Akron 1133204597
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AN OVERVIEW AND VALIDATION OF THE FITNESS-FOR-SERVICE ASSESSMENT PROCEDURES FOR LOCAL THIN AREAS A Thesis Presented to The Graduate Faculty of the University of Akron In Partial Fulfillment of the Requirements for the Degree Masters of Science – Mechanical Engineering J.L. Janelle December, 2005
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Akron 1133204597
Transcript of Akron 1133204597
AN OVERVIEW AND VALIDATION OF THE FITNESS-FOR-SERVICE ASSESSMENT
PROCEDURES FOR LOCAL THIN AREAS
A Thesis
Presented to
The Graduate Faculty of the University of Akron
In Partial Fulfillment
of the Requirements for the Degree
Masters of Science – Mechanical Engineering
J.L. Janelle
December, 2005
ii
AN OVERVIEW AND VALIDATION OF THE FITNESS-FOR-SERVICE ASSESSMENT
PROCEDURES FOR LOCAL THIN AREAS
J.L. Janelle
Thesis
Approved: Accepted:
Advisor Department Chair
Dr. Paul Lam
Dr. Celal Batur
Committee Member Dean of College
Dr. Jiang Zhe
Dr. George K. Haritos
Committee Member Dean of the Graduate School
Dr. Xiaosheng Gao
Dr. George R. Newkome
Date
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ABSTRACT
In today’s petroleum refining industry, aging infrastructure is a primary concern when
considering replacement costs and safe operation. As vessels, piping, and tankage age in
service, they are subjected to various forms of degradation or damage that may eventually
comprise structural integrity. An engineering or Fitness-For-Service (FFS) assessment is
required to evaluate structural integrity and safely extend the life of damaged equipment.
Guidelines for performing a FFS assessment have been documented in API RP 579. The goal of
API 579 is to ensure the safety of plant personnel and the public while aging equipment
continues to operate, provide technically sound Fitness-For-Service assessment procedures for
various forms of damage, and help optimize maintenance and operation of existing facilities while
enhancing long-term economic viability.
The procedures in API 579 (2000 release) provide computational methods to assess flaws
that are found in in-service equipment caused by various damage mechanisms. The focus of this
study is to review the technical basis for the Fitness-For-Service assessment procedures for
general and local metal loss. Extensive validation of these procedures along with additional
development is presented. The conclusions of the study are recommended as the best practices
to be included in future versions of API 579. The specific objectives for the study are as follows:
• Objective 1: Validate the API 579 Section 5 LTA rules in addition to the validation in WRC
465. The validation includes comparison of the API 579 methodology to other industry
method and to a database of full scale tests.
• Objective 2: Develop new or improve upon the existing methodology to increase the
accuracy of the assessment procedures and eliminate some of the limitations.
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• Objective 3: Standardize the safety margin between MAWP and failure pressure for
industry analysis methods and different Design Code margins on allowable stress.
• Objective 4: Improve the existing rules for LTAs subject to supplemental loading
(circumferential extent of the LTA).
This study is part of a series of WRC Bulletins that contain the technical background to the
assessment procedures in API 579:
• WRC 430 – Review of Existing Fitness-For-Service Criteria for Crack-Like Flaws
• WRC 465 – Technologies for the Evaluation of Erosion/Corrosion, Pitting, Blisters, Shell
Out-of-Roundness, Weld Misalignment, Bulges, and Dents in Pressurized Components
• WRC CCC – An Overview and Validation of The Fitness-For-Service Assessment
Procedures for Crack-Like Flaws in API 579 (not complete as of this printing)
• WRC 471 – Development of Stress Intensity Factor Solutions for Surface and Embedded
Cracks in API 579
• WRC 478 – Stress Intensity and Crack Growth Opening Area Solutions for Through-Wall
Cracks in Cylinders and Spheres
• WRC MMM – An Overview of the Fitness-For-Service Assessment Procedures for Weld
Misalignment and Shell Distortions in API 579 (not complete as of this printing)
• WRC PPP – An Overview of the Fitness-For-Service Assessment Procedures for Pitting
Damage in API 579 (not complete as of this printing).
This study represents a significant improvement to the current techniques available in the
public domain for the analysis of Local Thin Areas. Information is also included that can be used
to standardize the different LTA analysis techniques available in industry. However, further
research, development and testing is required to further increase the accuracy of LTA analysis
methods. The shortcomings of the assessment procedures are discussed as well as areas for
future research.
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TABLE OF CONTENTS
Page LIST OF TABLES................................................................................................................. xii LIST OF FIGURES............................................................................................................... xiv CHAPTER I. INTRODUCTION.......................................................................................................... 1 1.1 Industry Needs................................................................................................. 1 1.2 Flaw Types and Damage Mechanisms in API 579.......................................... 2 1.3 General Corrosion and Local Thin Areas (LTAs) ............................................ 3 1.4 Need for Standardized Assessment ................................................................ 3 II. LTA ASSESSMENT AND VALIDATION OVERVIEW ................................................. 5 2.1 Introduction ...................................................................................................... 5 2.2 Acceptance Criteria.......................................................................................... 6 2.2.1 Overview .......................................................................................... 6 2.2.2 Linear Elastic Allowable Stress Classification ................................. 6 2.2.3 Non-linear Elastic-Plastic Stress Criteria ......................................... 7 2.2.4 Remaining Strength Factor .............................................................. 8 2.3 Original LTA Assessment Methodology........................................................... 9 2.4 LTA Development and Validation Work........................................................... 10 2.4.1 Introduction....................................................................................... 10 2.4.2 Kiefner, et al ..................................................................................... 10 2.4.3 Stephens, Bubenik, Leis, et al.......................................................... 11 2.4.4 Coulson, Worthington....................................................................... 12
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2.4.5 Mok, Pick, Glover, Hoff .................................................................... 13 2.4.6 Chell ................................................................................................. 13 2.4.7 Hopkins, Jones, Turner, Ritchie, Last .............................................. 14 2.4.8 Kanninen, et al ................................................................................. 15 2.4.9 Chouchaoui, Pick ............................................................................. 15 2.4.10 Valenta, et al.................................................................................... 15 2.4.11 Zarrabi, et al .................................................................................... 16 2.4.12 Sims, et al ........................................................................................ 16 2.4.13 Batte, Fu, Vu, Kirkwood................................................................... 16 2.4.14 Fu, Stephens, Ritchie, Jones .......................................................... 17 2.5 ASME Section XI Class 2 and 3 Piping ........................................................... 17 2.6 Current In-Service Inspection Codes............................................................... 17 III. API 579 METAL LOSS ASSESSMENT PROCEDURES............................................. 19 3.1 Introduction...................................................................................................... 19 3.2 Multi-Level Assessment Procedure ................................................................ 20 3.3 Inspection Data Requirements........................................................................ 21 3.3.1 Point Thickness Readings ............................................................... 21 3.3.2 Critical Thickness Profiles ................................................................ 22 3.4 Assessment of General Metal Loss ................................................................ 23 3.4.1 Overview .......................................................................................... 23 3.4.2 Applicability and Limitations ............................................................. 24 3.4.3 Metal Loss Away from Structural Discontinuities............................. 25 3.4.3.1 Assessment with Point Thickness Readings................... 25 3.4.3.2 Assessment with Critical Thickness Profiles ................... 26 3.4.4 Metal Loss at Major Structural Discontinuities................................. 29 3.5 Assessment of Local Metal Loss .................................................................... 31 3.5.1 Overview .......................................................................................... 31 3.5.2 Applicability and Limitations ............................................................. 31
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3.5.3 Assessment Procedure – Circumferential Stress Direction............. 33 3.5.3.1 Overview .......................................................................... 33 3.5.3.2 API 579 Section 5, Level 1 Assessment ......................... 33 3.5.3.3 API 579 Section 5, Level 2 Assessment ......................... 34 3.5.4 Assessment Procedure – Longitudinal Stress Direction.................. 36 3.5.4.1 Overview .......................................................................... 36 3.5.4.2 API 579 Section 5, Level 1 Assessment.......................... 37 3.5.4.3 API 579 Section 5, Level 2 Assessment.......................... 38 3.5.5 Non-Cylindrical Shells ...................................................................... 41 3.5.5.1 Overview .......................................................................... 41 3.5.5.2 Spherical Shells and Formed Heads ............................... 41 3.5.5.3 Conical Shells .................................................................. 43 3.5.5.3 Elbows ............................................................................. 43 3.6 API 579 Advanced Assessment of Metal Loss ............................................... 44 3.6.1 Overview .......................................................................................... 44 3.6.2 Assessment with Numerical Analysis .............................................. 45 3.6.3 API 579, Level 3 Assessment (Lower Bound Limit Load)................ 46 3.6.4 Plastic Collapse Load....................................................................... 48 3.7 Comparison of General and Local Metal Loss ................................................ 49 3.8 Remaining Life Evaluation ............................................................................... 50 3.8.1 Overview .......................................................................................... 50 3.8.2 Thickness Approach......................................................................... 50 3.8.3 MAWP Approach.............................................................................. 51 IV. LTA ASSESSMENT PROCEDURES FOR CIRCUMFERENTIAL STRESS............... 52 4.1 Introduction...................................................................................................... 52 4.2 Calculation of Undamaged MAWP ................................................................. 52 4.3 Calculation of Undamaged Failure Pressure .................................................. 53
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4.4 Calculation of Damaged MAWP and Damaged Failure Pressure................... 55 4.5 Thickness Averaging Assessment................................................................... 57 4.5.1 Overview .......................................................................................... 57 4.5.2 API 510 Assessment (Method 8) ..................................................... 57 4.5.3 API 653 Assessment (Method 9) ..................................................... 58 4.5.4 API 579 Section 4, Level 1 and Level 2 Assessment (Methods
25 and 26) ........................................................................................
