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

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 $0.25\le h/r\le 2.0$$$C_1=0.723+2.845\cdot\sqrt{h/r}-0.504\cdot h/r$$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 $0.25\le h/r\le 2.0$$$C_2=-1.836-5.746\cdot\sqrt{h/r}+1.314\cdot h/r$$if $2.0\le h/r\le 50.0$$$C_2=0.024-5.383\cdot\sqrt{h/r}+0.126\cdot h/r$$

Coefficient $ C_3 $

if $0.25\le h/r\le 2.0$$$C_3=7.254-1.885\cdot\sqrt{h/r}+1.646\cdot h/r$$if $2.0\le h/r\le 50.0$$$C_3=-0.856+6.460\cdot\sqrt{h/r}-0.199\cdot h/r$$

Coefficient $ C_4 $

if $0.25\le h/r\le 2.0$$$C_4=-5.140+4.785\cdot\sqrt{h/r}-2.456\cdot h/r$$if $2.0\le h/r\le 50.0$$$C_4=0.999-3.146\cdot\sqrt{h/r}+0.082\cdot h/r$$

The elastic stress concentration factor

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

Requirements

$$0.25 \le h/r \le 50$$