GB/T 4732.3-2024 Pressure vessels design by analysis - Part 3: Formulae method
1 Scope
This document specifies the formulae method for the design of typical pressure components and structures under the action of pressure load (internal pressure or external pressure), as well as the rules for loads such as handling axial force and bending moments and thermal stresses within the specified range.
This document is applicable to typical pressure components and structures that are subjected to static loads such as pressure, axial force and bending moment, and those that are subjected to alternating loads but meet the fatigue analysis exemption clause specified in GB/T 4732.4-2024.
This document is applicable to pressure vessels specified in GB/T 4732.1-2024.
2 Normative references
The following documents contain provisions which, through reference in this text, constitute provisions of this document. For dated references, only the edition cited applies. For undated references, the latest edition of the referenced document (including any amendments) applies.
GB/T 150.2 Pressure vessels - Part 2: Materials
GB/T 150.3-2024 Pressure vessels - Part 3: Design
GB/T 151-2014 Heat exchangers
GB/T 4732.1-2024 Pressure vessels design by analysis - Part 1: General requirements
GB/T 4732.2-2024 Pressure vessels design by analysis - Part 2: Materials
GB/T 4732.4-2024 Pressure vessels design by analysis - Part 4: Stress classification method
GB/T 4732.5-2024 Pressure vessels design by analysis - Part 5: Elastic plastic analysis method
GB/T 4732.6-2024 Pressure vessels design by analysis - Part 6: Fabrication, inspection and testing and acceptance
GB/T 16749 Bellows expansion joints for pressure vessel
HG/T 20592 Steel pipe flanges (PN designated)
HG/T 20615 Steel pipe flanges (Class designated)
HG/T 20623 Large diameter steel pipe flanges (Class designated)
NB/T 47013.2 Nondestructive testing of pressure equipments - Part 2: Radiographic testing
NB/T 47013.3 Nondestructive testing of pressure equipment - Part 3: Ultrasonic testing
NB/T 47020 Type and specification for pressure vessel flanges
NB/T 47021 A-type socket-weld flange
NB/T 47022 B-type socket-weld flange
NB/T 47023 Welding neck flange
3 Terms and definitions
For the purpose of this document, the terms and definitions given in GB/T 4732.1-2024 apply.
4 Basic requirements
4.1 Stress analysis
The vessels shall be designed according to this document. For components or structural discontinuities whose design method is not given in the text of this document, such as components for which the thermal stress needs to be considered, a stress analysis shall be carried out according to Annex A.
Unless otherwise specified, when the allowable stress of a component is selected from the left side in the thick solid line in Tables B.1 to B.8 specified in GB/T 4732.2-2024, all the calculation formulae specified in this document apply; when the allowable stress of the component is selected from the right side in the thick solid line in Tables B.1 to B.8 specified in GB/T 4732.2-2024, the design criteria for components and structures whose thickness needs to be taken into account when determining the thickness, such as the connection between the large end of the conical shell and the cylinder and the radial opening of the cylindrical shell, as well as components or structures for which the buckling failure shall be considered, the design criteria shall be considered separately.
For components, structures or loads whose design criteria are not given in this document, the design method or the experimental method specified in GB/T 4732.4-2024 and GB/T 4732.5-2024 may be adopted for the stress analysis.
4.2 Exemption from stress analysis
4.2.1 In case the shape, material and load of components and structures meet the requirements of this document, and meet the requirements of either 4.2.2 or 4.2.3 as well as 4.2.4 and 4.2.5, the requirements specified in 4.1 may be exempted from stress analysis according to Annex A.
4.2.2 In case the components meet the requirements of Clauses 5, 6, 7 (except No. 6 in Table 7-2), 8, 9 and 10, the stress analysis may be exempted.
4.2.3 Based on the analysis results and actual application conditions, if it is proved that the vessels or components and structures with the same shape and load conditions can meet the analysis and design requirements, the stress analysis may be exempted.
