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U-notch in a circular shaft for elastic stress, axial tension

U-notch in a circular shaft D h r
U-notch in a circular shaft

Values for calculation

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

Calculation

Coefficient $ C_1 $

$\text{if }\ 0.25\le h/r\le 2.0$
$\text{if }\ 0.25\le h/r\le 2.0$
Equations in LaTeX code
\text{if }\ 0.25\le h/r\le 2.0
$$C_1=0.455+3.354\cdot\sqrt{h/r}-0.769\cdot h/r$$
$C_1=0.455+3.354\cdot\sqrt{h/r}-0.769\cdot h/r$
Equations in LaTeX code
C_1=0.455+3.354\cdot\sqrt{h/r}-0.769\cdot h/r
$\text{else}$
$\text{else}$
Equations in LaTeX code
\text{else}
$$C_1=0.935+1.922\cdot\sqrt{h/r}+0.004\cdot h/r$$
$C_1=0.935+1.922\cdot\sqrt{h/r}+0.004\cdot h/r$
Equations in LaTeX code
C_1=0.935+1.922\cdot\sqrt{h/r}+0.004\cdot h/r

Coefficient $ C_2 $

$\text{if }\ 0.25\le h/r\le 2.0$
$\text{if }\ 0.25\le h/r\le 2.0$
Equations in LaTeX code
\text{if }\ 0.25\le h/r\le 2.0
$$C_2=3.129-15.955\cdot\sqrt{h/r}+7.404\cdot h/r$$
$C_2=3.129-15.955\cdot\sqrt{h/r}+7.404\cdot h/r$
Equations in LaTeX code
C_2=3.129-15.955\cdot\sqrt{h/r}+7.404\cdot h/r
$\text{else}$
$\text{else}$
Equations in LaTeX code
\text{else}
$$C_2=0.537-3.708\cdot\sqrt{h/r}+0.040\cdot h/r$$
$C_2=0.537-3.708\cdot\sqrt{h/r}+0.040\cdot h/r$
Equations in LaTeX code
C_2=0.537-3.708\cdot\sqrt{h/r}+0.040\cdot h/r

Coefficient $ C_3 $

$\text{if }\ 0.25\le h/r\le 2.0$
$\text{if }\ 0.25\le h/r\le 2.0$
Equations in LaTeX code
\text{if }\ 0.25\le h/r\le 2.0
$$C_3=-6.909+29.286\cdot\sqrt{h/r}-16.104\cdot h/r$$
$C_3=-6.909+29.286\cdot\sqrt{h/r}-16.104\cdot h/r$
Equations in LaTeX code
C_3=-6.909+29.286\cdot\sqrt{h/r}-16.104\cdot h/r
$\text{else}$
$\text{else}$
Equations in LaTeX code
\text{else}
$$C_3=-2.538+3.438\cdot\sqrt{h/r}-0.012\cdot h/r$$
$C_3=-2.538+3.438\cdot\sqrt{h/r}-0.012\cdot h/r$
Equations in LaTeX code
C_3=-2.538+3.438\cdot\sqrt{h/r}-0.012\cdot h/r

Coefficient $ C_4 $

$\text{if }\ 0.25\le h/r\le 2.0$
$\text{if }\ 0.25\le h/r\le 2.0$
Equations in LaTeX code
\text{if }\ 0.25\le h/r\le 2.0
$$C_4=4.325-16.685\cdot\sqrt{h/r}+9.469\cdot h/r$$
$C_4=4.325-16.685\cdot\sqrt{h/r}+9.469\cdot h/r$
Equations in LaTeX code
C_4=4.325-16.685\cdot\sqrt{h/r}+9.469\cdot h/r
$\text{else}$
$\text{else}$
Equations in LaTeX code
\text{else}
$$C_4=2.066-1.652\cdot\sqrt{h/r}-0.031\cdot h/r$$
$C_4=2.066-1.652\cdot\sqrt{h/r}-0.031\cdot h/r$
Equations in LaTeX code
C_4=2.066-1.652\cdot\sqrt{h/r}-0.031\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

$$0.25 \le h/r \le 50$$
$0.25 \le h/r \le 50$
Equations in LaTeX code
0.25 \le h/r \le 50
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