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The presentation gives an introduction and general guideline for pressure vessel design by analysis.

The “design by analysis” procedures are intended to guard against eight possible pressure vessel failure modes by performing a detailed stress analysis of the vessel with the sufficient design factors. The failure modes are:

1.excessive elastic deformation, including elastic instability,

2.excessive plastic deformation,

3.brittle fracture,

4.stress rupture/creep deformation (inelastic),

5.plastic instability - incremental collapse,

6.high strain - low cycle fatigue,

7.stress corrosion, and

8.corrosion fatigue

Most of the “design by analysis” procedures that are given in ASME BPVC relate to designs based on “elastic analysis.”

The design-by-analysis requirements are organized based on protection against the failure modes listed below. The component shall be evaluated for each applicable failure mode. If multiple assessment procedures are provided for a failure mode, only one of these procedures must be satisfied to qualify the design of a component.

a)All pressure vessels within the scope of this Division, irrespective of size or pressure, shall be provided with protection against overpressure in accordance with the requirements of this Part.

b)Protection Against Plastic Collapse – these requirements apply to all components where the thickness and configuration of the component is established using design-by-analysis rules.

c)Protection Against Local Failure – these requirements apply to all components where the thickness and configuration of the component is established using design-by-analysis rules. It is not necessary to evaluate the local strain limit criterion if the component design is in accordance with Part 4 (i.e. component wall thickness and weld detail per paragraph 4.2).

d)Protection Against Collapse From Buckling – these requirements apply to all components where the thickness and configuration of the component is established using design-by-analysis rules and the applied loads result in a compressive stress field.

e)Protection Against Failure From Cyclic Loading – these requirements apply to all components where the thickness and configuration of the component is established using design-by-analysis rules and the applied loads are cyclic. In addition, these requirements can also be used to qualify a component for cyclic loading where the thickness and size of the component are established using the design-by-rule requirements of Part 4.

