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One U-notch in a member of rectangula of rectangular section for elastic stress, in-plane bending

One_U-notch_in_a_member_of_rectangular_section
One U-notch in a member of rectangular section

Values for calculation

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

Calculation

Coefficient $ C_1 $

$$C_1=0.721+2.394\cdot\sqrt{h/r}-0.127\cdot h/r$$

Coefficient $ C_2 $

$$C_2=-0.426-8.827\cdot\sqrt{h/r}+1.518\cdot h/r$$

Coefficient $ C_3 $

$$C_3=2.161+10.968\cdot\sqrt{h/r}-2.455\cdot h/r$$

Coefficient $ C_4 $

$$C_4=-1.456-4.535\cdot\sqrt{h/r}+1.064\cdot h/r$$

The elastic stress concentration factor

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

Requirements

$$0.5 \le h/r \le 4.0$$