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Square shoulder with fillet in a member of rectangular section for elastic stress, in-plane bending

Square shoulder with fillet in a member of rectangular section D h r L
Square shoulder with fillet in a member of rectangular section

Values for calculation

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

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
$$C_1=1.007+1.000\cdot\sqrt{h/r}-0.031\cdot h/r$$
$C_1=1.007+1.000\cdot\sqrt{h/r}-0.031\cdot h/r$
Equations in LaTeX code
C_1=1.007+1.000\cdot\sqrt{h/r}-0.031\cdot h/r
$\text{else}$
$\text{else}$
Equations in LaTeX code
\text{else}
$$C_1=1.042+0.982\cdot\sqrt{h/r}-0.036\cdot h/r$$
$C_1=1.042+0.982\cdot\sqrt{h/r}-0.036\cdot h/r$
Equations in LaTeX code
C_1=1.042+0.982\cdot\sqrt{h/r}-0.036\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
$$C_2=-0.270-2.404\cdot\sqrt{h/r}+0.749\cdot h/r$$
$C_2=-0.270-2.404\cdot\sqrt{h/r}+0.749\cdot h/r$
Equations in LaTeX code
C_2=-0.270-2.404\cdot\sqrt{h/r}+0.749\cdot h/r
$\text{else}$
$\text{else}$
Equations in LaTeX code
\text{else}
$$C_2=-3.599+1.619\cdot\sqrt{h/r}-0.431\cdot h/r$$
$C_2=-3.599+1.619\cdot\sqrt{h/r}-0.431\cdot h/r$
Equations in LaTeX code
C_2=-3.599+1.619\cdot\sqrt{h/r}-0.431\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
$$C_3=0.677+1.133\cdot\sqrt{h/r}-0.904\cdot h/r$$
$C_3=0.677+1.133\cdot\sqrt{h/r}-0.904\cdot h/r$
Equations in LaTeX code
C_3=0.677+1.133\cdot\sqrt{h/r}-0.904\cdot h/r
$\text{else}$
$\text{else}$
Equations in LaTeX code
\text{else}
$$C_3=6.084-5.607\cdot\sqrt{h/r}+1.158\cdot h/r$$
$C_3=6.084-5.607\cdot\sqrt{h/r}+1.158\cdot h/r$
Equations in LaTeX code
C_3=6.084-5.607\cdot\sqrt{h/r}+1.158\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
$$C_4=-0.414+0.271\cdot\sqrt{h/r}+0.186\cdot h/r$$
$C_4=-0.414+0.271\cdot\sqrt{h/r}+0.186\cdot h/r$
Equations in LaTeX code
C_4=-0.414+0.271\cdot\sqrt{h/r}+0.186\cdot h/r
$\text{else}$
$\text{else}$
Equations in LaTeX code
\text{else}
$$C_4=-2.527+3.006\cdot\sqrt{h/r}-0.691\cdot h/r$$
$C_4=-2.527+3.006\cdot\sqrt{h/r}-0.691\cdot h/r$
Equations in LaTeX code
C_4=-2.527+3.006\cdot\sqrt{h/r}-0.691\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

$$0.1 \le h/r \le 20$$
$0.1 \le h/r \le 20$
Equations in LaTeX code
0.1 \le h/r \le 20
$$\cfrac{L}{D} > \cfrac{0.8}{\left[r/\left(D-2\cdot h\right)\right]^{1/4}}$$
$\cfrac{L}{D} > \cfrac{0.8}{\left[r/\left(D-2\cdot h\right)\right]^{1/4}}$
Equations in LaTeX code
\cfrac{L}{D} > \cfrac{0.8}{\left[r/\left(D-2\cdot h\right)\right]^{1/4}}
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