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Thickness of shells under internal pressure for Toriconical Heads

Toriconical Head D D i L a r t s t s
Toriconical Head

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

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

Crown radius

$$L=\cfrac{D_i}{2\cdot\cos{α}}$$

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

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