# List of symbols

Symbol Name of the symbol Unit
material of the shell$\mathrm{ }$
material of the stiffening ring$\mathrm{ }$
flange category$\mathrm{ }$
material of bolt$\mathrm{ }$
material of nozzle neck, vessel or pipe wall$\mathrm{ }$
material of flange$\mathrm{ }$
material$\mathrm{ }$
$A$outside diameter of flange$\mathrm{mm}$
$A$factor $A$ $\mathrm{ }$
$A_b$cross‐sectional area of the bolts using the root diameter of the thread or least diameter of unthreaded portion, if less$\mathrm{mm^2}$
$A_s$cross‐sectional area of the stiffening ring$\mathrm{mm^2}$
$B$inside diameter of flange$\mathrm{mm}$
$B$factor $B$ $\mathrm{MPa}$
$B_1$diameter $B_1$ $\mathrm{mm}$
$C$factor $C$ $\mathrm{ }$
$C$bolt‐circle diameter$\mathrm{mm}$
$C_1$factor $C_1$ $\mathrm{ }$
$C_2$factor $C_2$ $\mathrm{ }$
$C_3$factor $C_3$ $\mathrm{ }$
$C_4$factor $C_4$ $\mathrm{ }$
$C_5$factor $C_5$ $\mathrm{ }$
$C_6$factor $C_6$ $\mathrm{ }$
$C_7$factor $C_7$ $\mathrm{ }$
$C_8$factor $C_8$ $\mathrm{ }$
$C_9$factor $C_9$ $\mathrm{ }$
$C_{10}$factor $C_{10}$ $\mathrm{ }$
$C_{11}$factor $C_{11}$ $\mathrm{ }$
$C_{12}$factor $C_{12}$ $\mathrm{ }$
$C_{13}$factor $C_{13}$ $\mathrm{ }$
$C_{14}$factor $C_{14}$ $\mathrm{ }$
$C_{15}$factor $C_{15}$ $\mathrm{ }$
$C_{16}$factor $C_{16}$ $\mathrm{ }$
$C_{17}$factor $C_{17}$ $\mathrm{ }$
$C_{18}$factor $C_{18}$ $\mathrm{ }$
$C_{19}$factor $C_{19}$ $\mathrm{ }$
$C_{20}$factor $C_{20}$ $\mathrm{ }$
$C_{21}$factor $C_{21}$ $\mathrm{ }$
$C_{22}$factor $C_{22}$ $\mathrm{ }$
$C_{23}$factor $C_{23}$ $\mathrm{ }$
$C_{24}$factor $C_{24}$ $\mathrm{ }$
$C_{25}$factor $C_{25}$ $\mathrm{ }$
$C_{26}$factor $C_{26}$ $\mathrm{ }$
$C_{27}$factor $C_{27}$ $\mathrm{ }$
$C_{28}$factor $C_{28}$ $\mathrm{ }$
$C_{29}$factor $C_{29}$ $\mathrm{ }$
$C_{30}$factor $C_{30}$ $\mathrm{ }$
$C_{31}$factor $C_{31}$ $\mathrm{ }$
$C_{32}$factor $C_{32}$ $\mathrm{ }$
$C_{33}$factor $C_{33}$ $\mathrm{ }$
$C_{34}$factor $C_{34}$ $\mathrm{ }$
$C_{35}$factor $C_{35}$ $\mathrm{ }$
$C_{36}$factor $C_{36}$ $\mathrm{ }$
$C_{37}$factor $C_{37}$ $\mathrm{ }$
$D$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$\mathrm{mm}$
$D$diameter of bolt hole$\mathrm{mm}$
$D_L$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 $D_o/t$ $\mathrm{ }$
$D_s$outside diameter at small end of conical section under consideration$\mathrm{mm}$
$D_{Ls}$outside diameter at large end of conical section under consideration $D_{Ls}$ $\mathrm{mm}$
$D_{ss}$outside diameter at small end of conical section under consideration $D_{ss}$ $\mathrm{mm}$
$E$joint efficiency$\mathrm{ }$
$E_1$factor $E_1$ $\mathrm{ }$
$E_2$factor $E_2$ $\mathrm{ }$
$E_3$factor $E_3$ $\mathrm{ }$
$E_4$factor $E_4$ $\mathrm{ }$
$E_5$factor $E_5$ $\mathrm{ }$
$E_6$factor $E_6$ $\mathrm{ }$
$Eθ_B$slope of Flange at Inside Diameter Times $E$ $\mathrm{ }$
$F$factor $F$ for integral type flanges$\mathrm{ }$
$F'$factor $F'$ $\mathrm{ }$
$F_L$factor $F_L$ for loose type flanges$\mathrm{ }$
$G$mean diameter of gasket$\mathrm{mm}$
$H$total hydrostatic end force$\mathrm{N}$
$H_C$contact force between flanges at $h_C$ $\mathrm{N}$
$H_D$hydrostatic end force on area inside of flange$\mathrm{N}$
$H_G$gasket load due to seating pressure, plus axial force generated by self‐sealing of gasket$\mathrm{N}$
$H_T$difference between total hydrostatic end force and the hydrostatic end force on area inside of flange$\mathrm{N}$
$I$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$\mathrm{mm^4}$
$J_P$factor $J_P$ $\mathrm{ }$
$J_S$factor $J_S$ $\mathrm{ }$
