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U-notch in a circular shaft for elastic stress, torsion

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
$$C_1=1.245+0.264\cdot\sqrt{h/r}+0.491\cdot h/r$$
$C_1=1.245+0.264\cdot\sqrt{h/r}+0.491\cdot h/r$
Equations in LaTeX code
C_1=1.245+0.264\cdot\sqrt{h/r}+0.491\cdot h/r
$\text{else}$
$\text{else}$
Equations in LaTeX code
\text{else}
$$C_1=1.651+0.614\cdot\sqrt{h/r}+0.040\cdot h/r$$
$C_1=1.651+0.614\cdot\sqrt{h/r}+0.040\cdot h/r$
Equations in LaTeX code
C_1=1.651+0.614\cdot\sqrt{h/r}+0.040\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
$$C_2=-3.030+3.269\cdot\sqrt{h/r}-3.633\cdot h/r$$
$C_2=-3.030+3.269\cdot\sqrt{h/r}-3.633\cdot h/r$
Equations in LaTeX code
C_2=-3.030+3.269\cdot\sqrt{h/r}-3.633\cdot h/r
$\text{else}$
$\text{else}$
Equations in LaTeX code
\text{else}
$$C_2=-4.794-0.314\cdot\sqrt{h/r}-0.217\cdot h/r$$
$C_2=-4.794-0.314\cdot\sqrt{h/r}-0.217\cdot h/r$
Equations in LaTeX code
C_2=-4.794-0.314\cdot\sqrt{h/r}-0.217\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
$$C_3=7.199-11.286\cdot\sqrt{h/r}+8.318\cdot h/r$$
$C_3=7.199-11.286\cdot\sqrt{h/r}+8.318\cdot h/r$
Equations in LaTeX code
C_3=7.199-11.286\cdot\sqrt{h/r}+8.318\cdot h/r
$\text{else}$
$\text{else}$
Equations in LaTeX code
\text{else}
$$C_3=8.457-0.962\cdot\sqrt{h/r}+0.389\cdot h/r$$
$C_3=8.457-0.962\cdot\sqrt{h/r}+0.389\cdot h/r$
Equations in LaTeX code
C_3=8.457-0.962\cdot\sqrt{h/r}+0.389\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
$$C_4=-4.414+7.753\cdot\sqrt{h/r}-5.176\cdot h/r$$
$C_4=-4.414+7.753\cdot\sqrt{h/r}-5.176\cdot h/r$
Equations in LaTeX code
C_4=-4.414+7.753\cdot\sqrt{h/r}-5.176\cdot h/r
$\text{else}$
$\text{else}$
Equations in LaTeX code
\text{else}
$$C_4=-4.314+0.662\cdot\sqrt{h/r}-0.212\cdot h/r$$
$C_4=-4.314+0.662\cdot\sqrt{h/r}-0.212\cdot h/r$
Equations in LaTeX code
C_4=-4.314+0.662\cdot\sqrt{h/r}-0.212\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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