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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

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