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

Two U-notches in a member of rectangular section D h r
Two U-notches in a member of rectangular section

Values for calculation

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

Calculation

Coefficient $ C_1 $

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

Coefficient $ C_2 $

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

Coefficient $ C_3 $

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

Coefficient $ C_4 $

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

The elastic stress concentration factor

$$K_t=C_1+C_2\cdot\left(\cfrac{2\cdot h}{D}\right)+C_3\cdot\left(\cfrac{2\cdot h}{D}\right)^2+C_4\cdot\left(\cfrac{2\cdot h}{D}\right)^3$$
$K_t=C_1+C_2\cdot\left(\cfrac{2\cdot h}{D}\right)+C_3\cdot\left(\cfrac{2\cdot h}{D}\right)^2+C_4\cdot\left(\cfrac{2\cdot h}{D}\right)^3$
Equations in LaTeX code
K_t=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

Requirements

$$0.1 \le h/r \le 50$$
$0.1 \le h/r \le 50$
Equations in LaTeX code
0.1 \le h/r \le 50
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