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- 1. DESIGN BY ANALYSIS HEDCO Spring 2009 G. Ghanbari A GENERAL GUIDELINE
- 2. Overall Design Procedure of Pressure Vessel ASME Sec VIII Div. 1 Input Data (Mechanical and Process Data Sheets) Shell Design (Thickness of Shell) under External Pressure (UG-16, 28, 31) Material Selection for Vessel Components 1. Service 2. Design Temperature (UG-23 and ASME Sec. II Tables) 3. MDMT and Impact Test (UCS-66, 67, UHA-51, UG-20 (f), UG-84) Shell Design (Thickness of Shell) under Internal Pressure (UG-16, 27, 31) Calculation of Stiffening Rings (UG-29, 30) Head Design (Thickness of Formed Head) under Internal Pressure (UG-16,32, 34) Head Design (Thickness of Formed Head) under External Pressure (UG-33, 34) Nozzle / Opening and Reinforcement Design (UG-36, 37, 38, 39, 40, 41, 42, 43, 44, 45, UW-15, 16) Calculation of Nozzle Load and Strength (WRC-107, 297) Welding Design (UW-9, 12, 13) Definition of PWHT (UW-40, UCS-56, UHA-32) Requirement for Examinations (UG-99, UW-11, 52) Support Design Skirt, Leg, etc. (Standard Drawings) Wind and Seismic Calculations for Vessel and Anchoring Design (Appendix L, UBC, ASCI-112) Design of External Attachments and Transportation Components lifting lug, Tailing lug, Piping clip (Standard Drawings) Tolerances (specification, UG-80,81) Vortex shedding, vibration analysis (Specification) Is External pressure applied YES Is External pressure applied YES NO Weight Calculations Design Review (QA procedure, Relevant Paragraphs) Cylindrical Shell YES NO NO
- 3. 0.00E+00 2.00E+07 4.00E+07 6.00E+07 8.00E+07 1.00E+08 1.20E+08 1.40E+08 1.60E+08 Div. 1 Div. 2 Div. 3 Pressure Scope Not Recommended Recommended Allowed 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 0.00E+00 2.00E+07 4.00E+07 6.00E+07 8.00E+07 1.00E+08 1.20E+08 1.40E+08 1.60E+08 Thickness/InnerRadius Pressure, Pa t/Ri Div 1 t/Ri Div 2 t/Ri Div 3 t/Ri Div 1 considering allowable stress of Div 2 PSE P R t i 6.0− = 1exp − = SE P R t i 1 2 3 exp − = yi S P R t
- 4. Introduction to DBA The “design by analysis” procedures are intended to guard against eight possible pressure vessel failure modes by performing a detailed stress analysis of the vessel with the sufficient design factors.The failure modes are: 1. excessive elastic deformation, including elastic instability, 2. excessive plastic deformation, 3. brittle fracture, 4. stress rupture/creep deformation (inelastic), 5. plastic instability - incremental collapse, 6. high strain - low cycle fatigue, 7. stress corrosion, and 8. corrosion fatigue Most of the “design by analysis” procedures that are given in ASME BPVC relate to designs based on “elastic analysis.”
- 5. Introduction to DBA The design-by-analysis requirements are organized based on protection against the failure modes listed below.The component shall be evaluated for each applicable failure mode. If multiple assessment procedures are provided for a failure mode, only one of these procedures must be satisfied to qualify the design of a component. a) All pressure vessels within the scope of this Division, irrespective of size or pressure, shall be provided with protection against overpressure in accordance with the requirements of this Part. b) Protection Against Plastic Collapse – these requirements apply to all components where the thickness and configuration of the component is established using design-by-analysis rules. c) Protection Against Local Failure – these requirements apply to all components where the thickness and configuration of the component is established using design-by-analysis rules. It is not necessary to evaluate the local strain limit criterion if the component design is in accordance with Part 4 (i.e. component wall thickness and weld detail per paragraph 4.2). d) Protection Against Collapse From Buckling – these requirements apply to all components where the thickness and configuration of the component is established using design-by-analysis rules and the applied loads result in a compressive stress field. e) Protection Against Failure From Cyclic Loading – these requirements apply to all components where the thickness and configuration of the component is established using design-by-analysis rules and the applied loads are cyclic. In addition, these requirements can also be used to qualify a component for cyclic loading where the thickness and size of the component are established using the design-by- rule requirements of Part 4.
