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Circular hole in a cylindrical shell with internal pressure

Circular hole in a cylindrical shell with internal pressure d R h p
Circular hole in a cylindrical shell with internal pressure

Values for calculation

$p$ $\mathrm{MPa}$
$R$ $\mathrm{mm}$
$d$ $\mathrm{mm}$
$h$ $\mathrm{mm}$
$ν$

Calculation

Parameter $ β $

$$β=\cfrac{\sqrt[4]{3\cdot\left(1-ν^2\right)}}{2}\cdot\left(\cfrac{d}{2\cdot\sqrt{R\cdot h}}\right)$$
$β=\cfrac{\sqrt[4]{3\cdot\left(1-ν^2\right)}}{2}\cdot\left(\cfrac{d}{2\cdot\sqrt{R\cdot h}}\right)$
Equations in LaTeX code
β=\cfrac{\sqrt[4]{3\cdot\left(1-ν^2\right)}}{2}\cdot\left(\cfrac{d}{2\cdot\sqrt{R\cdot h}}\right)
$$0\le β\le 3.14$$
$0\le β\le 3.14$
Equations in LaTeX code
0\le β\le 3.14

Stress concentration factor with the nominal stress based on gross area

$\text{if }\ 0\le β\le 0.5$
$\text{if }\ 0\le β\le 0.5$
Equations in LaTeX code
\text{if }\ 0\le β\le 0.5
$$K_{tg}=2.601+0.9147\cdot β+2.5\cdot β^2+30.556\cdot β^3-41.667\cdot β^4$$
$K_{tg}=2.601+0.9147\cdot β+2.5\cdot β^2+30.556\cdot β^3-41.667\cdot β^4$
Equations in LaTeX code
K_{tg}=2.601+0.9147\cdot β+2.5\cdot β^2+30.556\cdot β^3-41.667\cdot β^4
$\text{else}$
$\text{else}$
Equations in LaTeX code
\text{else}
$$K_{tg}=1.392+7.394\cdot β-0.908\cdot β^2+0.4158\cdot β^3-0.06115\cdot β^4$$
$K_{tg}=1.392+7.394\cdot β-0.908\cdot β^2+0.4158\cdot β^3-0.06115\cdot β^4$
Equations in LaTeX code
K_{tg}=1.392+7.394\cdot β-0.908\cdot β^2+0.4158\cdot β^3-0.06115\cdot β^4

Normal stress

$$σ=\cfrac{p\cdot R}{h}$$
$σ=\cfrac{p\cdot R}{h}$
Equations in LaTeX code
σ=\cfrac{p\cdot R}{h}

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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