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List of symbols

Symbol Name of the symbol Unit
$ $ material $\mathrm{ }$
$ $ testing group $\mathrm{ }$
$ $ production according to temperature $\mathrm{ }$
$ $ seamless product $\mathrm{ }$
$ $ material of bolt $\mathrm{ }$
$ $ material of the shell $\mathrm{ }$
$ $ type of material $\mathrm{ }$
$ $ class $\mathrm{ }$
$ $ type of material $\mathrm{ }$
$ $ min. elongation after fracture $\mathrm{ }$
$ $ type of material of the shell $\mathrm{ }$
$ $ min. elongation after fracture of the shell $\mathrm{ }$
$ $ type of material of bolt $\mathrm{ }$
$ $ material of the nozzle $\mathrm{ }$
$ $ type of material of the nozzle $\mathrm{ }$
$ $ min. elongation after fracture of the nozzle $\mathrm{ }$
$ $ material of nut $\mathrm{ }$
$2b''$ effective gasket pressure width $\mathrm{mm}$
$A$ outside diameter of the flange $\mathrm{mm}$
$A$ factor $ A $ $\mathrm{ }$
$A$ parameter $ A $ $\mathrm{ }$
$A$ factor $ A $ $\mathrm{ }$
$A$ total area of the reinforcement $\mathrm{mm^2}$
$A$ inside diameter of flange $\mathrm{mm}$
$A'$ nozzle reiforcement area $\mathrm{mm^2}$
$A_1$ factor $ A_1 $ $\mathrm{ }$
$A_1$ inside diameter of gasket contact face $\mathrm{mm}$
$A_B$ total cross-sectional area of bolts at the section of least bolt diameter $\mathrm{mm^2}$
$A_{1_{test}}$ factor $ A_{1_{test}} $ $\mathrm{ }$
$A_{B,min}$ total required cross-sectional area of bolts $\mathrm{mm^2}$
$A_{test}$ parameter $ A_{test} $ $\mathrm{ }$
$B$ inside diameter of flange $\mathrm{mm}$
$B$ parameter $ B $ $\mathrm{ }$
$B$ factor $ B $ $\mathrm{ }$
$B$ outside diameter of the flange $\mathrm{mm}$
$B_1$ factor $ B_1 $ $\mathrm{ }$
$B_{1_{test}}$ factor $ B_{1_{test}} $ $\mathrm{ }$
$B_{test}$ parameter $ B_{test} $ $\mathrm{ }$
$C$ bolt pitch circle diameter $\mathrm{mm}$
$C$ factor $ C $ $\mathrm{ }$
$C_1$ factor $ C_1 $ $\mathrm{ }$
$C_1$ shape factor for calculation of circular flat ends $\mathrm{ }$
$C_1$ constant $ C_1 $ $\mathrm{ }$
$C_2$ factor $ C_2 $ $\mathrm{ }$
$C_2$ shape factor for calculation of circular flat ends $\mathrm{ }$
$C_2$ constant $ C_2 $ $\mathrm{ }$
$C_3$ factor $ C_3 $ $\mathrm{ }$
$C_3$ shape factors for calculation of flat ends of non-circular shape $\mathrm{ }$
$C_4$ factor $ C_4 $ $\mathrm{ }$
$C_4$ shape factors for calculation of flat ends of non-circular shape $\mathrm{ }$
$C_5$ 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 $ $\mathrm{ }$
$C_F$ bolt pitch correction factor $\mathrm{ }$
$C_{10}$ 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} $ $\mathrm{ }$
$C_{1_{test}}$ shape factor for calculation of circular flat ends for testing load cases $\mathrm{ }$
$C_{20}$ 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} $ $\mathrm{ }$
$D_F$ diameter of the flat part of an end with a tapered hub $\mathrm{mm}$
$D_L$ inside diameter of seal weld lip $\mathrm{mm}$
$D_c$ mean diameter of the cylinder at the junction with the cone $\mathrm{mm}$
$D_e$ outside diameter of the cylindrical flange $\mathrm{mm}$
$D_i$ inside diameter of shell $\mathrm{mm}$
$D_i$ inside diameter of the cylindrical flange $\mathrm{mm}$
