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Elliptical or U-shaped notch in a semi-infinite thin element in tension

Elliptical notch t r σ σ σ max
Elliptical notch
U-shaped notch t r σ σ σ max
U-shaped notch

Values for calculation

$ \{r\in\mathbb{R}\mid r>0\} $
This set includes all real numbers that are greater than zero. Therefore, it contains only positive numbers. Zero and negative numbers are not included in this set.
$ r $ $ \mathrm{mm} $
$ \{t\in\mathbb{R}\mid t>0\} $
This set includes all real numbers that are greater than zero. Therefore, it contains only positive numbers. Zero and negative numbers are not included in this set.
$ t $ $ \mathrm{mm} $
$ \{σ\in\mathbb{R}\mid σ>0\} $
This set includes all real numbers that are greater than zero. Therefore, it contains only positive numbers. Zero and negative numbers are not included in this set.
$ σ $ $ \mathrm{MPa} $

Calculation

Stress concentration factor with the nominal stress based on gross area

$$K_{tg}=0.855+2.21\cdot\sqrt{t/r}$$
$K_{tg}=0.855+2.21\cdot\sqrt{t/r}$
Equations in LaTeX code
K_{tg}=0.855+2.21\cdot\sqrt{t/r}

Maximum normal stress

$$σ_{max}=K_{tg}\cdot σ$$
$σ_{max}=K_{tg}\cdot σ$
Equations in LaTeX code
σ_{max}=K_{tg}\cdot σ
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