# 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 $C_1$

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

### Coefficient $C_2$

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

### Coefficient $C_3$

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

### Coefficient $C_4$

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

### Stress concentration factor with the nominal stress based on gross area

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

### Normal stress

$$σ=\cfrac{p\cdot R}{2\cdot h}$$

### Maximum normal stress

$$σ_{max}=K_{tg}\cdot σ$$