4.2.4 The welded joints of components composed of dissimilar materials shall meet all the following requirements respectively.
a) Circumferential welded joints shall meet the following requirements:
1) in case components with unequal thickness are connected, overlay welding shall be carried out at the thinner end of the material;
2) except for the differences in wall thickness and elastic modulus, there are no other discontinuities (such as discontinuous structures);
3) shall be satisfied. Where, Sm is the allowable stress of the material, E is the elastic modulus, and the subscripts 1 and 2 represent the two materials respectively.
b) For the combination of reinforcing parts and vessel materials, the reinforcing metal and the vessel shell metal should have the same or similar allowable stress. In any case, the allowable stress of the reinforcing metal shall not be less than 80% of that of the vessel shell at the design temperature.
c) Welded joints other than those specified in a) and b) shall meet the following requirements:
1) in case components with unequal thickness are connected, overlay welding shall be carried out at the thinner end of the material;
2) shall be satisfied. Where, Sm is the allowable stress of the material, E is the elastic modulus, and the subscripts 1 and 2 represent the two materials respectively.
4.2.5 For assemblies composed of components of the same material but in different thicknesses, the butt welded joints shall meet all the following conditions:
a) in case the bus bar directions of the components are the same, the slope shall be processed at one end with thicker wall thickness or overlay welded at the side with thinner wall thickness;
b) in case the bus bar directions of the components are different, the slope shall be overlay welded on the side with thinner wall thickness.
4.3 Design of shared components
4.3.1 For vessels consisting of more than one independent or non-independent pressure chambers operating at the same or different pressures and temperatures, all components, including shared components, shall be designed based on the most severe conditions under which the components are expected to operate normally under the action of pressure and coexisting temperatures.
4.3.2 In case the operating pressure or the operating temperature on both sides of the shared component changes synchronously under any operating condition, the shared component may be designed in pressure difference or average metal temperature.
4.4 Loads
Various related loads shall be taken into account for the design of loads. The loads shall include but are not limited to those listed in 5.3.2 of GB/T 4732.1-2024, and the combined effects of loads under each operating condition shall be considered separately.
4.5 Allowable stress
Unless otherwise required, the performance parameters (mechanical and physical properties) and the allowable stresses of materials for pressure components shall be selected according to GB/T 4732.2-2024.
4.6 Welded structures
For Classes A and B welded joints of vessels (the welded joints shall be classified in accordance with the requirements of GB/T 4732.1-2024), the form of full-section penetration shall be adopted, and for Classes C and D welded joints and welded joints of jacket pressure vessels, full penetration structures shall be adopted. The welded joints shall also meet the requirements of GB/T 4732.6-2024. The basic requirements for common welded structures are shown in Annex B.
5 Internal pressure shell
5.1 General
5.1.1 This clause specifies the calculation method of the required thickness of typical pressure components, such as cylinders, conical shells, spherical shells, hemispherical heads, dish heads, elliptical heads and spherical crown heads, under internal pressure. The internal pressure is defined as the pressure acting on the concave side of a shell.
5.1.2 In case cylinders, spherical shells or conical shells are subjected to other loads except the internal pressure, the stress may be assessed according to the method specified in 5.7.
5.2 Symbols
For the purposes of Clause 5, the following symbols apply:
Di——the inner diameter of a cylinder or a head (or spherical shell), mm.
Do——the outer diameter of a cylinder or a head (or spherical shell), mm.
e——the base of a natural logarithm, e=2.71828.
Et——the elastic modulus of a material at the design temperature, MPa.
F——the axial force acting on the section of a shell, with the positive sign taken when the shell is tensioned, and the negative sign taken when the shell is compressed, N.
hi——the depth of the inner curved surface of a convex head, mm.
M——the bending moment acting on the section of a shell, N · mm.
pc——the calculation pressure, with the internal pressure as positive, MPa.
——the standard yield strength of a material at a design temperature (0.2% of non-proportional elongation strength), taken according to GB/T 4732.2-2024, MPa.
Ri——the inner radius of the spherical part of a spherical shell or a dish head, mm.
rL——the inner radius of the flanged transition zone of the large end of a conical shell, mm.
rm——the average radius of a shell, mm.
rs——the outer radius of the flanged transition zone at the small end of a conical shell, mm.
——the allowable stress of the shell material at the design temperature, taken according to GB/T 4732.2-2024 for single-layer shells, MPa.
Contents
1 Scope
2 Normative references
3 Terms and definitions
4 Basic requirements
5 Internal pressure shell
6 External pressure shells and allowable compressive stress
7 Flat covers
8 Flanges
9 Tubular heat exchanger tube sheets
10 Opening reinforcement
Annex A (Normative) Stress analysis of basic components and combined assemblies
Annex B (Informative) Welded joints
Annex C (Informative) Other recommended methods for tangent modulus
Bibliography
GB/T 4732.3-2024 Pressure vessels design by analysis - Part 3: Formulae method
1 Scope
This document specifies the formulae method for the design of typical pressure components and structures under the action of pressure load (internal pressure or external pressure), as well as the rules for loads such as handling axial force and bending moments and thermal stresses within the specified range.
