1 Calculation of Offset Conical Shell Subjected to Internal Pressure
1.1 Overview
1.1.1 This chapter is applicable to the design calculation of offset conical shell only subjected to internal pressure. Offset conical shell is shaped as Figure 1.1.1-1 and Figure 1.1.1-2 and the semiapex α of offset conical shell changes gradually along the perimeter direction: α1 is larger one, and α2 is smaller one; when α2= 0°, it is a common case of equilateral oblique cone.
Ends connected with offset conical shell are cylinder shells, the center lines of the two cylinders are parallel, and the eccentric throw (e) shall satisfy the following requirements:
1.1.2 The conical shell semiapex α used in the calculation takes the larger one in α1 and α2, and the design calculation for offset conical shell is conducted with the method for equilateral conical shell stated in this chapter.
Figure 1.1.1-1 refers to offset conical shell without knuckle, and it is usually used for α ≤ 30°; when α> 30°, offset conical shell with knuckle shown in Figure 1.1.1-2 shall be adopted, but α ≤ 60°.
The butt joints connecting the offset conical shell and the cylinder at both ends must be welded by full penetration welding seam.
Figure 1.1.1-1 Offset Conical Shell without Knuckle
Figure 1.1.1-2 Offset Conical Shell with Knuckle
1.2 Symbol and Description
DL——Interior diameter of cylinder at big end (mm)
DS——Interior diameter of cylinder at smaller end (mm)
RL——Internal radius of cylinder at big end (mm), RL= DL
RS——Internal radius of cylinder at smaller end (mm), RS= DS
rk1, rk2——Radius of the minimum and maximum rotating corner on the transition section at offset conical shell big end (mm)
rf1, rf2——Radius of the minimum and maximum rotating corner on the transition section at offset conical shell smaller end (mm)
rk——Radius of the rotating corner on the transition section at big end (mm), adopting rk= min (rk1, rk2) (see Figure 1.1.1-2 and Figure 1.6.1 in this Standard)
rf——Radius of the rotating corner on the transition section at smaller end (mm), adopting rf= min (rf1, rf2) (see Figure 1.1.1-2 and Figure 1.6.1 in this Standard)
δ——Wall thickness of offset conical shell (including additional thickness) (mm)
δL——Thickness of big end cylinder (excluding additional thickness) (mm)
δS——Thickness of smaller end cylinder (excluding additional thickness) (mm)
δC——Thickness of conical shell (excluding additional thickness) (mm)
δj——Thickness of cylinder or rotating angle at knuckle transition section joint (excluding additional thickness) (mm) (see Figure 1.5.1-2 in this Standard)
δk——Thickness of big end transition section at rotating angle (mm)
δf——Thickness of smaller end transition section at rotating angle (mm)
δSL——Required minimum thickness of big end cylinder (mm)
δSS——Required minimum thickness of smaller end cylinder (mm)
δCC——Required minimum thickness of conical shell (mm)
α1——Maximum semiapex of offset conical shell (°), expressed in arc scale in the numerical computation with formula
α2——Minimum semiapex of offset conical shell (°), expressed in arc scale in the numerical computation with formula
α——Maximum semiapex of conical shell used in the calculation (°), adopting the larger one of α 1 and α 2, expressed in arc scale in the numerical computation with formula
LC——Projected length of conical shell (mm), adopting the length of conical shell generatrix on the side of α1 (see Figure 1.6.1 in this Standard)
Lk——Length (mm) used for the stress calculation of transition section at conical shell big end, when there is rotating angle (see Figure 1.5.1-2 in this Standard)
Lf——Length (mm) used for the stress calculation of transition section at conical shell smaller end, when there is rotating angle (see Figure 1.5.1-2 in this Standard)
Lcy——Length (mm) of cylinder transition section in the stress calculation where there is rotating angle
Lco——Length (mm) of conical shell transition section in the stress calculation where there is rotating angle
L1k——Length (mm) of conical shell transition section in the stress calculation when there is rotating angle at big end
——Length (mm) of conical shell transition section in the stress calculation when there is rotating angle at big end
L1f——Length (mm) of conical shell transition section in the stress calculation when there is rotating angle at smaller end
——Length (mm) of conical shell transition section in the stress calculation where there is rotating angle when there is rotating angle at smaller end
n——Thickness ratio of conical shell and cylinder
H——Calculating parameter
B——Calculating parameter
βcy——Geometric parameter of cylinder
βco——Geometric parameter of conical shell
βk——Angle (°) used in the calculation of conical shell transition section (expressed in arc scale in the numerical computation) when there is rotating angle at big end
βf——Angle (°) used in the calculation of conical shell transition section (expressed in arc scale in the numerical computation) when there is rotating angle at smaller end
Km——Length factor in the calculation of conical shell with knuckle, Km= 0.7
KPC——Correction factor in the stress calculation of cylinder, KPC= 1.0
KCPC——Correction factor in the stress calculation of conical shell, KCPC= 1.0
Rk——Radius from big end knuckle arc center to shell center axis (mm)
