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Thickness of shells under external pressure for Torispherical Heads having values $t_s/L≥ 0.002$

Torispherical Head D t s L r
Torispherical Head

Values for calculation

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

Calculation

Factor $ M $

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

Minimum required thickness of head after forming

$$t=\cfrac{1.67\cdot P\cdot L\cdot M}{2\cdot S\cdot E-0.2\cdot1.67\cdot P}$$

$$t_s\geq t$$

Outside radius

$$R_o=L+t_s$$

Factor $ A $

$$A=\cfrac{0.125}{\left(R_o/t_s\right)}$$

Calculated value of maximum allowable external working pressure for the assumed value of $ t_s $

$$P_a=\cfrac{B}{\left(R_o/t_s\right)}$$

$$P\le P_a$$

Requirements

$$ t_s/L \geq 0.002 $$ $$ L \le D+2\cdot t_s $$ $$ r \geq 0.06\cdot\left(D+2\cdot t_s\right) $$ $$ r > 3\cdot t_s $$