$D_i$ inside diameter of the cone $\mathrm{mm}$
$D_i$ inside diameter of the cylindrical shell welded to a flat end $\mathrm{mm}$
$D_{eq}$ equivalent diameter of an end with a hub $\mathrm{mm}$
$E_1$ 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 $ $\mathrm{ }$
$E_T$ modulus of elasticity for normal operating load cases $\mathrm{MPa}$
$E_{T_{test}}$ modulus of elasticity for testing load cases $\mathrm{MPa}$
$F$ factor $ F $ $\mathrm{ }$
$F_e$ coefficient $ F_e $ $\mathrm{ }$
$F_s$ coefficient $ F_s $ $\mathrm{ }$
$G$ diameter of gasket load reaction $\mathrm{mm}$
$G$ factor $ G $ $\mathrm{ }$
$G$ diameter at location of gasket load reaction $\mathrm{mm}$
$G_0$ outside diameter of gasket or outside diameter of flange, whichever is less $\mathrm{mm}$
$H$ total hydrostatic end force $\mathrm{N}$
$H$ factor $ H $ $\mathrm{ }$
$H_D$ hydrostatic end force applied via shell to flange $\mathrm{N}$
$H_G$ compression load on gasket to ensure tight joint $\mathrm{N}$
$H_R$ balancing reaction force outside bolt circle in opposition to moments due to loads inside bolt circle $\mathrm{N}$
$H_T$ hydrostatic end force due to pressure on flange face $\mathrm{N}$
$H_T$ net pressure load on the flange faces $\mathrm{N}$
$H_{D_{test}}$ hydrostatic end force applied via shell to flange for testing load cases $\mathrm{N}$
$H_{G_{test}}$ compression load on gasket to ensure tight joint for testing load cases $\mathrm{N}$
$H_{R_{test}}$ balancing reaction force outside bolt circle in opposition to moments due to loads inside bolt circle for testing load cases $\mathrm{N}$
$H_{T_{test}}$ hydrostatic end force due to pressure on flange face for testing load cases $\mathrm{N}$
$H_{T_{test}}$ net pressure load on the flange faces for testing load cases $\mathrm{N}$
$H_{test}$ total hydrostatic end force for testing load cases $\mathrm{N}$
$J$ factor $ J $ $\mathrm{ }$
$K$ shape factor for an ellipsoidal end $\mathrm{ }$
$K$ ratio of the flange diameters $\mathrm{ }$
$K$ factor $ K $ $\mathrm{ }$
$L$ unsupported length of the shell $\mathrm{mm}$
$L_{con}$ axial length of a cone $\mathrm{mm}$
$L_{cyl}$ cylinder length between tangent lines $\mathrm{mm}$
$M$ mean stress sensitivity factor $\mathrm{ }$
$M_R$ balancing radial moment in flange along line of bolt holes $\mathrm{Nmm}$
$M_{A}$ moment exerted on the flange per unit of length for assembly condition $\mathrm{Nmm/mm}$
$M_{R_{test}}$ balancing radial moment in flange along line of bolt holes for testing load cases $\mathrm{Nmm}$
$M_{T-A}$ total moment acting upon flange for assembly condition $\mathrm{Nmm}$
$M_{T-op}$ total moment acting upon flange for operating condition $\mathrm{Nmm}$
$M_{T-test}$ total moment acting upon flange for testing load cases $\mathrm{Nmm}$
$M_{op}$ moment exerted on the flange per unit of length for operating condition $\mathrm{Nmm/mm}$
$M_{test}$ moment exerted on the flange per unit of length for testing load cases $\mathrm{Nmm/mm}$
$N$ parameter $ N $ $\mathrm{ }$
$N$ factor $ N $ $\mathrm{ }$
$N$ allowable number of cycles obtained from the fatigue design curves $\mathrm{ }$
$P$ calculation pressure $\mathrm{MPa}$
$P_c$ design pressure in a heating/cooling channel $\mathrm{MPa}$
