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

Ellipsoidal head h D t s L r
Ellipsoidal Head

Values for calculation

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

Calculation

Factor $ K $

$$K=\cfrac{1}{6}\cdot\left[2+\left(\cfrac{D}{2\cdot h}\right)^2\right]$$

Minimum required thickness of head after forming

$$t=\cfrac{1.67\cdot P\cdot D\cdot K}{2\cdot S\cdot E-0.2\cdot1.67\cdot P}$$$$t_s \geq t$$

Crown radius

$$L=K\cdot D$$

Inside knuckle radius

$$r=K_r\cdot D$$

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

$$t_s/L \geq 0.002$$