58 4.6 ASME B31.G Assessment ............................................................................... 59 4.6.1 Overview .......................................................................................... 59 4.6.2 Original ASME B31.G Assessment (Method 7) ............................... 59 4.6.3 Modified B31.G Assessment, 0.85dl Area (Method 4)..................... 62 4.6.4 Modified B31.G Assessment, Exact Area (Method 6) ..................... 64 4.7 RSTRENG Method (Method 5)........................................................................ 65 4.8 PCORR Assessment (Method 20)................................................................... 66 4.9 API 579 Assessment........................................................................................ 68 4.9.1 Overview .......................................................................................... 68 4.9.2 API 579, Level 1 Assessment (Method 1)........................................ 69 4.9.3 API 579, Level 2 Assessment, Effective Area (Method 2) ............... 69 4.9.4 API 579, Level 2 Assessment, Exact Area (Method 3).................... 70 4.9.5 API 579 Hybrid 1, Level 1 Assessment (Method 14) ....................... 70 4.9.6 API 579 Hybrid 1, Level 2 Assessment (Method 15) ....................... 71 4.9.7 API 579 Hybrid 2, Level 1 Assessment (Method 16) ....................... 72 4.9.8 API 579 Hybrid 2, Level 2 Assessment (Method 17) ....................... 72 4.9.9 API 579 Hybrid 3, Level 1 Assessment (Method 18) ....................... 73 4.9.10 API 579 Hybrid 3, Level 2 Assessment (Method 19) ...................... 74 4.9.11 API 579 Modified, Level 1 Assessment (Method 27) ...................... 74 4.9.12 API 579 Modified, Level 2 Assessment (Method 28) ...................... 75 4.10 Chell Assessment .......................................................................................... 76
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4.10.1 Overview.......................................................................................... 76 4.10.2 Chell Assessment (Method 12) ....................................................... 78 4.10.3 Modified Chell Assessment (Method 13) ........................................ 79 4.11 British Gas Assessment................................................................................. 79 4.11.1 Overview.......................................................................................... 79 4.11.2 British Gas Single Defect Analysis (Method 10) ............................. 81 4.11.3 British Gas Complex Defect Analysis (Method 11) ......................... 83 4.12 BS 7910 Assessment..................................................................................... 86 4.12.1 BS 7910, Appendix G Assessment, Isolated Defect (Method 21) .. 86 4.12.2 BS 7910, Appendix G Assessment, Interacting Flaws (Method
22)...................................................................................................
87 4.13 Kanninen Assessment (Method 23)............................................................... 87 4.14 Shell Theory Assessment (Method 24).......................................................... 89 4.15 Janelle Method............................................................................................... 90 4.15.1 Janelle Level 1 Assessment (Method 29) ....................................... 90 4.15.2 Janelle Level 2 Assessment (Method 30) ....................................... 91 V. VALIDATION OF LTA ASSESSMENT PROCEDURES FOR CIRCUMFERENTIAL
STRESS.......................................................................................................................
93 5.1 Introduction...................................................................................................... 93 5.2 Validation Databases ...................................................................................... 93 5.3 New LTA Analysis Methods ............................................................................ 94 5.3.1 API 579 Hybrid Assessment Procedures......................................... 95 5.3.2 New Folias Factor Development for Hybrid Methods ...................... 96 5.3.3 Modified API 579, Level 2 Folias Factor for Long Flaws ................. 97 5.3.4 Janelle Method................................................................................. 99 5.4 Statistical Validation of LTA Methodology Using a Failure Ratio.................... 100 5.5 Summary of Validation Results ....................................................................... 101 VI. ALLOWABLE RSF FOR DIFFERENT DESIGN CODES ............................................ 102 6.1 Introduction...................................................................................................... 102
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6.2 Design Codes for Pressurized Equipment...................................................... 102 6.3 Margin of MAWP to Failure Pressure per Design Code ................................. 105 6.4 Allowable RSF Results.................................................................................... 105 VII. LTA ASSESSMENT PROCEDURES FOR LONGITUDINAL STRESS ...................... 106 7.1 Introduction...................................................................................................... 106 7.2 Kanninen Assessment Method ....................................................................... 106 7.3 Thickness Averaging....................................................................................... 106 7.3.1 API 510............................................................................................. 107 7.3.2 API 653............................................................................................. 107 7.4 API 579 Assessment Methods......................................................................... 107 7.4.1 API 579 Section 5, Level 1 Analysis ................................................ 107 7.4.2 API 579 Section 5, Level 2 Analysis ................................................ 107 7.4.3 Modified API 579 Section 5, Level 2 Analysis.................................. 107 7.4.4 Janelle, Level 1 Analysis.................................................................. 108 7.4.5 Janelle. Level 2 Analysis.................................................................. 112 VIII. VALIDATION OF LTA ASSESSMENT PROCEDURES FOR LONGITUDINAL
STRESS.......................................................................................................................
116 8.1 Introduction...................................................................................................... 116 8.2 Validation Databases ...................................................................................... 116 8.3 Summary of Validation Results ....................................................................... 117 IX. LTA PROCEDURES FOR HIC DAMAGE.................................................................... 118 9.1 Introduction...................................................................................................... 118 9.2 Subsurface HIC Damage ................................................................................ 118 9.3 Surface Breaking HIC Damage....................................................................... 120 X. LTA PROCEDURES FOR EXTERNAL PRESSURE .................................................. 123 XI. CONCLUSIONS AND RECOMMENDATIONS............................................................ 125 11.1 Introduction .................................................................................................... 125 11.2 LTA Assessment Procedures for Circumferential Stress .............................. 125
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11.2.1 Recommended Methods for Circumferential Stress ....................... 125 11.2.2 Allowable Remaining Strength Factors ........................................... 126 11.3 Recommended Methods for Longitudinal Stress........................................... 126 11.4 Further LTA Assessment Development......................................................... 127 11.4.1 Material Toughness Effects............................................................. 127 11.4.2 Stress Triaxiality from LTAs ............................................................ 128 11.4.3 Rules for LTAs Near Structural Discontinuities ............................... 128 XII. NOMENCLATURE ....................................................................................................... 129 XIII. TABLES........................................................................................................................ 134 XIV. FIGURES ..................................................................................................................... 224 REFERENCES..................................................................................................................... 258
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LIST OF TABLES
Table Page
1 Stress Classification ................................................................................................ 134 2 Examples of Stress Classification ........................................................................... 135 3 Thickness Averaging for In-Service Inspection Codes............................................ 138 4 Section Properties for Computation of Longitudinal Stress in a Cylinder with a
LTA ..........................................................................................................................
139 5 LTA Assessment Methods....................................................................................... 141 6 Validation Cases for the Undamaged Failure Pressure Calculation Method.......... 143 7 Parameters for a Through-Wall Longitudinal Crack in a Cylinder Subject to a
Through-Wall Membrane and Bending Stress ........................................................
144 8 LTA Database 1 Case Descriptions ........................................................................ 145 9 LTA Database 2 Case Descriptions ........................................................................ 147
10 LTA Database 3 Case Descriptions ........................................................................ 147
11 LTA Database 4 Case Descriptions ........................................................................ 148
12 FEA Results for a Cylindrical Shell with a LTA........................................................ 149
13 FEA Results for a Spherical Shell with a LTA ......................................................... 150
14 API 579 Folias Factor Values for a Cylinder and a Sphere..................................... 151
15 Cases Omitted from Statistics ................................................................................. 153
16 Stress Limits Based on Design Codes .................................................................... 154
17 Stress Limits Based on Design Codes .................................................................... 157
18 MAWP Ratio vs. Allowable Stress for ASME Section VIII, Division 1 (Pre 1999) and ASME B31.1 (Pre 1999) ...................................................................................
158
19 MAWP Ratio vs. Allowable Stress for ASME Section VIII, Division 1 (Post 1999)
and ASME B31.1 (Post 1999) .................................................................................
163
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20 MAWP Ratio vs. Allowable Stress for ASME Section VIII, Division 2 and ASME B31.3........................................................................................................................
168
21 MAWP Ratio vs. Allowable Stress for the New Proposed ASME Section VIII,
Division 2 .................................................................................................................
173
22 MAWP Ratio vs. Allowable Stress for CODAP........................................................ 178
23 MAWP Ratio vs. Allowable Stress for AS 1210 and BS 5500................................. 183
24 MAWP Ratio vs. Allowable Stress for ASME B31.4 and ASME B31.8, Class 1, Division 2 .................................................................................................................
188
25 MAWP Ratio vs. Allowable Stress for ASME B31.8, Class 1, Division 1 ................ 193
26 MAWP Ratio vs. Allowable Stress for ASME B31.8, Class 2.................................. 198
27 MAWP Ratio vs. Allowable Stress for ASME B31.8, Class 3.................................. 203
28 MAWP Ratio vs. Allowable Stress for ASME B31.8, Class 4.................................. 208
29 MAWP Ratio vs. Allowable Stress for API 620........................................................ 213
30 MAWP Ratio vs. Allowable Stress for API 650........................................................ 218
31 Geometry Parameters for the Circumferential Extent Validation Cases ................. 223
32 Circumferential Extent Validation Results ............................................................... 223
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LIST OF FIGURES
Figure Page
1 Logic Diagram for the Assessment of General or Local Metal Loss in API 579 ..... 224 2 Logic Diagram for the Assessment of Local Thin Areas in API 579 ....................... 225 3 Coefficient of Variation for Thickness Reading Data
(a) Small Variability in Thickness Profiles and the COV (b) Large Variability in Thickness Profiles and the COV..............................................................................
226 4 Examples of an Inspection Grid to Define the Extent of Metal Loss Damage ........ 227 5 Establishing Longitudinal and Circumferential Critical Thickness Profiles from an
Inspection Grid (a) Inspection Planes and Critical Thickness Profile (b) Critical Thickness Profile (CTP) – Longitudinal Plane (Projection of Line M) (c) Critical Thickness Profile (CTP) – Circumferential Plane (Projection of Line C) .............................................
228 6 Critical Thickness Profiles for Isolated and Multiple Flaws
(a) Isolated Flaw (b) Network of Flaws...................................................................
229 7 Zone for Thickness Averaging in a Nozzle.............................................................. 230 8 LTA to Major Structural Discontinuity Spacing Requirements in API 579............... 231 9 Example of a Zone for Thickness Averaging at a Major Structural Discontinuity ... 232
10 Level 1 Assessment Procedure for Local Metal Loss I Cylindrical Shells (Circumferential Stress)...........................................................................................
233
11 Determination of the RSF for the Effective Area Procedure
(a) Subsection for the Effective Area Procedure (b) Minimum RSF Determination ..........................................................................................................
234
12 Exact Area Integration Bounds................................................................................ 235
13 Supplemental Loads for a Longitudinal Stress Assessment ................................... 236
14 Assessment Locations and Parameters for a Longitudinal Stress Assessment (a) Region of Local Metal Loss Located on the Inside Surface (b) Region of Local Metal Loss Located on the Outside Surface..................................................