$P_e$ external calculation pressure $\mathrm{MPa}$
$P_m$ theoretical elastic instability pressure for collapse of a perfect cylindrical, conical or spherical shell for normal operating load cases $\mathrm{MPa}$
$P_m/P_y$ radio $ P_m/P_y $ $\mathrm{ }$
$P_r/P_y$ radio $ P_r/P_y $ $\mathrm{ }$
$P_y$ pressure at which mean circumferential stress in cylindrical or conical shell midway between stiffeners, or in a spherical shell, reaches yield point for normal operating load cases $\mathrm{MPa}$
$P_{e_{test}}$ external test pressure $\mathrm{MPa}$
$P_{m_{test}}$ theoretical elastic instability pressure for collapse of a perfect cylindrical, conical or spherical shell for testing load cases $\mathrm{MPa}$
$P_{m_{test}}/P_{y_{test}}$ radio $ P_{m_{test}}/P_{y_{test}} $ $\mathrm{ }$
$P_{r_{test}}/P_{y_{test}}$ radio $ P_{r_{test}}/P_{y_{test}} $ $\mathrm{ }$
$P_{test}$ test pressure $\mathrm{MPa}$
$P_{y_{test}}$ pressure at which mean circumferential stress in cylindrical or conical shell midway between stiffeners, or in a spherical shell, reaches yield point for testing load cases $\mathrm{MPa}$
$Q$ factor $ Q $ $\mathrm{ }$
$R$ inside spherical radius of central part of torispherical end $\mathrm{mm}$
$R$ mean radius of a cylindrical or spherical shell, or mean crown radius of a torispherical end $\mathrm{mm}$
$R_m$ tensile strength $\mathrm{MPa}$
$R_p$ proof strength $\mathrm{MPa}$
$R_z$ surface roughness (peak to valley height) $\mathrm{μm}$
$R_{m/20/bolt}$ tensile strength of bolt $\mathrm{MPa}$
$R_{m/20/n}$ tensile strength of the nozzle $\mathrm{MPa}$
$R_{m/20/s}$ tensile strength of the shell $\mathrm{MPa}$
$R_{m/20}$ tensile strength $\mathrm{MPa}$
$R_{m/T/n}$ tensile strength at temperature $ T $ of the nozzle $\mathrm{MPa}$
$R_{m/T/s}$ tensile strength at temperature $ T $ of the shell $\mathrm{MPa}$
$R_{m/T^*}$ tensile strength at temperature $ T^* $ $\mathrm{MPa}$
$R_{m/T_{assembly}}$ tensile strength at temperature $ T_{assembly} $ $\mathrm{MPa}$
$R_{m/T_{test}/n}$ tensile strength at temperature $ T_{test} $ of the nozzle $\mathrm{MPa}$
$R_{m/T_{test}/s}$ tensile strength at temperature $ T_{test} $ of the shell $\mathrm{MPa}$
$R_{m/T_{test}}$ tensile strength at temperature $ T_{test} $ $\mathrm{MPa}$
$R_{m/T}$ tensile strength at temperature $ T $ $\mathrm{MPa}$
$R_{m/bolt/T^*}$ tensile strength of bolt at temperature $ T^* $ $\mathrm{MPa}$
$R_{m/bolt/T_{assembly}}$ tensile strength of bolt at temperature $ T_{assembly} $ $\mathrm{MPa}$
$R_{m/bolt/T_{test}}$ tensile strength of bolt at temperature $ T_{test} $ $\mathrm{MPa}$
$R_{m/bolt/T}$ tensile strength of bolt at temperature $ T $ $\mathrm{MPa}$
$R_{p0.2/T/n}$ 0.2 % proof strength at temperature $ T $ of the nozzle $\mathrm{MPa}$
$R_{p0.2/T/s}$ 0.2 % proof strength at temperature $ T $ of the shell $\mathrm{MPa}$
$R_{p0.2/T^*}$ 0.2 % proof strength at temperature $ T^* $ $\mathrm{MPa}$
$R_{p0.2/T_{assembly}}$ 0.2 % proof strength at temperature $ T_{assembly} $ $\mathrm{MPa}$
$R_{p0.2/T_{test}/n}$ 0.2 % proof strength at temperature $ T_{test} $ of the nozzle $\mathrm{MPa}$