- 6. Overall Design Procedure of Pressure Vessel ASME Sec VIII Div. 2 Vessel Design Data (Generally extracted from UDS) P>3000 psi 1-Engineering judgment 2-Client’s Specification 3-Economics YES NODiv 1 Div 2 Design By Rule Is the DBR enough? (1-Engineering judgment 2-Client’s Specification) Material Properties: E, ν, App. 3.D Material Model: Actual, Associated Plasticity, von Misses Formulation: Large Displacement Updated Lagrangian Material Properties: E, ν, Sy Material Model: Elastic perfectly Plastic Formulation: Small Displacement Total Lagrangian Material Properties: E, ν Material Model: Linear Elastic Formulation: Small Displacement Limit Load YES Vessel Design calculation Report Tentative Geometry for Analysis NO Stress Analysis Method (R/t)>4 ElasticElastic Plastic YES 1-Modify the configurations 2-Reduce applied Loads Limit Check Fig 5.1 Does the problem converge? Does the problem converge? NO NONO Specifying Vessel Areas to be Locally Evaluated YES YES Load-Control Loads Displacement-Control Loads Establishing Design Load Combinations Table 5.3 Determine of Load Parameters Table 5.2 Definition of Loading Conditions Table 5.1 Post-processing and Classification of Stresses Table 5.6 Appendix 5.A Establishing Design Load Combinations and Load Factors Table 5.4 Establishing Design Load Combinations and Load Factors Table 5.5
- 7. Overall Design Procedure of Pressure Vessel ASME Sec VIII Div. 2 (Con.) Fabrication Detail Non-Standard Standard Elastic Analysis Elastic-Plastic Analysis σ1+σ2+σ3≤4Sεpeq+εcf≤εL 1-Modify the configurations 2-Reduce applied Loads NO NO Buckling Analysis YESYES Analysis Type Bifercation Determination of Capacity Reduction Factor, βcr Determination of Minimum Design Factor, ФB Load Factors of Table 5.5 Explicit 1-Modify the configurations 2-Reduce applied Loads Probable Buckling Modes occur at loads greater than design Loads multiplied by ФB NO Does the problem converge? NO Cyclic Analysis Requirement Check YESYES
- 8. Table 5.1 – Loads and Load Cases To Be Considered in a Design Loading Condition Design Loads PressureTesting 1. Dead load of component plus insulation, fireproofing, installed internals, platforms and other equipment supported from the component in the installed position. 2. Piping loads including pressure thrust 3. Applicable live loads excluding vibration and maintenance live loads. 4. Pressure and fluid loads (water) for testing and flushing equipment and piping unless a pneumatic test is specified. 5.Wind loads NormalOperation 1. Dead load of component plus insulation, refractory, fireproofing, installed internals, catalyst, packing, platforms and other equipment supported from the component in the installed position. 2. Piping loads including pressure thrust 3. Applicable live loads. 4. Pressure and fluid loading during normal operation. 5.Thermal loads. NormalOperation plus Occasional (note: occasional loads are usually governed by wind and earthquake; however, other load types such as snow and ice loads may govern, see ASCE-7) 1. Dead load of component plus insulation, refractory, fireproofing, installed internals, catalyst, packing, platforms and other equipment supported from the component in the installed position. 2. Piping loads including pressure thrust 3. Applicable live loads. 4. Pressure and fluid loading during normal operation. 5. Thermal loads. 6. Wind, earthquake or other occasional loads, whichever is greater. 7. Loads due to wave action Abnormal or Start-up Operation plus Occasional (see note above) 1. Dead load of component plus insulation, refractory, fireproofing, installed internals, catalyst, packing, platforms and other equipment supported from the component in the installed position. 2. Piping loads including pressure thrust 3. Applicable live loads. 4. Pressure and fluid loading associated with the abnormal or start-up conditions. 5. Thermal loads. 6. Wind loads.