237
15 Longitudinal Stress, Level 1 Screening Curve ........................................................ 238
16 BG Depth Increment Approach ............................................................................... 238
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17 Table Curve 3D Fit of the Shell Theory Folias Factor ............................................. 239
18 Comparison Between Analysis Methods and FEA Trends for a Cylinder with a LTA ..........................................................................................................................
239
19 3D Solid FEA Model Geometry of a Cylinder for λ = 5............................................ 240
20 Axisymmetric FEA Model Geometry of a Cylinder for λ = 5.................................... 240
21 Table Curve 2D Fit of the Modified API 579 Folias Factor ...................................... 241
22 Comparison of the Old API 579 Folias Factor to the Modified Folias Factor and
the Original Folias Factor ........................................................................................
241
23 Screening Curve for the Circumferential Extent of an LTA ..................................... 242
24 Comparison of the Old API 579 Level 1 Screening Curve to the Modified API 579 Folias Factor Level 1 Screening Curve ...................................................................
243
25 Axisymmetric FEA Model Geometry of a Sphere for λ = 5 ..................................... 244
26 Comparison Between Analysis Methods and FEA Trends for a Sphere with a
LTA ..........................................................................................................................
244
27 Table Curve 3D Plot of the Janelle Method............................................................. 245
28 RSFA vs. MAWP Ratio for ASME Section VIII, Division 1 (Pre 1999) and ASME B31.1 (Pre 1999) for the Modified API 579 Assessment (Method 28) ....................
246
29 RSFA vs. MAWP Ratio for ASME Section VIII, Division 1 (Post 1999) and ASME
B31.1 (Post 1999) for the Modified API 579 Assessment (Method 28) ..................
246
30 RSFA vs. MAWP Ratio for ASME Section VIII, Division 2 and ASME B31.3 for the Modified API 579 Assessment (Method 28) ......................................................
247
31 RSFA vs. MAWP Ratio for the New Proposed ASME Section VIII, Division 2 for
the Modified API 579 Assessment (Method 28) ......................................................
247
32 RSFA vs. MAWP Ratio for CODAP for the Modified API 579 Assessment (Method 28) .............................................................................................................
248
33 RSFA vs. MAWP Ratio for AS 1210 and BS 5500 for the Modified API 579
Assessment (Method 28).........................................................................................
248
34 RSFA vs. MAWP Ratio for ASME B31.4 and ASME B31.8, Class 1, Division 2 for the Modified API 579 Assessment (Method 28).................................................
249
35 RSFA vs. MAWP Ratio for ASME B31.8, Class 1, Division 1 for the Modified API
579 Assessment (Method 28)..................................................................................
249
36 RSFA vs. MAWP Ratio for ASME B31.8, Class 2 for the Modified API 579 Assessment (Method 28).........................................................................................
250
37 RSFA vs. MAWP Ratio for ASME B31.8, Class 3 for the Modified API 579
Assessment (Method 28).........................................................................................
250
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38 RSFA vs. MAWP Ratio for ASME B31.8, Class 4 for the Modified API 579 Assessment (Method 28).........................................................................................
251
39 RSFA vs. MAWP Ratio for API 620 for the Modified API 579 Assessment
(Method 28) .............................................................................................................
251
40 RSFA vs. MAWP Ratio for API 650 for the Modified API 579 Assessment (Method 28) .............................................................................................................
252
41 Maximum Bending Factor as a Function of the Radius to Thickness Ratio............ 252
42 Screening Curve for the Circumferential Extent of a LTA ....................................... 253
43 Longitudinal Stress Folias Factor ............................................................................ 254
44 Subsurface HIC Damage
(a) Subsurface HIC Damage – Actual Area (b) Subsurface HIC Damage – Area Modeled as an Equivalent Rectangle......................................................................
255
45 Surface Breaking HIC Damage (a) Surface Breaking HIC Damage – Actual Area (b) Surface Breaking HIC Damage – Area Modeled as an Equivalent Rectangle ...........................................
256
46 Idealized Geometry for a LTA Subject to External Pressure................................... 257
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CHAPTER I
INTRODUCTION
1.1 INDUSTRY NEEDS
Most US design codes and standards for pressure containing equipment do not
adequately address degradation and damage during operation. In the pressure vessel and
pipeline industries, surface flaws are major limiting factors of vessel or pipe life, and this type of
degradation due to age and aggressive environment eventually threatens the structural integrity
of equipment. Replacing vessel and piping equipment is expensive, making it cost effective and
desirable to operate slightly damaged equipment. For corrosion beyond a specified limit or other
damage mechanism like cracking, a Fitness-For-Service (FFS) assessment is required.
A FFS assessment is a quantitative engineering evaluation to determine the structural
integrity of equipment containing a flaw or damage. The American Petroleum Institute (API)
Recommended Practice (RP) 579 [1] is a comprehensive document for evaluating common flaws
and damage in pressure vessels, piping, and tankage. The guidelines presented in API 579 may
also be used in other industries as long as the applicability and limitations for an assessment are
satisfied. API 579 is intended to supplement and expand upon the requirements in the inspection
codes NBIC [2], API 510 [3], API 570 [4], and API 653 [5]. The goals are to ensure an acceptable
margin of safety, provide accurate remaining life predictions, and help optimize maintenance and
inspection for damaged equipment still in operation. The focus of this study is to further develop
and validate the rules for assessing metal loss or corrosion damage in API 579.
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1.2 FLAW TYPES AND DAMAGE MECHANISMS IN API 579
Various types of flaws can occur in piping systems and pressure vessels due to
environmental and in-service factors. API 579 addresses the following geometric flaws and
damage mechanisms:
• Brittle Fracture: Brittle fracture is the susceptibility of a material to form crack-like flaws or
experience a catastrophic failure typically at lower temperatures.
• General Metal Loss: General metal loss is a uniform reduction in wall thickness caused
by corrosion and is one of the simplest defects to assess.
• Local Metal Loss: Local metal loss or Local Thin Areas (LTAs) are similar to general
metal loss. The geometry of these defects is more complex than general metal loss and
includes most types of isolated metal loss that can occur in pipe and vessel walls.
• Pitting: Pitting corrosion is closely related to local metal loss and is characterized by large
numbers of small pits in a given area of pipe or vessel wall. The damage can be
assessed with the same rules that are provided for LTAs with a few additional
requirements.
• Blisters and Laminations: Blisters most often appear in equipment that is in some form of
hydrogen service. Hydrogen molecules impregnate the steel, forming high-pressure
bubbles of hydrogen gas or blisters in the vessel wall. Laminations occur during the steel
plate manufacturing process and are a plane of non-fusion in the interior of the steel
plate. Blisters may also be evaluated with the analysis methodology provided for LTAs
with additional requirements.
• Weld Misalignment and Shell Distortion: Weld misalignment is an offset of plate
centerlines that occurs in the longitudinal or circumferential weld joints of vessels during
the vessel fabrication process. Shell distortion usually occurs during fabrication and is
the result of improperly rolled shell plates.
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• Crack-Like Flaws: Crack-like flaws can have widely varying geometry and are caused by
multiple mechanisms. Rules are provided for analyzing crack-like flaws as they are, or
grinding them out and treating them like a LTA.
• Creep Damage: Creep damage occurs mostly in high temperature service and is a
relation between time, temperature, stress, and excessive strain. This damage can also
lead to cracks and crack growth.
• Dents and Gouges: Dents and gouges are forms of damage usually resulting from
mechanically cold working a material. These defects are similar to shell distortions and
LTAs respectively, but additional requirements must be met to prevent brittle fracture.
1.3 GENERAL CORROSION AND LOCAL THIN AREAS (LTAS)
Local thin areas appear in several different geometries. The first is isolated areas of general
corrosion. These "patches" of corrosion are areas of isolated uniform corrosion in a pipe or
vessel wall and are characterized by a non-varying flaw thickness profile. Areas of local metal
loss are similar to general metal loss but may have extreme variations in the flaw thickness
profile. Isolated pits are another classification of local thin area that have a circular shape and
are usually smaller than areas of general corrosion. Combinations of general metal loss, local
metal loss, and pitting can give rise to an infinite number of local thin area geometries. General
pitting, blisters, and gouges can also be thought of as local thin areas and assessed using similar
analysis methods. Likewise, a crack-like flaw may be ground out and the resulting groove
evaluated like a LTA. With many types of common defects being classified as local thin areas,
the importance of finding a reliable analysis method is evident.
1.4 NEED FOR STANDARDIZED ASSESSMENT
Currently there are twenty-five different methods compiled in this study for analyzing local
thin areas in pipes and vessels. These analysis methods all have roots in various industries,
codes, and standards. In industry, at least five of these methods are actively used in Fitness-For-
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Service assessments today. This can make communication difficult between parties using
different assessment procedures, and some parties may be using methods with low accuracy or
reliability. Depending on the assessment code that is used, assessment results may vary
drastically. One standardized set of analysis guidelines is needed to eliminate confusion
regarding which method should be used. The focus of this study is to find the most statistically
accurate and reliable method currently available and to validate the guidelines in API 579.
5
CHAPTER II
LTA ASSESSMENT AND VALIDATION OVERVIEW
2.1 INTRODUCTION
Determining the Fitness-For-Service or safe operating pressure of corroded equipment is
not yet an exact science. As such, assessment accuracy is extremely important. In an attempt to
improve reliability, researchers have implemented test programs involving full-scale burst tests
and finite element analysis of corroded pipes and vessels. With the data collected from test
programs, many different methods and acceptance criteria for analyzing LTAs have evolved.
The questions are: which of these methods are the most accurate and can the accuracy be
further improved? In an attempt to answer these questions, large databases of burst tests and
finite element analysis have been compiled in this study from various sources. The cases in
each database are analyzed with each of analysis methods available in the public domain and
some newly developed methods. Statistical analysis of the various Fitness-For-Service
assessment methods will provide the best gage for measuring the accuracy of each method.
Alterations to the current API 579 Fitness-For-Service guidelines will be recommended
based on the findings of this study. The current procedures for inspection and analysis of an LTA
from the document are presented in later sections. The assessment methods in API 579 will be
validated and compared to all other closed formed methods presented in this study. The
validated assessment methods will be used with various construction codes, and code based
assessment guidelines will be developed and included in API 579. This will allow standardized
assessment of components designed to different construction codes.