Rf——Radius from smaller end knuckle arc center to shell center axis (mm)
RC——Calculated radius considering cone angle (mm)
v——Poisson ratio, v= 0.3 for steel
φk——Angle (°) used in the calculation of transition section of conical shell with knuckle at big end (expressed in arc scale in the numerical computation)
——Angle (°) used in the calculation of conical shell transition section (expressed in arc scale in the numerical computation) when the strength is not enough at big end rotating angle
——Angle (°) used in the calculation of conical shell transition section (expressed in arc scale in the numerical computation) when the strength is not enough at big end rotating angle
——Angle (°) used in the calculation of conical shell transition section (expressed in arc scale in the numerical computation) when the strength is not enough at big end rotating angle
φf——Angle (°) used in the calculation of transition section of conical shell with knuckle at smaller end (expressed in arc scale in the numerical computation)
——Angle (°) used in the calculation of conical shell transition section (expressed in arc scale in the numerical computation) when the strength is not enough at smaller end rotating angle
——Angle (°) used in the calculation of conical shell transition section (expressed in arc scale in the numerical computation) when the strength is not enough at smaller end rotating angle
——Angle (°) used in the calculation of conical shell transition section (expressed in arc scale in the numerical computation) when the strength is not enough at smaller end rotating angle
MS——Radial force moment, at the joint of cylinder and conical shell, of the internal pressure acted on cylinder (N•mm)
MCS——Radial force moment of internal pressure acted on conical shell (N•mm)
MSN——Radial force moment acted on cylinder used for the calculation (N•mm)
QP——Shear force, at the joint of cylinder and conical shell, of the internal pressure acted on cylinder (N)
QC——Shear force of internal pressure acted on conical shell (N)
QN——Shear force of internal pressure acted on cylinder, used for the calculation (N)
NS——Radial membrane force of internal pressure acted on cylinder (N)
——Circumferential membrane force of internal pressure acted on cylinder (N)
NC——Radial membrane force of internal pressure acted on conical shell (N)
——Circumferential membrane force of internal pressure acted on conical shell (N)
p——Design pressure (MPa)
[σ]t——Allowable stress of the materials at the design temperature (MPa)
φ——Welded joint coefficient
σsm——Radial membrane stress of shell (MPa)
σsb——Radial bend stress of shell (MPa)
——Circumferential membrane stress of shell (MPa)
——Circumferential bend stress of shell (MPa)
——Radial membrane stress at the calculation position (j) of rotating angle (MPa)
——Circumferential membrane stress at the calculation position (j) of rotating angle (MPa)
1.3 Minimum Thickness of Shell
1.3.1 Required minimum thickness of cylinder shell
The required minimum thickness of big end cylinder is calculated according to formula (1.3.1-1):
1 Calculation of Offset Conical Shell Subjected to Internal Pressure 2 Design and calculation of conical closure with large apex angle 3 Design of Vessels with Half Pipe Jacket 4 Design of Reducers with Knuckle and Subjected to Internal Pressure and Axial Force 5 Design and Calculation of Thin Convex Closures Subjected to Internal Pressure 6 Reinforcement for Shell with Lateral or Hillside Nozzle 7 Reinforcement for Large Opening 8 Calculation of Enhancement of Load Bearing Capacity of Cylinders with Supporting Rings and Subjected to External Pressure 9 Calculation of Equivalent Design Pressure for Flange Subjected to External Loading 10 Covered Serrated Metal Gasket 11 Design and Calculation of Welding Sealed Flange without Gasket 12 Design and Calculation of Noncircular Flange 13 Design of Clamp Connections 14 Design of Serrated Clamp Connections 15 Design of Integral Serrated Clamp Connections 16 Design and Calculation of Flanged Collar 17 Design and Calculation of High Pressure Screw Flange with Lens Shape Gasket 18 Design and Calculation of Multi Saddle Supported Horizontal Vessel 19 Design and Calculation of Lug Support with Rigid Ring 20 Design and Calculation of Circular Flat with Strengtheners 21 Calculation of Internal Pressurized Bend 22 Design and Calculation of Miter Bend (Shrimps-shaped) 23 Calculation of Welded T Joint 24 Design and Calculation of Y Shape Pipe 25 Design and Calculation of Toroidal Expansion Joint 26 Calculation of Local Stresses in Cylinder due to External Loadings 27 Calculation of Local Stresses in Spherical Shell Due to External Loadings Acting on Nozzle Or Attachment 28 Calculation of Local Stresses in Cylinder and Nozzle Due to External Loadings 29 Alternative Design Method for Flanged Connection
1 Calculation of Offset Conical Shell Subjected to Internal Pressure
1.1 Overview
1.1.1 This chapter is applicable to the design calculation of offset conical shell only subjected to internal pressure. Offset conical shell is shaped as Figure 1.1.1-1 and Figure 1.1.1-2 and the semiapex α of offset conical shell changes gradually along the perimeter direction: α1 is larger one, and α2 is smaller one; when α2= 0°, it is a common case of equilateral oblique cone.