$R_{p0.2/T_{test}/s}$ 0.2 % proof strength at temperature $ T_{test} $ of the shell $\mathrm{MPa}$
$R_{p0.2/T_{test}}$ 0.2 % proof strength at temperature $ T_{test} $ $\mathrm{MPa}$
$R_{p0.2/T}$ 0.2 % proof strength at temperature $ T $ $\mathrm{MPa}$
$R_{p0.2/bolt/T_{assembly}}$ 0.2 % proof strength of bolt at temperature $ T_{assembly} $ $\mathrm{MPa}$
$R_{p0.2/bolt/T_{test}}$ 0.2 % proof strength of bolt at temperature $ T_{test} $ $\mathrm{MPa}$
$R_{p0.2/bolt/T}$ 0.2 % proof strength of bolt at temperature $ T $ $\mathrm{MPa}$
$R_{p0.2/nut/T_{assembly}}$ 0.2 % proof strength of nut at temperature $ T_{assembly} $ $\mathrm{MPa}$
$R_{p0.2/nut/T_{test}}$ 0.2 % proof strength of nut at temperature $ T_{test} $ $\mathrm{MPa}$
$R_{p0.2/nut/T}$ 0.2 % proof strength of nut at temperature $ T $ $\mathrm{MPa}$
$R_{p1.0/T/n}$ 1.0 % proof strength at temperature $ T $ of the nozzle $\mathrm{MPa}$
$R_{p1.0/T/s}$ 1.0 % proof strength at temperature $ T $ of the shell $\mathrm{MPa}$
$R_{p1.0/T^*}$ 1.0 % proof strength at temperature $ T^* $ $\mathrm{MPa}$
$R_{p1.0/T_{assembly}}$ 1.0 % proof strength at temperature $ T_{assembly} $ $\mathrm{MPa}$
$R_{p1.0/T_{test}/n}$ 1.0 % proof strength at temperature $ T_{test} $ of the nozzle $\mathrm{MPa}$
$R_{p1.0/T_{test}/s}$ 1.0 % proof strength at temperature $ T_{test} $ of the shell $\mathrm{MPa}$
$R_{p1.0/T_{test}}$ 1.0 % proof strength at temperature $ T_{test} $ $\mathrm{MPa}$
$R_{p1.0/T}$ 1.0 % proof strength at temperature $ T $ $\mathrm{MPa}$
$S$ factor $ S $ $\mathrm{ }$
$T$ calculation temperature $\mathrm{°C}$
$T^*$ assumed mean cycle temperature $\mathrm{°C}$
$T_{assembly}$ assembly temperature $\mathrm{°C}$
$T_{test}$ test temperature $\mathrm{°C}$
$U$ factor $ U $ $\mathrm{ }$
$V$ parameter $ V $ $\mathrm{ }$
$V_{test}$ parameter $ V_{test} $ $\mathrm{ }$
$W$ design bolt load for assembly condition $\mathrm{N}$
$W_A$ minimum required bolt load for assembly condition $\mathrm{N}$
$W_{op}$ minimum required bolt load for operating condition $\mathrm{N}$
$W_{test}$ minimum required bolt load for testing load cases $\mathrm{N}$
$X$ ratio of knuckle inside radius to shell inside diameter $\mathrm{ }$
$Y$ parameter $ Y $ $\mathrm{ }$
$Y_1$ calculation coefficient $ Y_1 $ for opening reinforcement $\mathrm{ }$
$Y_2$ calculation coefficient $ Y_2 $ for opening reinforcement $\mathrm{ }$
$Z$ parameter $ Z $ $\mathrm{ }$
$\overline{σ}_{eq,r}$ reduced mean equivalent stress for elastic-plastic conditions $\mathrm{MPa}$
$\overline{σ}_{eq}$ mean equivalent stress $\mathrm{MPa}$
$a$ factor $ a $ $\mathrm{ }$
$a$ length of shell covered by heating/cooling coil $\mathrm{mm}$
$a'$ smaller width dimension in a rectangular, elliptical or obround end $\mathrm{mm}$
$b$ effective gasket or joint seating width $\mathrm{mm}$
$b$ factor $ b $ $\mathrm{ }$
$b'$ greater width dimension in a rectangular, elliptical or obround end $\mathrm{mm}$
$b'$ effective assembly width $\mathrm{mm}$
$b'_0$ basic assembly width effective under initial tightening up $\mathrm{mm}$
$c$ factor $ c $ $\mathrm{ }$
$c$ mean distance between the gasket reaction and the bolt pitch circle diameter $\mathrm{mm}$