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2.2 ACCEPTANCE CRITERIA 2.2.1 Overview
Depending of the type of mechanical analysis being performed, different acceptance criteria
have been developed for various failure modes to insure safety in a given design. For example, a
primary concern in the design of a vacuum tower is buckling of the shell wall due to external
pressure. To prevent this type of failure, structural stability criteria have been developed for use
with buckling analysis for equipment with large compressive stresses. There are other types of
acceptance criteria such as fatigue initiation used to evaluate components subject to cyclical
loading, and similarly, creep-fatigue initiation criteria used for components exposed to cyclical
loading in the creep regime. One of the most widely used acceptance criterion is stress criteria.
Stress criteria are limits placed on stresses generated in a given component due to geometry,
loading, damage (such as an LTA), or other conditions and is based on material properties of the
component at a given temperature. The two types of stress criteria that are relevant to a LTA
assessment are linear elastic stress classification and non-linear elastic-plastic stress evaluation.
A separate approach for evaluating a LTA is the Remaining Strength Factor (RSF) criteria. With
the RSF approach, the load carrying capacity of a damaged component is compared to the load
carrying capacity of the undamaged component to calculate a reduction in strength. Either linear
elastic stress or RSF criteria are used for the closed form assessment procedures presented in
this report. Non-linear elastic-plastic stress criteria is most commonly used for advanced
(numeric) analysis of a LTA, but other criteria for fatigue, buckling, creep, or any other failure
mode may also be used.
2.2.2 Linear Elastic Allowable Stress Classification
For LTAs a quantity known as stress intensity can be computed and compared to an
allowable value of stress intensity. Stress intensity is a measure of stress derived from a yield
criterion. Two yield criteria to establish stress intensity are recommended by API 579. Maximum
7
yield stress intensity is equal to twice the maximum shear stress which is equal to the difference
between the largest and smallest principle stress as follows:
max 1 2 2 3 3 12 max , ,S τ σ σ σ σ σ σ= = − − − (1)
The other yield criterion is maximum distortion energy. This is the preferred criteria and is
also known as the Von Mises equivalent stress.
( ) ( ) ( )0.52 2 2
1 2 2 3 3 112von MisesS σ σ σ σ σ σ σ = = − + − + − (2)
Determination of structural integrity is based on a comparison between calculated stress
intensity and the allowable stress intensity of the material.
There are five stress intensity categories based on location and origin of the stress field.
The five categories and their associated limits along with the tri-axial stress limits are shown in
Table 1. Examples of stress classification based on component, location, and loading is provided
in Table 2. Establishment of the allowable stress intensity for structural integrity comparison is
based on the design code used to construct the component. A detailed description of the design
codes and associated allowable stress intensities can be found in Paragraph 6.2.
2.2.3 Non-linear Elastic-Plastic Stress Criteria
Non-linear elastic-plastic stress criteria typically provide a better prediction of safe load
carrying capacity for a component. Traditional linear elastic stress classification and allowable
stress criteria make only a rough estimate of failure loads because they ignore non-linear
phenomenon that may occur in component failure. Non-linear elastic plastic analysis takes into
account geometric, material, and combined non-linearity directly, to develop plastic collapse
loads. Plastic collapse loads are defined as the maximum load where material response is
elastic-plastic including strain hardening and large displacement effects. Closed form solutions
for plastic collapse loads are not readily available, so numerical techniques such as Finite
Element Analysis (FEA) may be used to obtain a solution. The calculated stress intensity for limit
8
or plastic collapse loads can be compared to allowable stress intensities to determine a
component’s structural integrity. The concept of plastic collapse load can be used to develop a
simplified strength factor for LTAs called the Remaining Strength Factor.
2.2.4 Remaining Strength Factor
The Remaining Strength Factor (RSF) has been introduced to define the acceptability for
continued service of components containing a flaw in terms non-linear elastic plastic stress
criteria. For a LTA analysis, plastic collapse loads can be calculated using FEA or full scale burst
tests. The RSF was originally proposed by Sims [6] to evaluate LTAs and is defined as:
{ }{ }
Collapse Load of Damaged ComponentRSF
Collapse Load of Undamaged Component= (3)
Acceptance criteria can be established using the RSF in combination with traditional code
formulas, elastic stress analysis, limit load theory, or elastic-plastic analysis, depending on
complexity of the assessment. The RSF is the value calculated by many of the assessment
procedures presented in API 579. Each of the LTA assessment methods presented in this study
has been reworked in terms of the RSF where possible for ease of comparison. Detailed
procedures for calculating the RSF for each analysis method are found in Paragraphs 4.6
through 4.14. The RSF can be used to calculate either the failure pressure or the Maximum
Allowable Working Pressure (MAWP) of damaged components. The calculation for determining
the failure pressure of damaged equipment is:
0fP P RSF= ⋅ (4)
The MAWP is slightly different and can be calculated using the RSF and an allowable RSF
as follows:
0 aa
RSFMAWP MAWP for RSF RSFRSF
= <
(5)
9
0 aMAWP MAWP for RSF RSF= ≥ (6)
In a Fitness-For-Service assessment, the calculated RSF is compared to an allowable value.
If the calculated RSF is greater than the allowable, the component may be returned to service. If
the calculated RSF is less than the allowable, the component may be derated using Equation (5).
The recommended value for the allowable remaining strength factor that is currently in API 579 is
0.9 for equipment in process services. This value can be overly conservative or un-conservative
based on the design code used in construction, type of loading, or consequence of failure. One
of the objectives of this study is to standardize the amount of conservatism in the determination of
a damaged MAWP for different design codes and assessment methods. This will be achieved by
tuning the allowable RSF so that a fixed margin on MAWP to failure pressure is maintained
regardless of design code.
2.3 ORIGINAL LTA ASSESSMENT METHODOLOGY
Before specific LTA assessment procedures were developed, regions of metal loss in were
assessed using thickness averaging techniques. The origins of this method are unclear,
although some guidelines still use these procedures which have been shown to be greatly
conservative. To improve the assessment techniques for corroded pipelines, additional criteria
was developed in the late 1960’s and early 1970’s through research sponsored by Texas Eastern
Transmission Corporation and the AGA pipeline research committee. The criterion was
incorporated into ASME B31.4 and B31.8 piping design codes and is commonly referred to as the
B31.G [7] assessment criteria. The B31.G criteria are based on a fracture mechanics
relationship developed by the AGA NG-18 Line Pipe Research Committee. The relationship was
introduced by Maxey [8] and is based on a Dugdale plastic zone model, a Folias [9] bulging factor
for a through wall crack in a cylindrical shell, and a flaw depth to thickness relationship. A series
of corroded pipe burst tests were performed by Kiefner [10] to demonstrate the relationship
between the remaining strength of pipes with and without LTAs. The B31.G method is the
10
foundation for most of the local thin area assessments that are currently in use. Details of the
original B31.G calculation procedure are presented in Paragraph 4.6.2.
2.4 LTA DEVELOPMENT AND VALIDATION WORK 2.4.1 Introduction
Since initial development of local thin area assessment in the late 1960’s, many other
groups and individuals have conducted research related to this topic. Twenty-five analysis
methods developed by various authors are contained in this study for general LTAs, and many
more methods exist for analyzing specific cases. In addition to new development work, much
effort has gone into validating the existing methods and comparing the methods to determine
which is the most accurate. The following paragraphs have a brief summary of the validation and
development work that is available in the public domain.
2.4.2 Kiefner, et al
Kiefner [11], [12], [13], [14], [15], [16], [17] has published multiple papers with other authors
on the subject of local thin area assessments for pipes. Contained in the papers from the late
1960’s and early 1970’s is the basis for most of today’s assessment procedures, in addition to a
large number of corroded pipe burst test cases that were used to validate the developed
methodology. Kiefner also contributed to the development of techniques that improved upon the
basic procedure, including the RSTRENG [18] (see Paragraph 4.7) method and software analysis
tool.
11
2.4.3 Stephens, Bubenik, Leis, et al
Bubenik [19] showed that finite element analysis can be used to predict the load carrying
capacity of corroded pipes. Comparisons between FEA and over 80 burst tests showed that
failure stresses were well over yield. It was also concluded that load redistribution is dependent
on geometry and strain hardening and is more significant for small deep corroded regions than
for large corrosion regions.
Stephens [20] conducted research with full scale testing and FEA on the failure of corroded
pipe subjected to internal pressure and axial loading. For pipe defects subjected only to internal
pressure, defect width was of secondary importance to defect length and depth. For pipe defects
subject to combined axial and pressure loads, defect width is significant, and results indicated
that axial loads increased the combined von Mises stress in the pipe, resulting in lower failure
pressure. Interaction of separated defects was also examined. The interaction of separated
defects is dependant on the defect size. Small defects have small interaction length and large
defects have large interaction lengths. Axial spaced defects increase the stresses when
compared to an isolated defect, which may decrease failure pressure. Circumferentially spaced
defects decrease the stresses when compared to an isolated defect, which may increase failure
pressure. This study was also used in the development of PCORR. The PCORR analytic model
uses traditional finite element analysis applied to local thin areas in pipelines.
Stephens [21] compared some of the prominent LTA assessment methods to determine the
most accurate method. Methods used in the comparison were B31.G, modified B31.G,
RSTRENG, Chell, Kanninen, Ritchie, Sims, and API 579. Conclusions showed the API 579
method to have the least variability. The modified B31.G, RSTRENG, and Chell methods also
had small variability.
Stephens [22], [23], [24], [25], [26] has investigated the fundamental mechanisms driving
failure of pipeline corrosion defects. The research involved three phases: development of an
analytic model known as PCORR, comparative evaluation of material and defect geometry
variables controlling failure, and development of a simple closed form failure assessment
12
method. A parametric study with PCORR was used to identify variables that influence failure in
moderate to high toughness pipe. The variables are ranked according to the magnitude of their
influence as follows:
1. Internal pressure
2. Vessel or pipe diameter
3. Flaw depth and wall thickness
4. Ultimate material strength
5. Defect Length
6. Defect shape and characteristics
7. Yield strength and strain hardening characteristics
8. Defect Width
9. Fracture toughness
The authors observed that pipes with low material toughness may fail at stresses below
ultimate stress. This could be caused by crack initiation at the base of corrosion defects,
resulting in failure pressures below the fully ductile prediction. PCORR was also used to develop
a closed form solution for analyzing corrosion defects. The method is fully described in
Paragraph 4.8 and is called the PCORR Assessment Method.
