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Pressurized spherical shell with elliptical hole

Pressurized spherical shell with elliptical hole R h p 2 b 2a
Pressurized spherical shell with elliptical hole

Values for calculation

$p$ $\mathrm{MPa}$
$R$ $\mathrm{mm}$
$a$ $\mathrm{mm}$
$b$ $\mathrm{mm}$
$h$ $\mathrm{mm}$

Calculation

Coefficient $ C_1 $

$$C_1=-1.9869+5.3403\cdot\left(\cfrac{b}{a}\right)-1.556\cdot\left(\cfrac{b}{a}\right)^2$$
$C_1=-1.9869+5.3403\cdot\left(\cfrac{b}{a}\right)-1.556\cdot\left(\cfrac{b}{a}\right)^2$
Equations in LaTeX code
C_1=-1.9869+5.3403\cdot\left(\cfrac{b}{a}\right)-1.556\cdot\left(\cfrac{b}{a}\right)^2

Coefficient $ C_2 $

$$C_2=5.4355-6.75\cdot\left(\cfrac{b}{a}\right)+4.993\cdot\left(\cfrac{b}{a}\right)^2$$
$C_2=5.4355-6.75\cdot\left(\cfrac{b}{a}\right)+4.993\cdot\left(\cfrac{b}{a}\right)^2$
Equations in LaTeX code
C_2=5.4355-6.75\cdot\left(\cfrac{b}{a}\right)+4.993\cdot\left(\cfrac{b}{a}\right)^2

Coefficient $ C_3 $

$$C_3=-7.8057+13.2508\cdot\left(\cfrac{b}{a}\right)-5.8544\cdot\left(\cfrac{b}{a}\right)^2$$
$C_3=-7.8057+13.2508\cdot\left(\cfrac{b}{a}\right)-5.8544\cdot\left(\cfrac{b}{a}\right)^2$
Equations in LaTeX code
C_3=-7.8057+13.2508\cdot\left(\cfrac{b}{a}\right)-5.8544\cdot\left(\cfrac{b}{a}\right)^2

Coefficient $ C_4 $

$$C_4=1.9069-3.3306\cdot\left(\cfrac{b}{a}\right)+1.4238\cdot\left(\cfrac{b}{a}\right)^2$$
$C_4=1.9069-3.3306\cdot\left(\cfrac{b}{a}\right)+1.4238\cdot\left(\cfrac{b}{a}\right)^2$
Equations in LaTeX code
C_4=1.9069-3.3306\cdot\left(\cfrac{b}{a}\right)+1.4238\cdot\left(\cfrac{b}{a}\right)^2

Stress concentration factor with the nominal stress based on gross area

$$K_{tg}=C_1+C_2\cdot\left(\cfrac{a}{R}\cdot\sqrt{\cfrac{R}{h}}\right)+C_3\cdot\left(\cfrac{a}{R}\cdot\sqrt{\cfrac{R}{h}}\right)^2+C_4\cdot\left(\cfrac{a}{R}\cdot\sqrt{\cfrac{R}{h}}\right)^3$$
$K_{tg}=C_1+C_2\cdot\left(\cfrac{a}{R}\cdot\sqrt{\cfrac{R}{h}}\right)+C_3\cdot\left(\cfrac{a}{R}\cdot\sqrt{\cfrac{R}{h}}\right)^2+C_4\cdot\left(\cfrac{a}{R}\cdot\sqrt{\cfrac{R}{h}}\right)^3$
Equations in LaTeX code
K_{tg}=C_1+C_2\cdot\left(\cfrac{a}{R}\cdot\sqrt{\cfrac{R}{h}}\right)+C_3\cdot\left(\cfrac{a}{R}\cdot\sqrt{\cfrac{R}{h}}\right)^2+C_4\cdot\left(\cfrac{a}{R}\cdot\sqrt{\cfrac{R}{h}}\right)^3

Normal stress

$$σ=\cfrac{p\cdot R}{2\cdot h}$$
$σ=\cfrac{p\cdot R}{2\cdot h}$
Equations in LaTeX code
σ=\cfrac{p\cdot R}{2\cdot 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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