt{t/r}+0.932\cdot t/r$$
$\text{else}$
$$C_4=-1.528-1.893\cdot\sqrt{t/r}-0.066\cdot t/r$$

### Stress concentration factor with the nominal stress based on net area

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

### Nominal or reference normal stress

$$σ_{nom}=\cfrac{6\cdot M\cdot 10^3}{h\cdot\left(H-2\cdot t\right)^2}$$

### Maximum normal stress

$$σ_{max}=K_{tn}\cdot σ_{nom}$$

### Normal stress

$$σ=\cfrac{6\cdot M\cdot 10^3}{H^2\cdot h}$$

### Stress concentration factor with the nominal stress based on gross area

$$K_{tg}=\cfrac{σ_{max}}{σ}$$