Ends connected with offset conical shell are cylinder shells, the center lines of the two cylinders are parallel, and the eccentric throw (e) shall satisfy the following requirements:
1.1.2 The conical shell semiapex α used in the calculation takes the larger one in α1 and α2, and the design calculation for offset conical shell is conducted with the method for equilateral conical shell stated in this chapter.
Figure 1.1.1-1 refers to offset conical shell without knuckle, and it is usually used for α ≤ 30°; when α> 30°, offset conical shell with knuckle shown in Figure 1.1.1-2 shall be adopted, but α ≤ 60°.
The butt joints connecting the offset conical shell and the cylinder at both ends must be welded by full penetration welding seam.
Figure 1.1.1-1 Offset Conical Shell without Knuckle
Figure 1.1.1-2 Offset Conical Shell with Knuckle
1.2 Symbol and Description
DL——Interior diameter of cylinder at big end (mm)
DS——Interior diameter of cylinder at smaller end (mm)
RL——Internal radius of cylinder at big end (mm), RL= DL
RS——Internal radius of cylinder at smaller end (mm), RS= DS
rk1, rk2——Radius of the minimum and maximum rotating corner on the transition section at offset conical shell big end (mm)
rf1, rf2——Radius of the minimum and maximum rotating corner on the transition section at offset conical shell smaller end (mm)
rk——Radius of the rotating corner on the transition section at big end (mm), adopting rk= min (rk1, rk2) (see Figure 1.1.1-2 and Figure 1.6.1 in this Standard)
rf——Radius of the rotating corner on the transition section at smaller end (mm), adopting rf= min (rf1, rf2) (see Figure 1.1.1-2 and Figure 1.6.1 in this Standard)
δ——Wall thickness of offset conical shell (including additional thickness) (mm)
δL——Thickness of big end cylinder (excluding additional thickness) (mm)
δS——Thickness of smaller end cylinder (excluding additional thickness) (mm)
δC——Thickness of conical shell (excluding additional thickness) (mm)
δj——Thickness of cylinder or rotating angle at knuckle transition section joint (excluding additional thickness) (mm) (see Figure 1.5.1-2 in this Standard)
δk——Thickness of big end transition section at rotating angle (mm)
δf——Thickness of smaller end transition section at rotating angle (mm)
δSL——Required minimum thickness of big end cylinder (mm)
δSS——Required minimum thickness of smaller end cylinder (mm)
δCC——Required minimum thickness of conical shell (mm)
α1——Maximum semiapex of offset conical shell (°), expressed in arc scale in the numerical computation with formula
α2——Minimum semiapex of offset conical shell (°), expressed in arc scale in the numerical computation with formula
α——Maximum semiapex of conical shell used in the calculation (°), adopting the larger one of α 1 and α 2, expressed in arc scale in the numerical computation with formula
LC——Projected length of conical shell (mm), adopting the length of conical shell generatrix on the side of α1 (see Figure 1.6.1 in this Standard)
Lk——Length (mm) used for the stress calculation of transition section at conical shell big end, when there is rotating angle (see Figure 1.5.1-2 in this Standard)
Lf——Length (mm) used for the stress calculation of transition section at conical shell smaller end, when there is rotating angle (see Figure 1.5.1-2 in this Standard)
Lcy——Length (mm) of cylinder transition section in the stress calculation where there is rotating angle
Lco——Length (mm) of conical shell transition section in the stress calculation where there is rotating angle
L1k——Length (mm) of conical shell transition section in the stress calculation when there is rotating angle at big end
——Length (mm) of conical shell transition section in the stress calculation when there is rotating angle at big end
L1f——Length (mm) of conical shell transition section in the stress calculation when there is rotating angle at smaller end
——Length (mm) of conical shell transition section in the stress calculation where there is rotating angle when there is rotating angle at smaller end
n——Thickness ratio of conical shell and cylinder
H——Calculating parameter
B——Calculating parameter
βcy——Geometric parameter of cylinder
βco——Geometric parameter of conical shell
βk——Angle (°) used in the calculation of conical shell transition section (expressed in arc scale in the numerical computation) when there is rotating angle at big end
βf——Angle (°) used in the calculation of conical shell transition section (expressed in arc scale in the numerical computation) when there is rotating angle at smaller end
Km——Length factor in the calculation of conical shell with knuckle, Km= 0.7
KPC——Correction factor in the stress calculation of cylinder, KPC= 1.0
KCPC——Correction factor in the stress calculation of conical shell, KCPC= 1.0
Rk——Radius from big end knuckle arc center to shell center axis (mm)