2.4.4 Coulson, Worthington
Coulson and Worthington [27], [28] examined spirally oriented local thin areas and the
interaction spacing between adjacent local thin areas. A full-scale burst test program was used
in the study. Axial oriented flaws were compared to spiral flaws of equal length, and it was found
that the spirally oriented flaws were less severe. A factor was developed that scaled the severity
of spiral flaws to axial flaws of equal length. Failure pressure for spiral flaws is determined by
calculating the failure pressure of an equivalent axial flaw and multiplying the result by the spiral
factor. Additionally, general rules for the interaction of adjacent defects were developed as
follows:
13
• Flaws may interact in the axial direction if the separation between them is less than or
equal to the length of the shortest flaw.
• Flaws may interact in the circumferential direction if the separation between them is less
than or equal to the width of the narrowest flaw.
• Spiral flaws may interact if the separation between them along the spiral direction is less
than or equal to the length.
• Spiral flaws separated by at least 12 inches normal to the spiral direction are not
expected to interact.
• For the assessment of interacting flaws, assessment of the individual components is also
necessary.
The burst tests to verify these rules consisted of four spiral flaw tests, two axial flaw tests,
three axial spaced flaw tests, one spirally spaced flaw test, and two circumferentially spaced flaw
tests. Further validation of this method was performed by British Gas.
2.4.5 Mok, Pick, Glover, Hoff
Mok, Pick, Glover, and Hoff [29], [30] examined the effects of long external corrosion by
expanding on the work by Coulson and Worthington. Their objective was to develop a less
conservative approach for evaluating long and long spiral flaws. Using previous tests and FEA
analysis, the authors developed a burst pressure criterion for those types of flaws based on an
orientation angle with respect to the circumferential plane of a cylindrical shell.
2.4.6 Chell
In the original B31.G assessment methodology, a Folias factor is calculated based on a non-
dimensional length parameter for the LTA. The Folias factor is used with the flaw profile to
calculate a surface correction factor and subsequent acceptance criterion. Chell [31] developed
14
an alternate form for the surface correction factor for LTA assessments. Details of the Chell
surface correction factor are presented in Paragraph 4.10.1.
2.4.7 Hopkins, Jones, Turner, Ritchie, Last
Hopkins and Jones [32] performed experimental tests to examine long flaws, interactions of
slots, interaction of small and moderate size flaws, and short deep flaws contained in a larger
shallow flaw. The experiments were performed in 24 inch pipe and included the following tests.
• Long slots: 4 cases
• Ring slots: 4 cases
• Short flaws and pits: 9 cases
• Interaction of medium flaws: 9 cases
• Short, deep flaws in a larger shallow flaw: 6 cases
Jones, Turner, and Rithcie [33] performed FEA tests to examine plane stress failures (infinite
length flaw) in 36 inch pipe. The authors were able to show that the failure sequence for the
flaws were as follows.
• Yielding of the thinned section
• Full plastic behavior of the thinned section.
• Bending stresses exceeding yield develop in the undamaged section adjacent to the
thinned section.
• Ductile failure occurs in the thinned section
Ritchie and Last [34] developed a calculation procedure to calculated the failure pressure of
a corroded shell based on the original B31.G equations. The authors modified the procedure to
remove some of the conservatism and take into account ultimate strength and strain hardening
for the damaged component.
15
2.4.8 Kanninen, et al
Kanninen [35], [36], [37], [38] and others developed methodology to analyze the failure of
LTAs subject to supplemental loading. As part of the research, full scale failure tests were
performed to study the behavior of a LTA defect in a cylindrical shell that fails due to an applied
net section bending moment. The assessment methodology developed by Kanninen is the bases
for the evaluation of the circumferential (longitudinal stress) profile of a LTA. The details of his
assessment method are presented in Paragraphs 4.13 and 7.2.
2.4.9 Chouchaoui, Pick
Chouchaoui and Pick [39], [40], [41], [42], [43], [44] investigated the behavior of isolated or
closely spaced corrosion flaws oriented circumferentially or longitudinally in pipe. The study
included full scale burst tests and FEA of the test cases. For isolated flaws, it was shown that the
B31.G and RSTRENG methods result in reasonable characterization of the damage. It was also
concluded that longitudinally aligned pits within a certain spacing decreases the failure pressure
of the pipe.
2.4.10 Valenta, et al
Valenta [45], [46] developed a Finite Element Analysis model and a theoretical model for
evaluating corrosion defects in gas transmission pipelines. The models were compared to the
B31.G assessment and experimental verification. It was concluded that the FEA model would
more accurately predict failure in corroded gas transmission pipelines than the ASME B31.G
assessment method.
16
2.4.11 Zarrabi, et al
Zarrabi [47] has presented methodology for assessing the integrity of cracked, eroded, or
corroded vessels, tubes, or pipe. The methodology involves Finite Element models of cylindrical
shells with part through rectangular slots. Plastic collapse pressures from the FEA are reported
for a wide range of shells and slots through the use of non-dimensional parameters.
Zarrabi [48] has developed methodology for assessing locally thin boiler tubes. By using
elastic-plastic Finite Element Analysis models of boiler tubes with local thinning, a procedure is
presented to calculate primary stress in the thinned section. The primary stress combined,
material properties of the boiler tube, and operating conditions are used to calculate the creep
and plastic lives of the boiler tube.
2.4.12 Sims, et al
Sims [49], [50] was responsible for developing the RSF acceptability criterion for LTAs as
described in Paragraph 2.2.4. In addition the authors reviewed existing methodology and
developed modified rules for evaluating LTAs and groove-like flaws.
2.4.13 Batte, Fu, Vu, Kirkwood
Batte, Fu, Vu, and Kirkwood [51], [52] undertook a British Gas group sponsored project to
improve the assessment of corroded pipelines, resulting in the BG assessment methods.
Included in that study are numerous full-scale pipe burst tests and FEA models. The burst tests
were performed on high strength steel pipes with machined single or adjacent local thin areas.
The full scale burst tests were reproduced with FEA models and the numeric results were
compared to the actual results. The BG methods are presented in Paragraph 4.11 and the
databases are presented in Paragraph 5.2.
17
2.4.14 Fu, Stephens, Ritchie, Jones
Fu, Stephens, Ritchie, Jones [53] are the authors of the most current publication from the
Pipeline Research Council. In the document, the original B31.G, modified B31.G, RSTRENG,
and British Gas (BG) closed form methods for assessing local thin areas are compared. The
study did not include the methodology currently in API 579. The cases are validated with full
scale tests which are included in Database 1 and Database 3 of this report. The study
recommends using the B31.G method for analyzing low toughness pipes and the RSTRENG and
BG methods for high toughness pipes based on statistical analysis of the burst pressures
predicted by the different methods. The BG methods (10 and 11) presented in this report have
been expanded on to include methodology for analyzing groups of closely spaced local thin
areas. Some spacing criteria is presented, but the method is still largely empirical.
2.5 ASME SECTION XI CLASS 2 AND 3 PIPING
The ASME Section XI [54], [55], [56], group on pipe flaw evaluation is currently developing
requirements for analytical evaluation of pipe wall thinning. The evaluation involves two separate
assessments for a LTA in a pipe, elbow, or reducer. The first assessment is a thickness
evaluation to determine if the minimum wall thickness is acceptable for internal pressure loads.
The second is a stress evaluation to determine if primary and secondary loads cause stress that
exceeds the material allowable limits specified by the code of construction.
2.6 CURRENT IN-SERVICE INSPECTION CODES
Current in-service inspection codes for pressure vessels, piping, and tankage in the refinery
and petrochemical industries contain assessment guidelines to evaluate LTAs. Although these
rules have been in existence for many years, they are empirically based and do not have a sound
technical background that is required to extend current limitations. A summary of the existing
rules for the API 510, API 653, API 570, and NBIC inspection codes is shown in Table 3. These
18
rules are based on average measured thickness data over a prescribed length. The advantages
and limitations of thickness averaging are discussed in Chapter 3. As an alternative, the in-
service inspection codes provide an option for evaluation by stress analysis. In this option,
assessment results are evaluated using the ASME Boiler and Pressure Vessel Code, Section
VIII, Division 2, Appendix 4 (Hopper diagram). This option provides flexibility in the analysis but
becomes difficult to apply because the categorization procedure in Appendix 4. However, results
may be arbitrary due to stress classification with the Hopper diagram.
19
CHAPTER III
API 579 METAL LOSS ASSESSMENT PROCEDURES
3.1 INTRODUCTION
The Fitness-For-Service (FFS) assessment procedures proposed in API 579 were
developed to provide a standardized assessment methodology for inspectors, plant engineers,
and engineering specialists. The rules include classification, limitations, and acceptance criteria
for different types of metal loss. The option to calculate a derated MAWP based on the extent of
damage is also provided. The procedures are valuable for extending the life of damaged
equipment, setting inspection intervals, or determining the remaining life of damaged equipment.
Most in-service inspection codes and standards use a thickness averaging procedure to
evaluate areas of metal loss. API 579 includes modified thickness averaging rules as well as
specific LTA analysis methodology to be consistent with the inspection standards. Therefore,
metal loss is divided into two categories in API 579. General metal loss includes regions of
corrosion or erosion that have uniform or non-uniform remaining thickness. The rules for
evaluating general metal loss are presented in Section 4 of API 579. Local Metal Loss includes
regions of metal loss that have a non-uniform thickness and more detailed assessment rules are
used to provide an accurate result. The rules for evaluating local metal loss are presented in
Section 5 of API 579. The difference between general and local metal loss assessments has to
do with the amount and type of data that is required for the assessment. For general metal loss,
point thickness readings or detailed thickness profiles are required. For local metal loss, detailed
thickness profile information, which involves thickness readings and their spacing, is required.
20
The assessment procedures for general metal loss in API 579 are based on a thickness
averaging approach similar to other existing codes and provide a suitable result when applied to
uniform metal loss. For local areas of metal loss, the thickness averaging approach may still be
used; however, the results will be overly conservative. For these cases, the API 579 assessment
procedures for local metal loss can be used to reduce the conservatism in the analysis. The local
metal loss rules may also be used to evaluate general metal loss, but the amount of inspection
data and complexity of the analysis is greater. The distinction between general and local metal
loss is difficult to make without detailed knowledge of the metal loss profile, so the rules in API
579 have been structured to provide consistent results between the two methods. It is
recommended that a simpler general metal loss assessment be initially performed for either type
of metal loss. If the results are not satisfactory, an assessment using the local metal loss rules
can be used for a less conservative estimate.
