# Two V-notches in a member of rectangular section for elastic stress, axial tension

## Values for calculation

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

## Calculation

### Coefficient $C_1$

$\text{if }\ 0.1\le h/r\le 2.0$
$$C_1=0.850+2.628\cdot\sqrt{h/r}-0.413\cdot h/r$$
$\text{else}$
$$C_1=0.833+2.069\cdot\sqrt{h/r}-0.009\cdot h/r$$

### Coefficient $C_2$

$\text{if }\ 0.1\le h/r\le 2.0$
$$C_2=-1.119-4.826\cdot\sqrt{h/r}+2.575\cdot h/r$$
$\text{else}$
$$C_2=2.732-4.157\cdot\sqrt{h/r}+0.176\cdot h/r$$

### Coefficient $C_3$

$\text{if }\ 0.1\le h/r\le 2.0$
$$C_3=3.563-0.514\cdot\sqrt{h/r}-2.402\cdot h/r$$
$\text{else}$
$$C_3=-8.859+5.327\cdot\sqrt{h/r}-0.320\cdot h/r$$

### Coefficient $C_4$

$\text{if }\ 0.1\le h/r\le 2.0$
$$C_4=-2.294+2.713\cdot\sqrt{h/r}+0.240\cdot h/r$$
$\text{else}$
$$C_4=6.294-3.239\cdot\sqrt{h/r}+0.154\cdot h/r$$

### The elastic stress concentration factor for a U-notch

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

### The elastic stress concentration factor

$\text{if }\ \cfrac{2\cdot h}{D}= 0.4$
$$K_t=\min\left\{1.11\cdot K_{tu}-\left[0.0275+0.000145\cdot θ+0.0164\cdot\left(\cfrac{θ}{120}\right)^8\right]\cdot K_{tu}^2, K_{tu}\right\}$$
$\text{else if }\ \cfrac{2\cdot h}{D}= \cfrac{2}{3}$
$$K_t=\min\left\{1.11\cdot K_{tu}-\left[0.0275+0.00042\cdot θ+0.0075\cdot\left(\cfrac{θ}{120}\right)^8\right]\cdot K_{tu}^2, K_{tu}\right\}$$
$\text{else}$
$$K_t=K_{tu}$$

## Requirements

$$θ \le 120$$