$d$ diameter of an opening or equivalent diameter of a nozzle $\mathrm{mm}$
$d$ arithmetic mean of the diameters of the openings or the mean equivalent diameter of the nozzles $\mathrm{mm}$
$d$ equivalent diameter of a nozzle $\mathrm{mm}$
$d_b$ bolt outside diameter $\mathrm{mm}$
$d_e$ nozzle outside diameter $\mathrm{mm}$
$d_h$ diameter of bore holes $\mathrm{mm}$
$d_h$ diameter of bolt holes $\mathrm{mm}$
$d_i$ inside diameter of the nozzle $\mathrm{mm}$
$d_n$ bolt nominal diameter $\mathrm{mm}$
$e$ required thickness $\mathrm{mm}$
$e$ minimum flange thickness, measured at the thinnest section $\mathrm{mm}$
$e$ minimum required thickness for a flat end with a hub $\mathrm{mm}$
$e$ minimum thickness within the gasket $\mathrm{mm}$
$e$ the minimum thickness for a flat end with a full-face gasket $\mathrm{mm}$
$e$ thickness of the flat end $\mathrm{mm}$
$e$ cylinder thickness required to carry the pressure in the channels $\mathrm{mm}$
$e_1$ minimum thickness for the flanged extension $\mathrm{mm}$
$e_1$ required thickness of cylinder at junction $\mathrm{mm}$
$e_2$ required thickness of cone and knuckle at junction $\mathrm{mm}$
$e_A$ minimum thickness within the gasket for assembly cases $\mathrm{mm}$
$e_a$ analysis thickness $\mathrm{mm}$
$e_b$ required thickness of knuckle to avoid plastic buckling $\mathrm{mm}$
$e_j$ required or analysis thickness at a junction at the large end of a cone $\mathrm{mm}$
$e_j$ required or analysis thickness at a junction at the small end of a cone $\mathrm{mm}$
$e_n$ bolt diameter $\mathrm{mm}$
$e_n$ material thickness $\mathrm{mm}$
$e_p$ minimum thickness within the gasket for calculation pressure $\mathrm{mm}$
$e_r$ minimum required thickness under a relief groove $\mathrm{mm}$
$e_s$ required thickness of end to limit membrane stress in central part $\mathrm{mm}$
$e_s$ analysis thickness of a uniform cylindrical shell, or the equivalent thickness of a tapered cylindrical shell, adjacent to a flat end $\mathrm{mm}$
$e_y$ required thickness of knuckle to avoid axisymmetric yielding $\mathrm{mm}$
$e_{1,a}$ analysis thickness for the flanged extension $\mathrm{mm}$
$e_{af}$ analysis thickness of an end with a hub $\mathrm{mm}$
$e_{af}$ analysis thickness $\mathrm{mm}$
$e_{b_{test}}$ required thickness of knuckle to avoid plastic buckling for testing load cases $\mathrm{mm}$
$e_{con_{test}}$ required thickness of cone for testing load cases $\mathrm{mm}$
$e_{con}$ required thickness of cone $\mathrm{mm}$
$e_{cyl}$ required thickness of cylinder $\mathrm{mm}$
$e_{p1}$ minimum thickness for the flanged extension for calculation pressure $\mathrm{mm}$
$e_{p_{test}1}$ minimum thickness for the flanged extension for test pressure $\mathrm{mm}$
$e_{p_{test}}$ minimum thickness within the gasket for test pressure $\mathrm{mm}$
$e_{r_{test}}$ minimum required thickness under a relief groove for testing load cases $\mathrm{mm}$
$e_{s_{test}}$ required thickness of end to limit membrane stress in central part for testing load cases $\mathrm{mm}$
$e_{test}$ required thickness for testing load cases $\mathrm{mm}$
$e_{test}$ minimum flange thickness, measured at the thinnest section for testing load cases $\mathrm{mm}$