3.2 MULTI-LEVEL ASSESSMENT PROCEDURE
Three levels of assessment are provided in API 579 for each flaw and damage type. In
general, each assessment level has a balance between degree of conservatism, the amount of
information required to perform the assessment, the skill of the personnel performing the
assessment and the complexity of the analysis. A logic diagram is included in each section to
illustrate how these assessment levels are interrelated. The overall logic diagram for assessing
general or local metal loss is shown in Figure 1, and the logic diagram for evaluating local metal
loss specifically is shown in Figure 2. Level 1 is the most conservative, but is easiest to use.
Practitioners usually proceed sequentially from a Level 1 to a Level 3 assessment (unless
otherwise directed by the assessment techniques) if the current assessment level does not
provide an acceptable result or a clear course of action cannot be determined. A general
overview of each assessment level and its intended use are described below:
• Level 1: The assessment procedures included in this level provide conservative
screening criteria that require a minimum amount of inspection or component information.
21
The Level 1 assessment procedures are intended for use by either plant inspection or
engineering personnel.
• Level 2: The assessment procedures included in this level provide a more detailed
evaluation that is less conservative than those from a Level 1 assessment. In a Level 2
assessment, inspection information similar to that required for a Level 1 assessment is
required; however, more detailed calculations are used in the evaluation. Level 2
assessments are intended for use by plant engineers or engineering specialists
experienced and knowledgeable in performing FFS assessments.
• Level 3: The assessment procedures included in this level provide the most detailed
evaluation that produces results that are less conservative than those from a Level 2
assessment. In a Level 3 assessment additional inspection and component information
is typically required, and the recommended analysis is based on numerical techniques
such as finite element analysis. The Level 3 assessment procedures are intended for
use by engineering specialists experienced and knowledgeable in performing FFS
evaluations.
3.3 INSPECTION DATA REQUIREMENTS 3.3.1 Point Thickness Readings (PTR)
There are two inspection techniques that may be used when characterizing a region of metal
loss. Point Thickness Readings (PTR) are a random sampling of thickness measurements in a
corroded region. PTR are only suitable for assessments where the variation in thickness
readings is statistically small. The test for significance in the variability is based on the
Coefficient of Variation (COV) of the thickness reading population. The COV is defined as the
standard deviation of a sample divided by the mean of a sample. As shown in Figure 3, if the
COV of the thickness reading population is small, then the variability in thickness readings is
small. Alternatively, if the variability in thickness readings is large, so is the COV. If the COV of
the thickness reading population minus the Future Corrosion Allowance (FCA) is less than 10%,
22
then the general metal loss is defined to be uniform and the average thickness can be computed
directly from the population of thickness readings. If the COV is greater than 10%, then the use
of thickness profiles is required to determine the average thickness. PTR data may only be used
for an API 579 Section 4 general metal loss assessment. As recommended in API 579, if point
thickness readings are used in an assessment, the assumption of general metal loss should be
confirmed considering the following:
• A minimum of 15 thickness readings is recommended unless the level of NDE utilized
can be used to confirm that the metal loss is general. In some cases, additional readings
may be required based on the size of the component, the construction details utilized,
and the nature of the environment resulting in the metal loss.
• Additional inspection may be required such as visual examination, radiography or other
NDE methods.
3.3.2 Critical Thickness Profiles (CTP)
The other technique for characterizing metal loss is by using a Critical Thickness Profile
(CTP). If possible, it is recommended that CTPs are always used for the assessment of metal
loss. They are required for a detailed API 579 Section 5 local metal loss assessment and may
also be used for an API 579 Section 4 general metal loss assessment. In addition the CTPs are
better for inspections records if continued damage is expected. If the COV test for point
thickness readings is greater than 10%, then the general metal loss is defined to be non-uniform
and the use of thickness profiles is required. An inspection grid covering the region of metal loss
is typically required to determine the extent of the damage. Examples of inspection grids used to
map the metal loss damage on a cylinder, cone, and elbow are shown in Figure 4. Once the
inspection grids have been established and the thickness readings are taken, the Critical
Thickness Profiles (CTPs) can be determined. The CTPs in the longitudinal and circumferential
directions are required for the assessment. The process to establish the CTP is shown in Figure
5. The longitudinal and circumferential CTPs are found by taking the lowest readings along the
23
lines designated by Mi and Ci, respectively, as noted in the figure. This establishes the maximum
metal loss or minimum thickness readings in the region of damage by using a "river bottom"
approach. Once the minimum thicknesses along all of the lines identified with Mi and Ci lines are
taken, these values are projected onto longitudinal and circumferential planes, respectively, to
form the CTP in these directions as shown in Figure 5. In the figure, the dimension s is the length
of the longitudinal CTP and the dimension c is the length of the circumferential CTP. The spacing
of the CTPs is the spacing of the thickness grid in the longitudinal and circumferential directions.
This process can be used for both isolated and multiple flaws as shown in Figure 6.
3.4 ASSESSMENT OF GENERAL METAL LOSS 3.4.1 Overview
The API 579 Section 4 assessment procedures can be used to evaluate uniform and non-
uniform metal loss on the outside diameter or inside diameter of a component. The results
obtained for general metal loss may be overly conservative for flaws with significant thickness
variations. To account for this, an initial screening can be performed using general metal loss
guidelines, and an additional assessment may be performed using local metal loss guidelines if
the component does not meet the general metal loss criteria.
Two procedures for evaluating general metal loss away from structural discontinuities are
provided based on the type of inspection data available. One procedure uses Point Thickness
Readings (PTR) and the other uses Critical Thickness Profiles (CTP). Point thickness readings
should be used in assessments where variance in thickness readings is small. Critical thickness
profiles are suited to handle all types of assessment. It is recommended that CTPs be used
whenever possible. Acceptability for both methods is determined from a strength criterion
dictated by the original construction code, and each has criteria to ensure against leakage. If the
strength criterion is not satisfied, rules are provided to determine the MAWP of pressurized
components or the maximum fill height for atmospheric storage tanks. Procedures are also
24
provided to establish an inspection interval based on a remaining life assessment, or to specify a
future corrosion allowance for continued operation.
A different procedure is required for metal loss at structural discontinuities. Structural
discontinuities include nozzles and branch connections, axisymmetric discontinuities such as
stiffening rings, piping systems which have thickness interdependency, or any other structural
component that affects the shell stiffness in the region of metal loss. The current assessment
methodology defines a zone of interaction between the shell and discontinuity. Acceptance for
the region of metal loss is established by determining an average thickness for each component
in the interaction zone and using the average thickness with the original design code equations
for each component and the interdependency of the two.
3.4.2 Applicability and Limitations
The following are the limitations and applicability for the Level 1 and Level 2 assessment
procedures specified in API 579.
• The component must be designed and constructed in accordance with a recognized
code or standard. This insures construction to a standard quality level and requires
normal scheduled inspections.
• The component must not be operating in the creep range. The assessment guidelines
presented here have not been validated for these conditions, although they may be
applicable. Accumulated creep strains usually become concentrated in reduced stiffness
regions. Stiffness reduction is a function of wall thickness, flaw geometry, material
properties, and load conditions. These effects have not yet been addressed, so this type
of assessment may not be conservative for these conditions.
• The region of metal loss must have relatively smooth contours without notches, crack-like
flaws, or other locations of stress concentration. Notches and other areas of stress
concentration may lead to cracking or brittle fracture, which is not considered in this type
of assessment. Similarly, the material of the component must have sufficient material
25
toughness. The local metal loss rules do not apply to materials that may be embrittled
due to temperature or operating environment
• The component is not subject to cyclic service. Fatigue screening guidelines in API 579
are separate from a general LTA assessment. The cut-off for cyclic service in API 579 is
150 cycles.
These limitations result in an acceptable level of conservatism when performing this type of
assessment.
Limitations based on loading conditions are also included. Internal pressure, maximum fill
height, or supplemental loads must be governed by equations that relate the load to a required
wall thickness. A summary of load limitations in API 579 for each assessment level are given as
follows.
• Level 1 assessments are applicable to internal or external pressure only
• Level 2 assessments may have internal or external pressure and/or supplemental
loading from weight and occasional loads
• Level 3 assessment can be performed when any of the above limitations are not satisfied
or for any load conditions.
3.4.3 Metal Loss Away from Structural Discontinuities 3.4.3.1 Assessment with Point Thickness Readings
The acceptance criteria for metal loss can be determined once the average and minimum
thicknesses have been established. The Level 1 Assessment criteria are shown below.
minamt FCA t− ≥ (7)
limmmt FCA t− ≥ (8)
Where the minimum permissible thickness for pressure vessels and piping is
[ ]lim minmax 0.5 , 0.10t t inches= (9)
26
and the minimum permissible thickness for tanks is
[ ]lim minmax 0.6 , 0.10t t inches= (10)
The Level 2 Assessment criteria are shown below.
minam at FCA RSF t− ≥ ⋅ (11)
limmmt FCA t− ≥ (12)
The minimum permissible thickness, tlim, is evaluated using Equations (9) and (10). If the
component fails the above criteria, a damaged MAWP can be determined by substituting the
average thickness back into the original design equations as long as the minimum thickness
requirement is satisfied. For example, for a cylindrical shell subjected to internal pressure, the
MAWP could be determined as follows using a typical design equation.
( )( )
10.6a am
a am
t FCAMAWP
RSF R t FCAσ −
= ⋅+ −
(13)
The Level 1 calculation does not include the allowable RSF. The MAWP with inclusion of
the allowable RSF may not be higher than the original calculated MAWP.
3.4.3.2 Assessment with Critical Thickness Profiles
To perform a thickness averaging assessment with CTPs, the length for thickness
averaging, L, is computed using the following equations.
minL Q Dt= (14)
0.5211.123 1
1t
t a
RQR RSF
− = − −
(15)
min
amt
t FCARt−
= (16)
27
The Q factor is actually derived from the API 579, section 5 assessment rules for regions of
local metal loss and can be thought of as a conservative screening method for local metal loss.
