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Circular hole in a cylindrical shell in tension

Circular hole in a cylindrical shell in tension d σ σ R h
Circular hole in a cylindrical shell in tension

Values for calculation

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

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)

Coefficient $ C_1 $

$$C_1=2.9127-3.4614\cdot\left(\cfrac{h}{R}\right)+277.38\cdot\left(\cfrac{h}{R}\right)^2$$
$C_1=2.9127-3.4614\cdot\left(\cfrac{h}{R}\right)+277.38\cdot\left(\cfrac{h}{R}\right)^2$
Equations in LaTeX code
C_1=2.9127-3.4614\cdot\left(\cfrac{h}{R}\right)+277.38\cdot\left(\cfrac{h}{R}\right)^2

Coefficient $ C_2 $

$$C_2=1.3633-1.9581\cdot\left(\cfrac{h}{R}\right)-1124.24\cdot\left(\cfrac{h}{R}\right)^2$$
$C_2=1.3633-1.9581\cdot\left(\cfrac{h}{R}\right)-1124.24\cdot\left(\cfrac{h}{R}\right)^2$
Equations in LaTeX code
C_2=1.3633-1.9581\cdot\left(\cfrac{h}{R}\right)-1124.24\cdot\left(\cfrac{h}{R}\right)^2

Coefficient $ C_3 $

$$C_3=1.3365-174.54\cdot\left(\cfrac{h}{R}\right)+21452.3\cdot\left(\cfrac{h}{R}\right)^2-683125\cdot\left(\cfrac{h}{R}\right)^3$$
$C_3=1.3365-174.54\cdot\left(\cfrac{h}{R}\right)+21452.3\cdot\left(\cfrac{h}{R}\right)^2-683125\cdot\left(\cfrac{h}{R}\right)^3$
Equations in LaTeX code
C_3=1.3365-174.54\cdot\left(\cfrac{h}{R}\right)+21452.3\cdot\left(\cfrac{h}{R}\right)^2-683125\cdot\left(\cfrac{h}{R}\right)^3

Coefficient $ C_4 $

$$C_4=-0.5115+13.918\cdot\left(\cfrac{h}{R}\right)-335.338\cdot\left(\cfrac{h}{R}\right)^2$$
$C_4=-0.5115+13.918\cdot\left(\cfrac{h}{R}\right)-335.338\cdot\left(\cfrac{h}{R}\right)^2$
Equations in LaTeX code
C_4=-0.5115+13.918\cdot\left(\cfrac{h}{R}\right)-335.338\cdot\left(\cfrac{h}{R}\right)^2

Coefficient $ C_5 $

$$C_5=0.06154-1.707\cdot\left(\cfrac{h}{R}\right)+34.614\cdot\left(\cfrac{h}{R}\right)^2$$
$C_5=0.06154-1.707\cdot\left(\cfrac{h}{R}\right)+34.614\cdot\left(\cfrac{h}{R}\right)^2$
Equations in LaTeX code
C_5=0.06154-1.707\cdot\left(\cfrac{h}{R}\right)+34.614\cdot\left(\cfrac{h}{R}\right)^2

Stress concentration factor with the nominal stress based on net area

$$K_{tn}=C_1+C_2\cdot β+C_3\cdot β^2+C_4\cdot β^3+C_5\cdot β^4$$
$K_{tn}=C_1+C_2\cdot β+C_3\cdot β^2+C_4\cdot β^3+C_5\cdot β^4$
Equations in LaTeX code
K_{tn}=C_1+C_2\cdot β+C_3\cdot β^2+C_4\cdot β^3+C_5\cdot β^4

Stress concentration factor with the nominal stress based on gross area

$$K_{tg}=\cfrac{K_{tn}}{1-\cfrac{d}{2\cdot π\cdot R}}$$
$K_{tg}=\cfrac{K_{tn}}{1-\cfrac{d}{2\cdot π\cdot R}}$
Equations in LaTeX code
K_{tg}=\cfrac{K_{tn}}{1-\cfrac{d}{2\cdot π\cdot 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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