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Central circular hole in a member of rectangular cross section for elastic stress, axial tension

Central circular hole in a member of rectangular cross section r t D
Central circular hole in a member of rectangular cross section
Elastic stress, axial tension P P σ max
Elastic stress, axial tension

Values for calculation

$ \{P\in\mathbb{R}\mid P>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.
$ P $ $ \mathrm{N} $
$ \{D\in\mathbb{R}\mid D>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.
$ D $ $ \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} $
$ \{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} $

Calculation

The elastic stress concentration factor

$$K_t=3-3.13\cdot\left(\cfrac{2\cdot r}{D}\right)+3.66\cdot\left(\cfrac{2\cdot r}{D}\right)^2-1.53\cdot\left(\cfrac{2\cdot r}{D}\right)^3$$
$K_t=3-3.13\cdot\left(\cfrac{2\cdot r}{D}\right)+3.66\cdot\left(\cfrac{2\cdot r}{D}\right)^2-1.53\cdot\left(\cfrac{2\cdot r}{D}\right)^3$
Equations in LaTeX code
K_t=3-3.13\cdot\left(\cfrac{2\cdot r}{D}\right)+3.66\cdot\left(\cfrac{2\cdot r}{D}\right)^2-1.53\cdot\left(\cfrac{2\cdot r}{D}\right)^3

Nominal or reference normal stress

$$σ_{nom}=\cfrac{P}{t\cdot\left(D-2\cdot r\right)}$$
$σ_{nom}=\cfrac{P}{t\cdot\left(D-2\cdot r\right)}$
Equations in LaTeX code
σ_{nom}=\cfrac{P}{t\cdot\left(D-2\cdot r\right)}

Maximum normal stress

$$σ_{max}=K_t\cdot σ_{nom}$$
$σ_{max}=K_t\cdot σ_{nom}$
Equations in LaTeX code
σ_{max}=K_t\cdot σ_{nom}
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