A remaining strength factor based on the remaining thickness ratio and the flaw length is
calculated as follows:
( )11 1t
tt
RRSFR
M
=− −
(17)
21 0.48tM λ= + (18)
1.285 lDt
λ = (19)
min
mmt
t FCARt−
= (20)
In the above equations, l is the length of the local thin area based on the CTP. By setting
the RSF equal to the allowable RSF and solving for l, conservative screening criteria can be
derived which relates the length for thickness averaging to the remaining thickness ratio as
follows:
1.285 lDt
λ = (21)
2
1 0.48 1.285tlMDt
= +
(22)
2
111 0.7926
ta
t
RRSF RlDt
=−
−
+
(23)
Solving for l or the length for thickness averaging yields:
28
2
11.262 11
t
t
a
Rl Dt RRSF
− = − −
(24)
Setting l equal to L and factoring out Q yields the following:
L Q Dt= (25)
0.52
11.123 11
t
t
a
RQ RRSF
− = − −
(26)
When the thickness averaging rules are applied to an area of metal loss that is an actual
LTA, the length for thickness averaging will be small because a small Rt ratio produces a small Q
value. This small length for thickness averaging when centered on the minimum thickness
reading will produce a small average thickness that subsequently results in a small or
conservative MAWP. The rules of API 579 have been structured to direct the user to the LTA
assessment procedures for these cases. Alternatively, when the LTA has a high remaining
thickness ratio, the value of Q becomes larger thus increasing the length for thickness averaging.
When this longer length is centered on the minimum thickness reading value, a large average
thickness and corresponding MAWP will result. This MAWP will approach the value that would
be obtained using the LTA assessment procedures. The consistency in the rules is guaranteed
because the length for thickness averaging given by Equation (14) is derived by substituting
RSFa for RSF in equation (35) and solving for l; the resulting value of l is then set to the length for
thickness averaging, L.
After the length for thickness averaging, L, is determined, the assessment is completed
based on the relative values of s and L:
• s > L the local metal loss assessment rules can be used for the evaluation
• s < L the general metal loss rules are used for the evaluation
29
When using the general metal loss rules, the average thickness for both the meridional and
circumferential planes must be considered. The average thickness in the meridional direction,
tsam, is determined by averaging the thickness readings within the dimension s over the length L,
and the average thickness is in the circumferential direction, tcam, is determined by averaging the
thickness readings within the dimension c over the length L. The minimum thickness is based on
the minimum thickness reading in the grid.
In a Level 1 assessment, tam = tsam for cylindrical shells because the only loading permitted is
internal pressure. For spheres and formed heads, the average thickness is taken as
tam=max[tsam, tcam].
In a Level 2 assessment, tsam and tcam are used directly in the analysis to account for
supplemental loads. For cylindrical shells, the acceptance criterion for the average thickness is
the same as specified in Paragraph 3.4.3.1 except Equation (11) is replaced with the following
equations.
mins Cam at FCA RSF t− ≥ ⋅ (27)
minc Lam at FCA RSF t− ≥ ⋅ (28)
For spherical shells and formed heads the assessment criterion is identical to the cylindrical
shell methodology. The only difference is how tmin is calculated. If the component fails the
specified criteria, a damaged MAWP can be determined as described in Paragraph 3.4.3.1.
3.4.4 Metal Loss at Major Structural Discontinuities
One advantage the general metal loss rules have over the local metal loss rules is that they
allow the assessment of metal loss at structural discontinuities. Examples of structural
discontinuities include local erosion and/or corrosion at vessel nozzle and piping branch
connections, internal tray support rings, stiffening rings, conical shell transitions, and flanges. In
the current edition of API 579, general and local areas of metal loss at structural discontinuities
are evaluated by determining an average thickness within a thickness averaging zone, and using
30
the thickness with the original construction code design rules to determine acceptability for
continued service. Design rules for components at a major structural discontinuity typically
involve satisfying a local reinforcement requirement (e.g. nozzle reinforcement area), stress
requirement based upon a given load condition, geometry, and thickness configuration (e.g.
flange design). These rules typically have a component with thickness that is dependent upon
the thickness of another component. To evaluate components with thickness interdependency,
the MAWP should be computed based upon the average measured thickness minus the future
corrosion allowance including the thickness required for supplemental loads for each component
using the equations in the original construction code. The calculated MAWP should be equal to
or exceed the design MAWP.
The average thickness of the region can be obtained as follows for components with
thickness interdependency as described in API 579.
• Nozzles and branch connections: The average measured thickness is determined as the
average of the thickness readings taken within the nozzle reinforcement zone as shown
in Figure 7.
• Axisymmetric Structural Discontinuities: Determine L using Equation (14) and Lv based
on the type of structural discontinuity as shown in Figures 8 and 9. The average
thickness is computed based on the smaller of these two distances. If L < Lv, the
midpoint of L should be located where the wall thickness is equal to tmm to establish a
length for thickness averaging unless the location of tmm is within L/2 of the zone for
thickness averaging. In this case, L should be positioned so that it is entirely within Lv to
compute the average thickness.
• Piping Systems: Piping systems have thickness interdependency because of the
relationship between the component thickness, piping flexibility, and the resulting stress.
For straight sections of piping, determine L using the procedure described above and
compute the average thickness to represent the section of pipe with metal loss in the
piping analysis. For elbows or bends, the thickness readings should be averaged within
the bend and a single thickness used in the piping analysis (i.e. to compute the flexibility
31
factor, system stiffness and stress intensification factor). For branch connections, the
thickness should be averaged within the reinforcement zones for the branch and header,
and these thicknesses should be used in the piping model (to compute the stress
intensification factor). An alternative assumption is to use the minimum measured
thickness to represent the component thickness in the piping model. This approach may
be warranted if the metal loss is localized; however, this may result in an overly
conservative evaluation.
3.5 ASSESSMENT OF LOCAL METAL LOSS 3.5.1 Overview
The local metal loss assessment rules are used to evaluate regions of metal loss resulting
from erosion/corrosion, mechanical damage such as grooves and gouges, blend ground areas
used to remove crack-like flaws, and the damage associated with pitting and blisters. The local
metal loss assessment rules may only be used with CTP data. These procedures use the
concept of an RSF for acceptance criteria, and contain separate rules for evaluating the
longitudinal and circumferential stress direction of a flaw in cylindrical shells.
The local metal loss rules are divided into rules for evaluating the circumferential stress
direction or longitudinal profile of an LTA and the longitudinal stress direction or circumferential
profile of an LTA. The circumferential stress assessment is used to evaluate LTAs in equipment
subject to internal pressure only where circumferential stresses dominate. The longitudinal
stress assessment is used to evaluate LTAs in equipment subject to internal pressure and
supplemental loads that may cause the longitudinal stresses to effect the flaw behavior. As in the
rules for general metal loss, two levels of assessment are provided.
32
3.5.2 Applicability and Limitations
The applicability and limitations of Level 1 and Level 2 local metal loss assessment
procedures have the same limitations as those described for general metal loss in Paragraph
3.4.2. In addition, the following limitations must be satisfied for an API 579 Section 5 LTA
assessment.
• A Level 1 assessment may only be used for components subject to internal pressure
• A Level 2 assessment may only be used for components subject to internal pressure or
cylinders subject to internal pressure and supplemental loads
• The length of a LTA may not exceed the following limitation for a Level 2 assessment.
3.891l Dt≤ (29)
• The assessment must be performed using CTP inspection data. PTR inspection data
may not be used.
• The assessment may not be used to evaluate components subjected to external
pressure.
• Local metal loss rules are currently limited to flaws that meet the following minimum wall
thickness criteria. The minimum measured wall thickness may not be less than 20% of
the original wall thickness or less than 0.1 inches
min
mmt
t FCARt−
= (30)
0.2tR ≥ (31)
0.10mmt FCA inches− ≥ (32)
• The local metal loss may not be near a structural discontinuity. If an LTA fails the
following criterion, the rules provided for analyzing regions of general metal loss near a
structural discontinuity in Paragraph 3.4.4 may be used.
min1.8msdL Dt≥ (33)
33
• The assessment is currently limited to the following components: cylindrical, conical,
spherical, elliptical, and torispherical shell sections away from structural discontinuities or
junction and head attachment locations. (See Paragraph 3.5.5)
• The assessment for longitudinal stress is only applicable to cylindrical shell sections.
3.5.3 Assessment Procedure – Circumferential Stress Direction 3.5.3.1 Overview
Due to geometry and loading of cylindrical shells, different assessment criteria are provided
in API 579 based on the stress direction. For most LTAs in cylindrical shaped shells, the
circumferential direction is limiting because hoop stresses are typically twice that of longitudinal
stresses. As a result, almost all LTA research and development has been concentrated on the
circumferential stress direction. This approach is valid for most cases where only pressure
loading is evaluated. If supplemental loads are included in the assessment, then the longitudinal
stress direction should be taken into consideration.
Two levels of assessment are provided for regions classified as local metal loss. The region
of metal loss is approximated as a simple rectangular section encompassing the critical thickness
profile for a Level 1 assessment. Level 2 uses an iterative process that slices the critical
thickness profile of the region of metal loss into subsections. Each subsection is evaluated, and
acceptance is based on the limiting subsection. These assessment methods may also be
applied to groove-like flaws and gouges. Additional geometric limitations are required for groove-
like flaws, and additional material limitations are required for gouges.
3.5.3.2 API 579 Section 5, Level 1 Analysis
A Level 1 assessment is based on a simple rectangular approximation for the area of metal
loss. This method may be overly conservative for flaws with significant variations in the critical
34
thickness profile or for groups of flaws that are closely spaced. The following procedure is
presented in API 579 for the Level 1 local metal loss assessment.
• Step 1: Determine the critical thickness profile as described in Paragraph 3.3.2.
• Step 2: Determine the minimum required thickness. For a cylinder, the minimum
required thickness for the circumferential stress direction is:
min 0.6cPRt
SE P=
− (34)
• Step 3: Check the restrictions covered in Paragraph 3.5.2.
• Step 4: Calculate an RSF as follows:
( )11 1t
tt
RRSFR
M
=− −
(35)
min
mmt
t FCARt−
= (36)
21 0.48tM λ= + (37)
1.285 lDt
λ = (38)
The above equations can be represented in graphical form by plotting the metal loss
damage parameter against the remaining thickness ratio. The resulting plot is shown in Figure
10. This plot can be considered as a failure assessment diagram for local metal loss. The
MAWP for the damaged component may also be calculated using the RSF and Equations (5) and
(6).
3.5.3.3 API 579 Section 5, Level 2 Assessment
In the Level 2 assessment, the remaining strength of an LTA is evaluated using an
incremental approach. The length limitation for an LTA can be expressed in terms of lambda as
follows.
35
5.0λ ≤ (39)
If the above limitation is satisfied, then the RSF can be computed using the following steps.
The procedure is also presented in a standard format in Paragraph 4.9.3.
• Steps 1 – 3: Use the same procedure as Steps 1 – 3 detailed in Paragraph 3.4.3.2.
• Step 4: Implement the incremental procedure as follows:
– Rank the thickness readings in ascending order based on metal loss.
