# Thickness of shells under internal pressure for Toriconical Heads

## Values for calculation

$E$
$P$ $\mathrm{MPa}$
$T$ $\mathrm{°C}$
$D$ $\mathrm{mm}$
$α$ $\mathrm{°}$
$t_s$ $\mathrm{mm}$
$r$ $\mathrm{mm}$
$S$ $\mathrm{MPa}$

## Calculation

### Inside diameter of the conical portion of a toriconical head at its point of tangency to the knuckle, measured perpendicular to the axis of the cone

$$D_i=D-2\cdot r\cdot\left(1-\cos(α)\right)$$

$$L=\cfrac{D_i}{2\cdot\cos(α)}$$

### Factor $M$

$$M=\cfrac{1}{4}\cdot\left(3+\sqrt{\cfrac{L}{r}}\right)$$

### Minimum required thickness of head after forming

$$t=\max\left(\cfrac{P\cdot D_i}{2\cdot\cos(α)\cdot\left(S\cdot E-0.6\cdot P\right)}, \cfrac{P\cdot L\cdot M}{2\cdot S\cdot E-0.2\cdot P}\right)$$$$t_s \geq t$$

### Requirements

$$r > 0.06\cdot D$$$$r > 3\cdot t_s$$