This document is applicable to typical pressure components and structures that are subjected to static loads such as pressure, axial force and bending moment, and those that are subjected to alternating loads but meet the fatigue analysis exemption clause specified in GB/T 4732.4-2024.
This document is applicable to pressure vessels specified in GB/T 4732.1-2024.
2 Normative references
The following documents contain provisions which, through reference in this text, constitute provisions of this document. For dated references, only the edition cited applies. For undated references, the latest edition of the referenced document (including any amendments) applies.
GB/T 150.2 Pressure vessels - Part 2: Materials
GB/T 150.3-2024 Pressure vessels - Part 3: Design
GB/T 151-2014 Heat exchangers
GB/T 4732.1-2024 Pressure vessels design by analysis - Part 1: General requirements
GB/T 4732.2-2024 Pressure vessels design by analysis - Part 2: Materials
GB/T 4732.4-2024 Pressure vessels design by analysis - Part 4: Stress classification method
GB/T 4732.5-2024 Pressure vessels design by analysis - Part 5: Elastic plastic analysis method
GB/T 4732.6-2024 Pressure vessels design by analysis - Part 6: Fabrication, inspection and testing and acceptance
GB/T 16749 Bellows expansion joints for pressure vessel
HG/T 20592 Steel pipe flanges (PN designated)
HG/T 20615 Steel pipe flanges (Class designated)
HG/T 20623 Large diameter steel pipe flanges (Class designated)
NB/T 47013.2 Nondestructive testing of pressure equipments - Part 2: Radiographic testing
NB/T 47013.3 Nondestructive testing of pressure equipment - Part 3: Ultrasonic testing
NB/T 47020 Type and specification for pressure vessel flanges
NB/T 47021 A-type socket-weld flange
NB/T 47022 B-type socket-weld flange
NB/T 47023 Welding neck flange
3 Terms and definitions
For the purpose of this document, the terms and definitions given in GB/T 4732.1-2024 apply.
4 Basic requirements
4.1 Stress analysis
The vessels shall be designed according to this document. For components or structural discontinuities whose design method is not given in the text of this document, such as components for which the thermal stress needs to be considered, a stress analysis shall be carried out according to Annex A.
Unless otherwise specified, when the allowable stress of a component is selected from the left side in the thick solid line in Tables B.1 to B.8 specified in GB/T 4732.2-2024, all the calculation formulae specified in this document apply; when the allowable stress of the component is selected from the right side in the thick solid line in Tables B.1 to B.8 specified in GB/T 4732.2-2024, the design criteria for components and structures whose thickness needs to be taken into account when determining the thickness, such as the connection between the large end of the conical shell and the cylinder and the radial opening of the cylindrical shell, as well as components or structures for which the buckling failure shall be considered, the design criteria shall be considered separately.
For components, structures or loads whose design criteria are not given in this document, the design method or the experimental method specified in GB/T 4732.4-2024 and GB/T 4732.5-2024 may be adopted for the stress analysis.
4.2 Exemption from stress analysis
4.2.1 In case the shape, material and load of components and structures meet the requirements of this document, and meet the requirements of either 4.2.2 or 4.2.3 as well as 4.2.4 and 4.2.5, the requirements specified in 4.1 may be exempted from stress analysis according to Annex A.
4.2.2 In case the components meet the requirements of Clauses 5, 6, 7 (except No. 6 in Table 7-2), 8, 9 and 10, the stress analysis may be exempted.
4.2.3 Based on the analysis results and actual application conditions, if it is proved that the vessels or components and structures with the same shape and load conditions can meet the analysis and design requirements, the stress analysis may be exempted.
