# List of symbols

Symbol Name of the symbol Unit
material of the shell$\mathrm{ }$
material of the stiffening ring$\mathrm{ }$
material$\mathrm{ }$
$A$factor $A$ $\mathrm{ }$
$A_s$cross‐sectional area of the stiffening ring$\mathrm{mm^2}$
$B$factor $B$ $\mathrm{MPa}$
$D$inside length of the major axis of an ellipsoidal head$\mathrm{mm}$
$D$inside length of the major axis of an torispherical head$\mathrm{mm}$
$D$inside diameter of a cone head$\mathrm{mm}$
$D$inside diameter of the head skirt$\mathrm{mm}$
$D_L$outside diameter at large end of conical section under consideration$\mathrm{mm}$
$D_L/t_e$ratio $D_L/t_e$ $\mathrm{ }$
$D_i$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$\mathrm{mm}$
$D_o$outside diameter of cylindrical shell course or tube$\mathrm{mm}$
$D_o/t$ratio $D_o/t$ $\mathrm{ }$
$E$joint efficiency$\mathrm{ }$
$I$available moment of inertia of the stiffening ring cross section about its neutral axis parallel to the axis of the shell$\mathrm{mm^4}$
$I^´$available moment of inertia of combined ring-shell cross section about its neutral axis parallel to the axis of the shell. The nominal shell thickness $t_s$ shall be used and the width of shell that is taken as contributing to the moment of inertia of the combined section shall not be greater than $1. 10\cdot\sqrt{D_o\cdot t_s}$ and shall be taken as lying one‐half on each side of the centroid of the ring. Portions of the shell plate shall not be considered as contributing area to more than one stiffening ring.$\mathrm{mm^4}$
$I^´_s$required moment of inertia of the combined ringshell cross section about its neutral axis parallel to the axis of the shell$\mathrm{mm^4}$
$I_s$required moment of inertia of the stiffening ring cross section about its neutral axis parallel to the axis of the shell$\mathrm{mm^4}$
$K$factor $K$ $\mathrm{ }$
$K_r$factor $K_r$ $\mathrm{ }$
$L$total length$\mathrm{mm}$
$L$crown radius$\mathrm{mm}$
$L$inside spherical radius$\mathrm{mm}$
$L/D_o$ratio $L/D_o$ $\mathrm{ }$
$L_e$equivalent length of conical head or Section between lines of support$\mathrm{mm}$
$L_e/D_L$ratio $L_e/D_L$ $\mathrm{ }$
$L_s$one‐half of the distance from the centerline of the stiffening ring to the next line of support on one side, plus one‐half of the centerline distance to the next line of support on the other side of the stiffening ring, both measured parallel to the axis of the cylinder$\mathrm{mm}$
$M$factor $M$ $\mathrm{ }$
$P$internal design pressure$\mathrm{MPa}$
$P$external design pressure$\mathrm{MPa}$
$P_a$calculated value of maximum allowable external working pressure for the assumed value of $t$ $\mathrm{MPa}$
$P_a$calculated value of maximum allowable external working pressure for the assumed value of $t_s$ $\mathrm{MPa}$
$P_a$calculated value of maximum allowable external working pressure for the assumed value of $t_e$ $\mathrm{MPa}$
$P_{a1}$calculated value of maximum allowable external working pressure 1 for the assumed value of $t$ $\mathrm{MPa}$
$P_{a1}$calculated value of maximum allowable external working pressure 1 for the assumed value of $t_e$ $\mathrm{MPa}$
$P_{a2}$calculated value of maximum allowable external working pressure 2 for the assumed value of $t$ $\mathrm{MPa}$
$P_{a2}$calculated value of maximum allowable external working pressure 2 for the assumed value of $t_e$ $\mathrm{MPa}$
$R$inside radius$\mathrm{mm}$
$R_o$outside radius$\mathrm{mm}$
$S$maximum allowable stress value$\mathrm{MPa}$
$T$temperature$\mathrm{°C}$
$h$the inside depth of the ellipsoidal head measured from the tangent line (head‐bend line)$\mathrm{mm}$
$r$inside knuckle radius$\mathrm{mm}$
$t$minimum required thickness of shell$\mathrm{mm}$
$t$minimum required thickness of head after forming$\mathrm{mm}$
$t_e$effective thickness of conical section$\mathrm{mm}$
$t_s$minimum specified thickness of head after forming$\mathrm{mm}$
$α$one‐half of the included (apex) angle of the cone at the centerline of the head$\mathrm{°}$