| $ $ | material | $\mathrm{ }$ |
| $ $ | testing group | $\mathrm{ }$ |
| $ $ | production according to temperature | $\mathrm{ }$ |
| $ $ | seamless product | $\mathrm{ }$ |
| $ $ | material of bolt | $\mathrm{ }$ |
| $ $ | material of the shell | $\mathrm{ }$ |
| $ $ | class | $\mathrm{ }$ |
| $A$ | outside diameter of the flange | $\mathrm{mm}$ |
| $A$ | factor $ A $ | $\mathrm{ }$ |
| $A$ | parameter $ A $ | $\mathrm{ }$ |
| $A$ | factor $ A $ | $\mathrm{ }$ |
| $A_1$ | factor $ A_1 $ | $\mathrm{ }$ |
| $A_B$ | 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 $ | $\mathrm{ }$ |
| $B_1$ | 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 $ | $\mathrm{ }$ |
| $C_4$ | 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 $ | $\mathrm{ }$ |
| $C_F$ | 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} $ | $\mathrm{ }$ |
| $D_e$ | outside diameter of the cylindrical flange | $\mathrm{mm}$ |
| $D_f$ | diameter of the flat part of an end with a tapered hub | $\mathrm{mm}$ |
| $D_i$ | 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 $ | $\mathrm{ }$ |
| $F$ | factor $ F $ | $\mathrm{ }$ |
| $F_e$ | coefficient $ F_e $ | $\mathrm{ }$ |
| $G$ | mean diameter of gasket | $\mathrm{mm}$ |
| $G$ | factor $ G $ | $\mathrm{ }$ |
| $H$ | 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 | $\mathrm{N}$ |
| $H_{D_{test}}$ | 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 | $\mathrm{N}$ |
| $H_{test}$ | 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 $ | $\mathrm{ }$ |
| $M_R$ | 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 | $\mathrm{MPa}$ |
| $P_e$ | external calculation pressure | $\mathrm{MPa}$ |
| $P_{e_{test}}$ | external test pressure | $\mathrm{MPa}$ |
| $P_{test}$ | test pressure | $\mathrm{MPa}$ |
| $Q$ | factor $ Q $ | $\mathrm{ }$ |
| $R$ | inside spherical radius of central part of torispherical end | $\mathrm{mm}$ |
| $R_m$ | tensile strength | $\mathrm{MPa}$ |
| $R_{m/20/bolt}$ | tensile strength of bolt | $\mathrm{MPa}$ |
| $R_{m/20/s}$ | tensile strength of the shell | $\mathrm{MPa}$ |
| $R_{m/20}$ | tensile strength | $\mathrm{MPa}$ |
| $R_{m/T/s}$ | tensile strength at temperature $ T $ of the shell | $\mathrm{MPa}$ |
| $R_{m/T_{test}/s}$ | 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 $ | $\mathrm{MPa}$ |
| $R_{p0.2/T/s}$ | 0.2 % proof strength at temperature $ T $ of the shell | $\mathrm{MPa}$ |
| $R_{p0.2/T_{test}/s}$ | 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 $ | $\mathrm{MPa}$ |
| $R_{p1.0/T/s}$ | 1.0 % proof strength at temperature $ T $ of the shell | $\mathrm{MPa}$ |
| $R_{p1.0/T_{test}/s}$ | 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 $ | $\mathrm{ }$ |
| $Z$ | parameter $ Z $ | $\mathrm{ }$ |
| $a$ | factor $ a $ | $\mathrm{ }$ |
| $b$ | effective gasket or joint seating width | $\mathrm{mm}$ |
| $b$ | factor $ b $ | $\mathrm{ }$ |
| $c$ | factor $ c $ | $\mathrm{ }$ |
| $d_b$ | bolt outside diameter | $\mathrm{mm}$ |
| $d_h$ | diameter of bore holes | $\mathrm{mm}$ |
| $d_i$ | inside diameter of the nozzle | $\mathrm{mm}$ |
| $e$ | 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 | $\mathrm{mm}$ |
| $e_b$ | required thickness of knuckle to avoid plastic buckling | $\mathrm{mm}$ |
| $e_n$ | bolt diameter | $\mathrm{mm}$ |
| $e_n$ | material thickness | $\mathrm{mm}$ |
| $e_r$ | 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 | $\mathrm{mm}$ |
| $e_{af}$ | 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 | $\mathrm{mm}$ |
| $e_{r_{test}}$ | 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 $ | $\mathrm{ }$ |
| $f_B$ | 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 value of the nominal design stress for normal operating load cases | $\mathrm{MPa}$ |
| $f_e$ | thickness correction factor in unwelded components | $\mathrm{ }$ |
| $f_s$ | nominal design stress at calculation temperature of the shell for normal operating load cases | $\mathrm{MPa}$ |
| $f_w$ | 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 | $\mathrm{MPa}$ |
| $f_{s_{test}}$ | nominal design stress at calculation temperature of the shell for testing load cases | $\mathrm{MPa}$ |
| $f_{t^*}$ | temperature correction factor | $\mathrm{ }$ |
| $f_{test}$ | maximum 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 | $\mathrm{mm}$ |
| $h_D$ | 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 | $\mathrm{ }$ |
| $l_0$ | length parameter | $\mathrm{ }$ |
| $l_{cyl}$ | 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 | $\mathrm{ }$ |
| $r$ | inside radius of curvature of a knuckle | $\mathrm{mm}$ |
| $r$ | inside radius of a hub | $\mathrm{mm}$ |
| $r_d$ | inside radius of the relief groove | $\mathrm{mm}$ |
| $type\ of\ material$ | type of material | $\mathrm{ }$ |
| $y$ | 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 | $\mathrm{MPa}$ |
| $α$ | semi angle of cone at apex | $\mathrm{°}$ |
| $β$ | factor $ β $ | $\mathrm{ }$ |
| $β_F$ | factor $ β_F $ | $\mathrm{ }$ |
| $β_K$ | 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} $ | $\mathrm{ }$ |
| $δ_b$ | distance between centre lines of adjacent bolts | $\mathrm{mm}$ |
| $λ$ | factor $ λ $ | $\mathrm{ }$ |
| $ν$ | Poisson's ratio | $\mathrm{ }$ |
| $σ_{H_{A}}$ | 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 | $\mathrm{MPa}$ |
| $σ_{r_{A}}$ | 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 | $\mathrm{MPa}$ |
| $φ$ | hub stress correction factor | $\mathrm{ }$ |