- 9. Table 5.2 – Load Descriptions Design Load Parameter Description P Internal and external maximum allowable working pressure Ps Static head from liquid or bulk materials (e.g. catalyst) D Dead weight of the vessel, contents, and appurtenances at the location of interest, including the following: • Weight of vessel including internals, supports (e.g. skirts, lugs, saddles, and legs), and appurtenances (e.g. platforms, ladders, etc.) • Weight of vessel contents under operating and test conditions • Refractory linings, insulation • Static reactions from the weight of attached equipment, such as motors, machinery, other vessels, and piping L • Appurtenance Live loading • Effects of fluid momentum, steady state and transient E Earthquake loads (see ASCE 7 for the specific definition of the earthquake load, as applicable) W Wind Loads Wpt Is the pressure test wind load case.The design wind speed for this case shall be specified by the Owner-User. Ss Snow Loads T Is the self-restraining load case (i.e. thermal loads, applied displacements). This load case does not typically affect the collapse load, but should be considered in cases where elastic follow-up causes stresses that do not relax sufficiently to redistribute the load without excessive deformation.
- 10. Table 5.3 – Load Case Combinations and Allowable Membrane Stresses for an Elastic Analysis Design Load Combination Allowable General Primary Membrane Stress (1),(2),(3) 1) P +Ps +D S 2) P + Ps + D + L S 3) P + Ps+ D + Ss S 4) 0.6D + (W or 0.7E) (4) S 5) 0.9P + Ps + D+ (W or 0.7E ) S 6) 0.9P + Ps + D + 0.75L + 0.75 Ss S 7) 0.9P + Ps + D + 0.75(W or 0.7E) + 0.75L + 0.75Ss S Notes 1) The parameters used in the Design Load Combination column are defined inTable 5.2. 2) The term 0.9P is considered an operating pressure. 3) S is the allowable stress for the load case combination.This value represents the general primary membrane stress limit for “load-controlled” loads. Stress limits for local membrane and bending stresses from “load-controlled” or “strain-controlled” loads are provided in paragraph 5.2.2.4. 4) This load combination addresses an overturning condition. If anchorage is included in the design, consideration of this load combination is not required.
- 11. Design Conditions Criteria Required Factored Load Combinations Global Criteria 1) 1.5 (P+ Ps+ D) 2) 1.3 (P+ Ps+ D+T ) + 1.7L + 0.54 Ss 3) 1.3 (P+ D) + 1.7Ss + max[1.1L , 0.86W] 4) 1.3 (P + D) + 1.7W + 1.1L + 0.54Ss 5) 1.3 (P + D) + 1.1E + 1.1L + 0.21Ss Local Criteria PerTable 5.5 Serviceability Criteria Per User’s Design Specification, if applicable, seeTable 5.5 Hydrostatic Test Conditions Global Criteria {max[1.43, 1.25 (ST/S)]}.(P + Ps + D) + 2.6 Wpt Serviceability Criteria Per User’s Design Specification, if applicable. Pneumatic Test Conditions Global Criteria 1.15 (ST/S).(P + Ps + D) + 2.6 Wpt Serviceability Criteria Per User’s Design Specification, if applicable. Notes: 1) The parameters used in the Design Load Combination column are defined inTable 5.2. 2) See paragraph 5.2.3.4 for descriptions of global and serviceability criteria. 3) S is the allowable membrane stress at the design temperature. 4) ST is the allowable membrane stress at the pressure test temperature. Table 5.4 – Load Case Combinations and Load Factors for a Limit Load Analysis
- 12. Design Conditions Criteria Required Factored Load Combinations Global Criteria 1) 2.4 (P+ Ps+ D) 2) 2.1 (P+ Ps+ D+T ) + 2.6L + 0.86 Ss 3) 2.1 (P+ D) + 2.6Ss + max[1.7L , 1.4W] 4) 2.4 (P + D) + 2.6W + 1.7L + 0.86Ss 5) 2.4 (P + D) + 1.7E + 1.7L + 0.34Ss Local Criteria 1.7 (P+ Ps+ D) Serviceability Criteria Per User’s Design Specification, if applicable, see paragraph 5.2.4.3.b. Hydrostatic Test Conditions Global Criteria {max[2.3, 2.0 (ST/S)]}.(P + Ps + D) +Wpt Serviceability Criteria Per User’s Design Specification, if applicable. Pneumatic Test Conditions Global Criteria 1.8 (ST/S).(P + Ps + D) +Wpt Serviceability Criteria Per User’s Design Specification, if applicable. Notes: 1) The parameters used in the Design Load Combination column are defined inTable 5.2. 2) See paragraph 5.2.4.3 for descriptions of global and serviceability criteria. 3) S is the allowable membrane stress at the design temperature. 4) ST is the allowable membrane stress at the pressure test temperature. Table 5.5 – Load Case Combinations and Load Factors for an Elastic-Plastic Analysis
- 13. Table 5.6 – Examples Of Stress Classification Vessel Component Location Origin of Stress Type of Stress Classification Any shell including cylinders, cones, spheres and formed heads Shell plate remote from discontinuities Internal pressure General membrane Gradient through plate thickness Pm Q Axial thermal gradient Membrane Bending Q Q Near nozzle or other opening Net-section axial force and/or bending moment applied to the nozzle, and/or internal pressure Local membrane Bending Peak (fillet or corner) PL Q F Any location Temperature difference between shell and head Membrane Bending Q Q Shell distortions such as out-of- roundness and dents Internal pressure Membrane Bending Pm Q Cylindrical or conical shell Any