Menu

Two U-notches in a member of rectangular section for elastic stress, in-plane bending

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 $

$\text{if }\ 0.25\le h/r\le 2.0$
$\text{if }\ 0.25\le h/r\le 2.0$
Equations in LaTeX code
\text{if }\ 0.25\le h/r\le 2.0
$$C_1=0.723+2.845\cdot\sqrt{h/r}-0.504\cdot h/r$$
$C_1=0.723+2.845\cdot\sqrt{h/r}-0.504\cdot h/r$
Equations in LaTeX code
C_1=0.723+2.845\cdot\sqrt{h/r}-0.504\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 $

$\text{if }\ 0.25\le h/r\le 2.0$
$\text{if }\ 0.25\le h/r\le 2.0$
Equations in LaTeX code
\text{if }\ 0.25\le h/r\le 2.0
$$C_2=-1.836-5.746\cdot\sqrt{h/r}+1.314\cdot h/r$$
$C_2=-1.836-5.746\cdot\sqrt{h/r}+1.314\cdot h/r$
Equations in LaTeX code
C_2=-1.836-5.746\cdot\sqrt{h/r}+1.314\cdot h/r
$\text{else}$
$\text{else}$
Equations in LaTeX code
\text{else}
$$C_2=0.024-5.383\cdot\sqrt{h/r}+0.126\cdot h/r$$
$C_2=0.024-5.383\cdot\sqrt{h/r}+0.126\cdot h/r$
Equations in LaTeX code
C_2=0.024-5.383\cdot\sqrt{h/r}+0.126\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
$$C_3=7.254-1.885\cdot\sqrt{h/r}+1.646\cdot h/r$$
$C_3=7.254-1.885\cdot\sqrt{h/r}+1.646\cdot h/r$
Equations in LaTeX code
C_3=7.254-1.885\cdot\sqrt{h/r}+1.646\cdot h/r
$\text{else}$
$\text{else}$
Equations in LaTeX code
\text{else}
$$C_3=-0.856+6.460\cdot\sqrt{h/r}-0.199\cdot h/r$$
$C_3=-0.856+6.460\cdot\sqrt{h/r}-0.199\cdot h/r$
Equations in LaTeX code
C_3=-0.856+6.460\cdot\sqrt{h/r}-0.199\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
$$C_4=-5.140+4.785\cdot\sqrt{h/r}-2.456\cdot h/r$$
$C_4=-5.140+4.785\cdot\sqrt{h/r}-2.456\cdot h/r$
Equations in LaTeX code
C_4=-5.140+4.785\cdot\sqrt{h/r}-2.456\cdot h/r
$\text{else}$
$\text{else}$
Equations in LaTeX code
\text{else}
$$C_4=0.999-3.146\cdot\sqrt{h/r}+0.082\cdot h/r$$
$C_4=0.999-3.146\cdot\sqrt{h/r}+0.082\cdot h/r$
Equations in LaTeX code
C_4=0.999-3.146\cdot\sqrt{h/r}+0.082\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
On this page