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Two U-notches in a member of rectangular section for elastic stress, axial tension

Two_U-notches_in_a_member_of_rectangular_section
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 $

if $0.1\le h/r\le 2.0$$$C_1=0.850+2.628\cdot\sqrt{h/r}-0.413\cdot h/r$$if $2.0\le h/r\le 50.0$$$C_1=0.833+2.069\cdot\sqrt{h/r}-0.009\cdot h/r$$

Coefficient $ C_2 $

if $0.1\le h/r\le 2.0$$$C_2=-1.119-4.826\cdot\sqrt{h/r}+2.575\cdot h/r$$if $2.0\le h/r\le 50.0$$$C_2=2.732-4.157\cdot\sqrt{h/r}+0.176\cdot h/r$$

Coefficient $ C_3 $

if $0.1\le h/r\le 2.0$$$C_3=3.563-0.514\cdot\sqrt{h/r}-2.402\cdot h/r$$if $2.0\le h/r\le 50.0$$$C_3=-8.859+5.327\cdot\sqrt{h/r}-0.320\cdot h/r$$

Coefficient $ C_4 $

if $0.1\le h/r\le 2.0$$$C_4=-2.294+2.713\cdot\sqrt{h/r}+0.240\cdot h/r$$if $2.0\le h/r\le 50.0$$$C_4=6.294-3.239\cdot\sqrt{h/r}+0.154\cdot h/r$$

The elastic stress concentration factor

$$K_t=C_1+C_2\cdot\left(\cfrac{2\cdot h}{D}\right)+C_3\cdot\left(\cfrac{2\cdot h}{D}\right)^2+C_4\cdot\left(\cfrac{2\cdot h}{D}\right)^3$$

Requirements

$$0.1 \le h/r \le 50$$