section across entire vessel Net-section axial force, bending moment applied to the cylinder or cone, and/or internal pressure Membrane stress averaged through the thickness, remote from discontinuities; stress component perpendicular to cross section Pm Bending stress through the thickness; stress component perpendicular to cross section P b Junction with head or flange Internal pressure Membrane Bending PL Q Dished head or conical head Crown Internal pressure Membrane Bending Pm P b Knuckle or junction to shell Internal pressure Membrane Bending PL [note (1)] Q Flat head Center region Internal pressure Membrane Bending Pm P b Junction to shell Internal pressure Membrane PL
- 14. Table 5.6 – Examples Of Stress Classification (Con.) Vessel Component Location Origin of Stress Type of Stress Classification Perforated head or shell Typical ligament in a uniform pattern Pressure Membrane (averaged through cross section) Bending (averaged through width of ligament., but gradient through plate) Peak Pm P b F Isolated or atypical ligament Pressure Membrane Bending Peak Q F F Nozzle (see paragraph 5.6) Within the limits of reinforcement given by paragraph 4.5 Pressure and external loads and moments including those attributable to restrained free end displacements of attached piping General membrane Bending (other than gross structural discontinuity stresses) averaged through nozzle thickness Pm Pm Outside the limits of reinforcement given by paragraph 4.5 Pressure and external axial, shear, and torsional loads including those attributable to restrained free end displacements of attached piping General Membrane Pm Pressure and external loads and moments, excluding those attributable to restrained free end displacements of attached piping Membrane Bending PL P b Pressure and all external loads and moments Membrane Bending Peak PL Q F Nozzle wall Gross structural discontinuities Membrane Bending Peak PL Q F Differential expansion Membrane Bending Peak Q Q F
- 15. Table 5.6 – Examples Of Stress Classification (Con.) Vessel Component Location Origin of Stress Type of Stress Classification Cladding Any Differential expansion Membrane Bending F F Any Any Radial temperature distribution [note (3)] Equivalent linear stress [note (4)] Nonlinear portion of stress distribution Q F Any Any Any Stress concentration (notch effect) F Notes: 1. Consideration shall be given to the possibility of wrinkling and excessive deformation in vessels with large diameter-to-thickness ratio. 2. If the bending moment at the edge is required to maintain the bending stress in the center region within acceptable limits, the edge bending is classified as Pb ; otherwise, it is classified as Q . 3. Consider possibility of thermal stress ratchet. 4. Equivalent linear stress is defined as the linear stress distribution that has the same net bending moment as the actual stress distribution.
- 16. Figure 5.1 – Stress Categories and Limits of Equivalent Stress Stress Category Primary Secondary Membrane plus Bending Peak General Membrane Local Membrane Bending Description (For examples, seeTable 5.6) Average primary equivalent stress across solid section. Excludes discontinuities and concentrations. Produced only by mechanical loads. Average equivalent stress across any solid section. Considers discontinuities but not concentrations. Produced only by mechanical loads. Component of primary equivalent stress proportional to distance from centroid of solid section. Excludes discontinuities and concentrations. Produced only by mechanical loads. Self-equilibrating equivalent stress necessary to satisfy continuity of structure. Occurs at structural discontinuities. Can be caused by mechanical load or by differential thermal expansion. Excludes local stress concentrations. 1.Increment added to primary or secondary equivalent stress by a concentration (notch). 2.Certain thermal stresses which may cause fatigue but not distortion of vessel shape. Symbol Pm PL Pb Q F Pm S SPS 1.5S PL PL+Pb 1.5S PL+Pb+Q Δ(PL+Pb+Q+F) 2Sa Design Load Operating Load SPS=max[3S, 2SY]
- 17. 0.E+00 1.E+08 2.E+08 3.E+08 4.E+08 5.E+08 6.E+08 0 0.02 0.04 0.06 0.08 0.1 0.12 Stress,Pa Strain Stress Linear Elastic Primary plus Secondary Stress Limit Primary Stress Limit 100% Primary 100% Secondary Mixed Responce Load-Control OriginalDisplacement-Control Mixed Loading δ σ=Kδ/A σ=W/(2A)σ=W/(2A) +Kδ/A
- 18. Stress Classification
- 19. THANKS FOR YOUR ATTENTION

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