Rf——Radius from smaller end knuckle arc center to shell center axis (mm)
RC——Calculated radius considering cone angle (mm)
v——Poisson ratio, v= 0.3 for steel
φk——Angle (°) used in the calculation of transition section of conical shell with knuckle at big end (expressed in arc scale in the numerical computation)
——Angle (°) used in the calculation of conical shell transition section (expressed in arc scale in the numerical computation) when the strength is not enough at big end rotating angle
——Angle (°) used in the calculation of conical shell transition section (expressed in arc scale in the numerical computation) when the strength is not enough at big end rotating angle
——Angle (°) used in the calculation of conical shell transition section (expressed in arc scale in the numerical computation) when the strength is not enough at big end rotating angle
φf——Angle (°) used in the calculation of transition section of conical shell with knuckle at smaller end (expressed in arc scale in the numerical computation)
——Angle (°) used in the calculation of conical shell transition section (expressed in arc scale in the numerical computation) when the strength is not enough at smaller end rotating angle
——Angle (°) used in the calculation of conical shell transition section (expressed in arc scale in the numerical computation) when the strength is not enough at smaller end rotating angle
——Angle (°) used in the calculation of conical shell transition section (expressed in arc scale in the numerical computation) when the strength is not enough at smaller end rotating angle
MS——Radial force moment, at the joint of cylinder and conical shell, of the internal pressure acted on cylinder (N•mm)
MCS——Radial force moment of internal pressure acted on conical shell (N•mm)
MSN——Radial force moment acted on cylinder used for the calculation (N•mm)
QP——Shear force, at the joint of cylinder and conical shell, of the internal pressure acted on cylinder (N)
QC——Shear force of internal pressure acted on conical shell (N)
QN——Shear force of internal pressure acted on cylinder, used for the calculation (N)
NS——Radial membrane force of internal pressure acted on cylinder (N)
——Circumferential membrane force of internal pressure acted on cylinder (N)
NC——Radial membrane force of internal pressure acted on conical shell (N)
——Circumferential membrane force of internal pressure acted on conical shell (N)
p——Design pressure (MPa)
[σ]t——Allowable stress of the materials at the design temperature (MPa)
φ——Welded joint coefficient
σsm——Radial membrane stress of shell (MPa)
σsb——Radial bend stress of shell (MPa)
——Circumferential membrane stress of shell (MPa)
——Circumferential bend stress of shell (MPa)
——Radial membrane stress at the calculation position (j) of rotating angle (MPa)
——Circumferential membrane stress at the calculation position (j) of rotating angle (MPa)
1.3 Minimum Thickness of Shell
1.3.1 Required minimum thickness of cylinder shell
The required minimum thickness of big end cylinder is calculated according to formula (1.3.1-1):
Contents of HG/T 20582-2011
1 Calculation of Offset Conical Shell Subjected to Internal Pressure
2 Design and calculation of conical closure with large apex angle
3 Design of Vessels with Half Pipe Jacket
4 Design of Reducers with Knuckle and Subjected to Internal Pressure and Axial Force
5 Design and Calculation of Thin Convex Closures Subjected to Internal Pressure
6 Reinforcement for Shell with Lateral or Hillside Nozzle
7 Reinforcement for Large Opening
8 Calculation of Enhancement of Load Bearing Capacity of Cylinders with Supporting Rings and Subjected to External Pressure
9 Calculation of Equivalent Design Pressure for Flange Subjected to External Loading
10 Covered Serrated Metal Gasket
11 Design and Calculation of Welding Sealed Flange without Gasket
12 Design and Calculation of Noncircular Flange
13 Design of Clamp Connections
14 Design of Serrated Clamp Connections
15 Design of Integral Serrated Clamp Connections
16 Design and Calculation of Flanged Collar
17 Design and Calculation of High Pressure Screw Flange with Lens Shape Gasket
18 Design and Calculation of Multi Saddle Supported Horizontal Vessel
19 Design and Calculation of Lug Support with Rigid Ring
20 Design and Calculation of Circular Flat with Strengtheners
21 Calculation of Internal Pressurized Bend
22 Design and Calculation of Miter Bend (Shrimps-shaped)
23 Calculation of Welded T Joint
24 Design and Calculation of Y Shape Pipe
25 Design and Calculation of Toroidal Expansion Joint
26 Calculation of Local Stresses in Cylinder due to External Loadings
27 Calculation of Local Stresses in Spherical Shell Due to External Loadings Acting on Nozzle Or Attachment
28 Calculation of Local Stresses in Cylinder and Nozzle Due to External Loadings
29 Alternative Design Method for Flanged Connection