$K$factor $K$ $\mathrm{ }$
$K$ratio of outside diameter of flange to inside diameter of flange$\mathrm{ }$
$K_r$factor $K_r$ $\mathrm{ }$
$L$total length$\mathrm{mm}$
$L$crown radius$\mathrm{mm}$
$L$inside spherical radius$\mathrm{mm}$
$L/D_o$ratio $L/D_o$ $\mathrm{ }$
$L_c$axial length of cone or conical section$\mathrm{mm}$
$L_e$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 $M$ $\mathrm{ }$
$M_P$moment due to $H_D$ , $H_T$ , $H_G$ $\mathrm{Nmm}$
$M_S$flange Moment Due to Flange‐Hub Interaction$\mathrm{Nmm}$
$P$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$\mathrm{mm}$
$R$radial distance from bolt circle to point of intersection of hub and back of flange$\mathrm{mm}$
$R_o$outside radius$\mathrm{mm}$
$S$maximum allowable stress value$\mathrm{MPa}$
$S_H$longitudinal hub stress$\mathrm{MPa}$
$S_R$radial flange stress at bolt circle$\mathrm{MPa}$
$S_R$radial flange stress at inside diameter$\mathrm{MPa}$
$S_T$tangential flange stress at inside diameter$\mathrm{MPa}$
$S_b$allowable bolt stress at design temperature$\mathrm{MPa}$
$S_f$allowable design stress for material of flange at design temperature (operating condition) or atmospheric temperature (gasket seating)$\mathrm{MPa}$
$S_i$design prestress in bolts$\mathrm{MPa}$
$S_n$allowable design stress for material of nozzle neck, vessel or pipe wall, at design temperature (operating condition) or atmospheric temperature (gasket seating)$\mathrm{MPa}$
$T$temperature$\mathrm{°C}$
$V$factor $V$ for integral type flanges$\mathrm{ }$
$V_L$factor $V_L$ for loose type flanges$\mathrm{ }$
$W_{m1}$bolt load at operating conditions$\mathrm{N}$
$Z$factor $Z$ $\mathrm{ }$
$\overline{AR}$bolt hole aspect ratio used in calculating bolthole flexibility factor $r_B$ $\mathrm{ }$
$a$shape factor$\mathrm{ }$
$d_b$nominal diameter of bolt$\mathrm{mm}$
$f$factor $f$ $\mathrm{ }$
$g_0$thickness of hub at small end$\mathrm{mm}$
$g_1$thickness of hub at back of flange$\mathrm{mm}$
$h$hub length$\mathrm{mm}$
$h$the inside depth of the ellipsoidal head measured from the tangent line (head‐bend line)$\mathrm{mm}$
$h_0$factor $h_0$ $\mathrm{ }$
$h_C$radial distance from bolt circle to flange‐spacer or flange‐flange bearing circle where tangential contact occurs$\mathrm{mm}$
$h_D$radial distance from the bolt circle, to the circle on which $H_D$ acts$\mathrm{mm}$
$h_G$radial distance from gasket load reaction to the bolt circle$\mathrm{mm}$
$h_T$radial distance from the bolt circle, to the circle on which $H_T$ acts$\mathrm{mm}$
$h_{Cmax}$radial distance from bolt circle to outer edge of flange or spacer$\mathrm{mm}$
$l$strain length of bolt$\mathrm{mm}$
$n$number of bolts$\mathrm{ }$
$r$inside knuckle radius$\mathrm{mm}$
$r_1$outside radius at large end of conical section under consideration$\mathrm{mm}$
$r_2$outside radius at small end of conical section under consideration$\mathrm{mm}$
$r_B$factor $r_B$ $\mathrm{ }$
$r_E$elasticity factor$\mathrm{ }$
$t$minimum required thickness of shell$\mathrm{mm}$
$t$minimum required thickness of head after forming$\mathrm{mm}$
$t$thickness of the flange under consideration$\mathrm{mm}$
$t_e$effective thickness of conical section$\mathrm{mm}$
$t_s$minimum specified thickness of head after forming$\mathrm{mm}$
$t_s$thickness of spacer$\mathrm{mm}$
$α$one‐half of the included (apex) angle of the cone at the centerline of the head$\mathrm{°}$
$β$shape factor for full face metal‐to‐metal contact flanges$\mathrm{ }$
$σ_b$operating bolt stress$\mathrm{MPa}$