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Square shoulder with fillet in circular shaft for elastic stress, bending

Square shoulder with fillet in circular shaft D h r
Square shoulder with fillet in 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
$$C_1=0.927+1.149\cdot\sqrt{h/r}-0.086\cdot h/r$$
$C_1=0.927+1.149\cdot\sqrt{h/r}-0.086\cdot h/r$
Equations in LaTeX code
C_1=0.927+1.149\cdot\sqrt{h/r}-0.086\cdot h/r
$\text{else}$
$\text{else}$
Equations in LaTeX code
\text{else}
$$C_1=1.225+0.831\cdot\sqrt{h/r}-0.010\cdot h/r$$
$C_1=1.225+0.831\cdot\sqrt{h/r}-0.010\cdot h/r$
Equations in LaTeX code
C_1=1.225+0.831\cdot\sqrt{h/r}-0.010\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
$$C_2=0.015-3.281\cdot\sqrt{h/r}+0.837\cdot h/r$$
$C_2=0.015-3.281\cdot\sqrt{h/r}+0.837\cdot h/r$
Equations in LaTeX code
C_2=0.015-3.281\cdot\sqrt{h/r}+0.837\cdot h/r
$\text{else}$
$\text{else}$
Equations in LaTeX code
\text{else}
$$C_2=-3.790+0.958\cdot\sqrt{h/r}-0.257\cdot h/r$$
$C_2=-3.790+0.958\cdot\sqrt{h/r}-0.257\cdot h/r$
Equations in LaTeX code
C_2=-3.790+0.958\cdot\sqrt{h/r}-0.257\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
$$C_3=0.847+1.716\cdot\sqrt{h/r}-0.506\cdot h/r$$
$C_3=0.847+1.716\cdot\sqrt{h/r}-0.506\cdot h/r$
Equations in LaTeX code
C_3=0.847+1.716\cdot\sqrt{h/r}-0.506\cdot h/r
$\text{else}$
$\text{else}$
Equations in LaTeX code
\text{else}
$$C_3=7.374-4.834\cdot\sqrt{h/r}+0.862\cdot h/r$$
$C_3=7.374-4.834\cdot\sqrt{h/r}+0.862\cdot h/r$
Equations in LaTeX code
C_3=7.374-4.834\cdot\sqrt{h/r}+0.862\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
$$C_4=-0.790+0.417\cdot\sqrt{h/r}-0.246\cdot h/r$$
$C_4=-0.790+0.417\cdot\sqrt{h/r}-0.246\cdot h/r$
Equations in LaTeX code
C_4=-0.790+0.417\cdot\sqrt{h/r}-0.246\cdot h/r
$\text{else}$
$\text{else}$
Equations in LaTeX code
\text{else}
$$C_4=-3.809+3.046\cdot\sqrt{h/r}-0.595\cdot h/r$$
$C_4=-3.809+3.046\cdot\sqrt{h/r}-0.595\cdot h/r$
Equations in LaTeX code
C_4=-3.809+3.046\cdot\sqrt{h/r}-0.595\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

$$0.25 \le h/r \le 20$$
$0.25 \le h/r \le 20$
Equations in LaTeX code
0.25 \le h/r \le 20
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