4.2.4 The welded joints of components composed of dissimilar materials shall meet all the following requirements respectively.
a) Circumferential welded joints shall meet the following requirements:
1) in case components with unequal thickness are connected, overlay welding shall be carried out at the thinner end of the material;
2) except for the differences in wall thickness and elastic modulus, there are no other discontinuities (such as discontinuous structures);
3) shall be satisfied. Where, Sm is the allowable stress of the material, E is the elastic modulus, and the subscripts 1 and 2 represent the two materials respectively.
b) For the combination of reinforcing parts and vessel materials, the reinforcing metal and the vessel shell metal should have the same or similar allowable stress. In any case, the allowable stress of the reinforcing metal shall not be less than 80% of that of the vessel shell at the design temperature.
c) Welded joints other than those specified in a) and b) shall meet the following requirements:
1) in case components with unequal thickness are connected, overlay welding shall be carried out at the thinner end of the material;
2) shall be satisfied. Where, Sm is the allowable stress of the material, E is the elastic modulus, and the subscripts 1 and 2 represent the two materials respectively.
4.2.5 For assemblies composed of components of the same material but in different thicknesses, the butt welded joints shall meet all the following conditions:
a) in case the bus bar directions of the components are the same, the slope shall be processed at one end with thicker wall thickness or overlay welded at the side with thinner wall thickness;
b) in case the bus bar directions of the components are different, the slope shall be overlay welded on the side with thinner wall thickness.
4.3 Design of shared components
4.3.1 For vessels consisting of more than one independent or non-independent pressure chambers operating at the same or different pressures and temperatures, all components, including shared components, shall be designed based on the most severe conditions under which the components are expected to operate normally under the action of pressure and coexisting temperatures.
4.3.2 In case the operating pressure or the operating temperature on both sides of the shared component changes synchronously under any operating condition, the shared component may be designed in pressure difference or average metal temperature.
4.4 Loads
Various related loads shall be taken into account for the design of loads. The loads shall include but are not limited to those listed in 5.3.2 of GB/T 4732.1-2024, and the combined effects of loads under each operating condition shall be considered separately.
4.5 Allowable stress
Unless otherwise required, the performance parameters (mechanical and physical properties) and the allowable stresses of materials for pressure components shall be selected according to GB/T 4732.2-2024.
4.6 Welded structures
For Classes A and B welded joints of vessels (the welded joints shall be classified in accordance with the requirements of GB/T 4732.1-2024), the form of full-section penetration shall be adopted, and for Classes C and D welded joints and welded joints of jacket pressure vessels, full penetration structures shall be adopted. The welded joints shall also meet the requirements of GB/T 4732.6-2024. The basic requirements for common welded structures are shown in Annex B.
5 Internal pressure shell
5.1 General
5.1.1 This clause specifies the calculation method of the required thickness of typical pressure components, such as cylinders, conical shells, spherical shells, hemispherical heads, dish heads, elliptical heads and spherical crown heads, under internal pressure. The internal pressure is defined as the pressure acting on the concave side of a shell.
5.1.2 In case cylinders, spherical shells or conical shells are subjected to other loads except the internal pressure, the stress may be assessed according to the method specified in 5.7.
5.2 Symbols
For the purposes of Clause 5, the following symbols apply:
Di——the inner diameter of a cylinder or a head (or spherical shell), mm.
Do——the outer diameter of a cylinder or a head (or spherical shell), mm.
e——the base of a natural logarithm, e=2.71828.
Et——the elastic modulus of a material at the design temperature, MPa.
F——the axial force acting on the section of a shell, with the positive sign taken when the shell is tensioned, and the negative sign taken when the shell is compressed, N.
hi——the depth of the inner curved surface of a convex head, mm.
M——the bending moment acting on the section of a shell, N · mm.
pc——the calculation pressure, with the internal pressure as positive, MPa.
——the standard yield strength of a material at a design temperature (0.2% of non-proportional elongation strength), taken according to GB/T 4732.2-2024, MPa.
Ri——the inner radius of the spherical part of a spherical shell or a dish head, mm.
rL——the inner radius of the flanged transition zone of the large end of a conical shell, mm.
rm——the average radius of a shell, mm.
rs——the outer radius of the flanged transition zone at the small end of a conical shell, mm.
——the allowable stress of the shell material at the design temperature, taken according to GB/T 4732.2-2024 for single-layer shells, MPa.
Contents of GB/T 4732.3-2024
Contents
1 Scope
2 Normative references
3 Terms and definitions
4 Basic requirements
5 Internal pressure shell
6 External pressure shells and allowable compressive stress
7 Flat covers
8 Flanges
9 Tubular heat exchanger tube sheets
10 Opening reinforcement
Annex A (Normative) Stress analysis of basic components and combined assemblies
Annex B (Informative) Welded joints
Annex C (Informative) Other recommended methods for tangent modulus
Bibliography
