$ $ |
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 |
$\mathrm{ }$ |
$ $ |
material group |
$\mathrm{ }$ |
$2b''$ |
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 |
$\mathrm{ }$ |