$e_{test}$ minimum required thickness for a flat end with a hub for testing load cases $\mathrm{mm}$
$e_{y_{test}}$ required thickness of knuckle to avoid axisymmetric yielding for testing load cases $\mathrm{mm}$
$f_1$ factor $ f_1 $ $\mathrm{ }$
$f_A$ maximum allowed value of the nominal design stress for assembly cases $\mathrm{MPa}$
$f_B$ bolt nominal design stress for normal operating load cases $\mathrm{MPa}$
$f_b$ design stress for buckling formula for normal operating load cases $\mathrm{MPa}$
$f_b$ overall correction factor applied to bolts $\mathrm{ }$
$f_d$ maximum allowed value of the nominal design stress for normal operating load cases $\mathrm{MPa}$
$f_e$ thickness correction factor in unwelded components $\mathrm{ }$
$f_m$ mean stress correction factor $\mathrm{ }$
$f_n$ nominal design stress at calculation temperature of the nozzle for normal operating load cases $\mathrm{MPa}$
$f_s$ nominal design stress at calculation temperature of the shell for normal operating load cases $\mathrm{MPa}$
$f_s$ surface finish correction factor $\mathrm{ }$
$f_u$ overall correction factor applied to unwelded components $\mathrm{ }$
$f_w$ overall correction factor applied to welded components $\mathrm{ }$
$f_{B,A}$ bolt nominal design stress at assembly temperature $\mathrm{MPa}$
$f_{B_{test}}$ bolt nominal design stress for testing load cases $\mathrm{MPa}$
$f_{b_{test}}$ design stress for buckling formula for testing load cases $\mathrm{MPa}$
$f_{ew}$ thickness correction factor in welded components $\mathrm{ }$
$f_{min_{test}}$ lower of the nominal design stresses $ f_{test} $ of the end and $ f_{s_{test}} $ of the shell for testing load cases $\mathrm{MPa}$
$f_{min}$ lower of the nominal design stresses $ f_d $ of the end and $ f_s $ of the shell for normal operating load cases $\mathrm{MPa}$
$f_{n_{test}}$ nominal design stress at calculation temperature of the nozzle for testing load cases $\mathrm{MPa}$
$f_{s_{test}}$ nominal design stress at calculation temperature of the shell for testing load cases $\mathrm{MPa}$
$f_{t^*}$ temperature correction factor $\mathrm{ }$
$f_{test}$ maximum allowed value of the nominal design stress for testing load cases $\mathrm{MPa}$
$g$ factor $ g $ $\mathrm{ }$
$g_0$ thickness of hub at small end $\mathrm{mm}$
$g_1$ thickness of hub at back of flange $\mathrm{mm}$
$h$ hub length $\mathrm{mm}$
$h$ smallest distance between the centre of an opening and the inside of the shell $\mathrm{mm}$
$h$ external height of dished end $ h $ $\mathrm{mm}$
$h'$ external height of dished end $ h' $ $\mathrm{mm}$
$h''$ external height of dished end $ h'' $ $\mathrm{mm}$
$h_D$ radial distance from bolt circle to circle on which $ H_D $ acts $\mathrm{mm}$
$h_G$ radial distance from gasket load reaction to bolt circle $\mathrm{mm}$
$h_R$ radial distance from bolt circle to circle on which $ H_R $ acts $\mathrm{mm}$
$h_T$ radial distance from bolt circle to circle on which $ H_T $ acts $\mathrm{mm}$
$h_i$ inside height of end measured from the tangent line $\mathrm{mm}$
$h_w$ distance between the external wall of an end with a relief groove and the weld on the shell $\mathrm{mm}$
