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Cylinder on a flat plate

Cylinder on a flat plate D 2 L b P
Cylinder on a flat plate

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_2\in\mathbb{R}\mid D_2>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_2 $ $ \mathrm{mm} $
$ \{L\in\mathbb{R}\mid L>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.
$ L $ $ \mathrm{mm} $
$ \{ν_1\in\mathbb{R}\mid ν_1>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.
$ ν_1 $
$ \{ν_2\in\mathbb{R}\mid ν_2>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.
$ ν_2 $
$ \{E_1\in\mathbb{R}\mid E_1>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.
$ E_1 $ $ \mathrm{MPa} $
$ \{E_2\in\mathbb{R}\mid E_2>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.
$ E_2 $ $ \mathrm{MPa} $

Calculation

Load per unit length

$$p=P/L$$
$p=P/L$
Equations in LaTeX code
p=P/L

Material coefficient

$$C_E=\cfrac{1-ν_1^2}{E_1}+\cfrac{1-ν_2^2}{E_2}$$
$C_E=\cfrac{1-ν_1^2}{E_1}+\cfrac{1-ν_2^2}{E_2}$
Equations in LaTeX code
C_E=\cfrac{1-ν_1^2}{E_1}+\cfrac{1-ν_2^2}{E_2}

Dimensional coefficient

$$K_D=D_2$$
$K_D=D_2$
Equations in LaTeX code
K_D=D_2

Width of rectangular contact area

$$b=1.60\cdot\sqrt{p\cdot K_D\cdot C_E}$$
$b=1.60\cdot\sqrt{p\cdot K_D\cdot C_E}$
Equations in LaTeX code
b=1.60\cdot\sqrt{p\cdot K_D\cdot C_E}

Contact stress

$$σ_c=0.798\cdot\sqrt{\cfrac{p}{K_D\cdot C_E}}$$
$σ_c=0.798\cdot\sqrt{\cfrac{p}{K_D\cdot C_E}}$
Equations in LaTeX code
σ_c=0.798\cdot\sqrt{\cfrac{p}{K_D\cdot C_E}}
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