$k$ stress factor $\mathrm{ }$
$k$ distance between the centres of the openings $\mathrm{mm}$
$l_0$ length parameter $\mathrm{ }$
$l_1$ length along cylinder $\mathrm{mm}$
$l_2$ length along cone at large or small end $\mathrm{mm}$
$l_b$ length of bolts in threaded holes $\mathrm{mm}$
$l_n$ length nut $\mathrm{mm}$
$l_{cyl}$ length of cylindrical shell $\mathrm{mm}$
$m$ gasket factor $\mathrm{ }$
$m_1$ exponent $ m_1 $ $\mathrm{ }$
$m_2$ exponent $ m_2 $ $\mathrm{ }$
$n$ number of bolts $\mathrm{ }$
$n_{EQ}$ equivalent bolt number $\mathrm{ }$
$n_{cyl}$ number of circumferential waves for an unstiffened part of a cylinder $\mathrm{ }$
$r$ inside radius of curvature of a knuckle $\mathrm{mm}$
$r$ inside radius of a hub $\mathrm{mm}$
$r$ knuckle radius $\mathrm{mm}$
$r_d$ inside radius of the relief groove $\mathrm{mm}$
$s$ factor $ s $ $\mathrm{ }$
$t_B$ mean bolt pitch in a bolted flat end $\mathrm{mm}$
$t_{Bmax}$ maximum bolt pitch $\mathrm{mm}$
$y$ minimum gasket or joint seating pressure $\mathrm{MPa}$
$z$ joint coefficient $\mathrm{ }$
$Δσ$ stress range $\mathrm{MPa}$
$Δσ_D$ endurance limit $\mathrm{MPa}$
$Δσ_{Cut}$ cut-off limit $\mathrm{MPa}$
$Δσ_{eq}$ equivalent stress range $\mathrm{MPa}$
$α$ semi angle of cone at apex $\mathrm{°}$
$β$ factor $ β $ $\mathrm{ }$
$β_F$ factor $ β_F $ $\mathrm{ }$
$β_H$ factor $ β_H $ $\mathrm{ }$
$β_K$ weakening factor due to presence of nozzle $\mathrm{ }$
$β_T$ factor $ β_T $ $\mathrm{ }$
$β_U$ factor $ β_U $ $\mathrm{ }$
$β_V$ factor $ β_V $ $\mathrm{ }$
$β_Y$ factor $ β_Y $ $\mathrm{ }$
$β_{0.06}$ factor $ β_{0.06} $ $\mathrm{ }$
$β_{0.1}$ factor $ β_{0.1} $ $\mathrm{ }$
$β_{0.2}$ factor $ β_{0.2} $ $\mathrm{ }$
$β_{FL}$ factor $ β_{FL} $ $\mathrm{ }$
$β_{K_{test}}$ weakening factor due to presence of nozzle for testing load cases $\mathrm{ }$
$β_{VL}$ factor $ β_{VL} $ $\mathrm{ }$
$γ$ factor $ γ $ $\mathrm{ }$
$δ_b$ distance between centre lines of adjacent bolts $\mathrm{mm}$
$ε$ mean elastic circumferential strain at collapse $\mathrm{ }$
$λ$ factor $ λ $ $\mathrm{ }$
$ν$ Poisson's ratio $\mathrm{ }$
$ρ$ factor $ ρ $ $\mathrm{ }$
$σ_e$ nominal elastic limit for shell for normal operating load cases $\mathrm{MPa}$
$σ_{H_{A}}$ longitudinal stress in hub for assembly condition $\mathrm{MPa}$
$σ_{H_{op}}$ longitudinal stress in hub for operating condition $\mathrm{MPa}$
$σ_{H_{test}}$ longitudinal stress in hub for testing load cases $\mathrm{MPa}$
$σ_{e_{test}}$ nominal elastic limit for shell for testing load cases $\mathrm{MPa}$
$σ_{eq\ max}$ maximum equivalent stress range $\mathrm{MPa}$
$σ_{r_{A}}$ radial stress in flange for assembly condition $\mathrm{MPa}$
$σ_{r_{op}}$ radial stress in flange for operating condition $\mathrm{MPa}$
$σ_{r_{test}}$ radial stress in flange for testing load cases $\mathrm{MPa}$
$σ_{θ_{A}}$ tangential stress in flange for assembly condition $\mathrm{MPa}$
$σ_{θ_{op}}$ tangential stress in flange for operating condition $\mathrm{MPa}$
$σ_{θ_{test}}$ tangential stress in flange for testing load cases $\mathrm{MPa}$
$τ$ factor $ τ $ $\mathrm{ }$
$φ$ hub stress correction factor $\mathrm{ }$