– As shown in Figure 11, set the initial evaluation starting point, s1, as the location of
maximum metal loss, this is the location in the thickness profile where tmm is
recorded; subsequent starting points should be in accordance with the ranking in
Step 1.
– At the current evaluation starting point, subdivide the thickness profile into a series
of subsections. The number and extent of the subsections should be chosen
based on the desired accuracy and should encompass the variations in metal loss.
– For each subsection, compute the Remaining Strength Factor using the following
equation where the term Ai is the area of metal loss associated with si (see Figure
12). The bulging factor for a cylindrical shell given by Equation (41) is based on the
original work by Folias.
1
11
i
ioi
i
i it o
AA
RSFA
M A
− =
−
(40)
( ) ( )( ) ( ) ( )
0.52 4
2 46
1.02 0.4411 0.0006124
1.0 0.02642 1.533 10
i iit i i
Mλ λ
λ λ−
+ + = + +
(41)
mini ioA s t= (42)
36
( )ie
is
li
l
A d x dx= ∫ (43)
• Step 5: Determine the minimum value of the Remaining Strength Factor, RSFi, for all
subsections (see Figure 11). This is the minimum value of the Remaining Strength
Factor for the current evaluation point.
• Step 6: Repeat Steps 3 through 5 of this calculation for the next evaluation point which
corresponds to the next thickness reading location in the ranked thickness profile list.
• Step 7: The Remaining Strength Factor to be used in the assessment, RSF, is the
minimum value determined for all evaluation points.
• Step 8: The MAWP for the damaged component may also be calculated using the RSF
and Equations (5) and (6).
3.5.4 Assessment Procedures – Longitudinal Stress Direction 3.5.4.1 Overview
Pressure vessels and piping are frequently subjected to significant axial and bending loads
as well as internal pressure. At this point there are no industry-accepted criteria for performance
of blunt defects under combined pressure and axial loads. To address this shortcoming, a simple
beam bending formulation is used to evaluate the longitudinal stress in cylinders due to
supplemental loads. Rules to evaluate net-section loads on cylindrical shells and pipes using
conventional elastic bending theory are provided in API 579. It is assumed in the methodology
that plane sections remain plane and that the pipe does not ovalize or distort during bending.
Section properties of net cross-sectional area and section modulus are computed based upon
uniform depth metal loss in the circumferential plane. In the event that the longitudinal stress is
compressive, a buckling check is also performed.
Supplemental loads applicable to a Level 2 assessment are shown in Figure 13. A level 1
assessment is a graphical representation of the Level 2 assessment procedure with
37
supplemental loads set to zero (internal pressure only). For a Level 2 assessment, two load
cases, weight and weight plus thermal, must be considered. The weight case includes load
controlled loads. The weight plus thermal case includes displacement controlled loads.
Acceptability is established by satisfying the von Mises equivalent stress criteria for two
critical stress locations on the cylinder cross section. The von Mises stress was used based on
the observation of full scale burst tests that ruptured due to a net section bending moment. It was
observed that flaws under the same loads failed differently depending on if the flaw was on the
tension or compression side of the pipe. The phenomenon follows the von Mises bi-axial stress
envelope. The points A and B are the critical assessment locations as shown in Figure 14.
Circumferential regions of non-uniform metal loss can be analyzed by bounding the area of metal
loss with a rectangular area. This method insures conservative results; for less conservative
results, a Level 3 assessment is required.
3.5.4.2 API 579, Section 5, Level 1 Assessment
The current API 579 Section 5, Level 1 assessment for the circumferential extent of a LTA is
a graphical procedure based on two parameters. The first parameter in the ratio of the
circumferential flaw length to the cylinder diameter and the second is the remaining thickness
ratio. The screening curve was developed using the Level 2 rules with the following
assumptions:
• The circumferential extent of the LTA can be approximated with a rectangular area
• The component was designed correctly with an allowable stress equal to two-thirds yield.
One-half of this stress was allocated for the longitudinal stress due to pressure and one-
half was allocated to a bending moment that causes maximum tension on the LTA. All
other end loads are assumed to be equal to zero.
• The graph is based on the maximum controlling radius to thickness ratio that varied from
5 to 1000 in the analysis.
• The curve is based on an allowable remaining strength factor of 0.9.
38
The actual curve was generated by back calculating remaining strength factors of 0.9 with a
range of circumferential flaw to diameter ratios and remaining thick ratios. The Level 1 screening
curve is shown in Figure 15.
3.5.4.3 API 579, Section 5, Level 2 Assessment
The Level 2 assessment procedure for longitudinal stress can be used to determine the
acceptability of the circumferential extent of a flaw in a cylindrical or conical shell subject to
pressure and/or supplemental loads. These types of loads may result in a net section axial force,
bending moment, torsion, and shear being applied to the cross section of the cylinder containing
the flaw. Supplemental loads will result in longitudinal membrane, bending, and shear stresses
acting on the flaw, in addition to the longitudinal and circumferential (hoop) membrane stress
caused by pressure.
The supplemental loads should include loads that produce both load-controlled and
displacement-controlled effects. Therefore, the net section axial force, bending moment, torsion,
and shear should be computed for two load cases; weight and weight plus thermal. The weight
load case includes pressure effects, weight of the component, occasional loads from wind or
earthquake, and other loads, which are considered as load-controlled. The weight plus thermal
load case includes the results from the weight case plus the results from a thermal case which
includes the effects of temperature, support displacements, and other loads which are considered
as displacement-controlled.
Longitudinal stresses are calculated using an elastic bending model for a beam with
cylindrical cross section subject to axial force and bending moment. The circumferential extent of
the flaw is approximated with a rectangular box bounding the circumferential critical thickness
profile. The cylinder section modulus in the beam equations is then modified to exclude the
bounding box area in the longitudinal stress calculation. Circumferential stresses are calculating
using a code equation with an increase in stress based on the RSF calculated to account for
bulging effects generated by the LTA. The API 579, Section 5, Level 2 assessment for the
39
circumferential stress direction as shown in Paragraph 3.5.3.3 is used to calculate the RSF. The
Level 2 assessment procedures are as follows:
• Step 1: For the circumferential inspection plane being evaluated, approximate the
circumferential extent of metal loss on the plane under evaluation as a rectangular
shape. for a region of local metal loss located on the inside surface,
( )2f o mmD D t FCA= − − (44)
and for a region of local metal loss located on the outside surface:
( )2f i mmD D t FCA= + − (45)
The circumferential angular extent of the region of local metal loss is:
180 ( )
f
c in DegreesD
θ θπ
=
(46)
• Step 2: Compute the section properties of a cylinder with and without a region of local
metal loss using the equations in Table 4.
• Step 3: Compute the maximum section longitudinal membrane stress for both the weight
and weight plus thermal load cases considering points A and B in the cross section:
( )
( )( )
A wlm r
m f m f
A Ar w x y
X Y
A FMAWPA A A A
y xy b MAWP A M MI I
σ = + +− −
+ + +
(47)
( )
( )( )
B wlm r
m f m f
B Br w x y
X Y
A FMAWPA A A A
y xy b MAWP A M MI I
σ = + +− −
+ + +
(48)
max ,A Blm lm lmσ σ σ = (49)
40
• Step 4: Evaluate the results as follows. The following relationship should be satisfied for
either a tensile and compressive longitudinal stress for both the weight and weight plus
thermal load cases:
2 2 23cm cm lm lm ysHσ σ σ σ τ σ− + + ≤ (50)
with,
0.6ircm
L o i
DMAWPE RSF D D
σ
= + ⋅ − (51)
( )2T
m ft tf
M VA AA A d
τ = +−+
(52)
– The elastically calculated von Mises stress must be satisfied for both the weight
and weight plus thermal load cases for positions on the cross section defined by x
and y (see Figure 14). The critical points that are required to be check are labeled
A and B in the figure. For the weight case, H = 0.75, and for the weight plus
thermal case, H = 1.5. The value H = 0.75 is established considering a RSFa = 0.9
factor applied to a two-thirds factor that is typically applied to the yield stress to
establish a design stress value for a load-controlled stress (H = 0.9x0.67 ~ 0.75).
For the weight plus thermal case, a margin of two is typically applied to the yield
stress. The value of H = 1.5 represents an allowable stress reduction factor that is
typically applied to a weight plus thermal load case. This reduction was included to
compensate for possible elastic follow-up that can occur in some structures
because of a significant localized change in stiffness.
• Step 5: If the maximum longitudinal stress computed in Step 4 is compressive, then this
stress should be less than or equal to the allowable compressive stress or the allowable
tensile stress, whichever is smaller. When using this methodology to establish an
41
allowable compressive stress, an average thickness representative of the region of local
metal loss in the compressive stress zone should be used in the calculations.
• Step 6: If the longitudinal membrane stress computed in Step 3 does not satisfy the
requirements of Step 4, then the MAWP and/or supplemental loads should be reduced,
and the evaluation repeated.
If the metal loss in the circumferential plane is composed of several distinct regions, then a
conservative approach is to define a continuous region of local metal loss that encompasses all
of these regions. If this assumption is too conservative or the metal loss has significant variability
making the rectangular approximation for the remaining thickness too conservative, a numerical
procedure such as the Monte Carlo integration method may be used to compute the section
properties.
3.5.5 Non-Cylindrical Shells 3.5.5.1 Overview
Non-cylindrical shells include spherical shells, formed heads, conical shells, and elbows.
Very little technical development and experimental validation has been performed for flaws in
components with these types of geometry. The assessment procedure for non-cylindrical shells
is based on the procedure for cylindrical shells with minor modifications.
3.5.5.2 Spherical Shells and Formed Heads
The Level 1 assessment procedure for spherical shells and formed heads is the same
procedure used in an API 579, Section 5, Level 1 assessment for cylindrical shells. The Level 2
assessment uses the API 579, Section 5, Level 2 assessment for cylindrical shells with a different
Folias factor. The Folias factor for a spherical shells and formed heads replaces Equation (41) in
the API 579, Section 5, Level 2 assessment for cylindrical shells and is from the original work by
Folias [57] and is defined as follows.
42
( ) ( )
( ) ( )
2
2
1.0005 0.49001 0.324091.0 0.50144 0.011067tM
λ λ
λ λ
+ +=
+ − (53)
The LTA assessment procedures for formed heads in API 579 are limited to LTAs occurring
within the 0.8D center zone of the head. The minimum required thickness and maximum
allowable working pressure for spherical heads is defined as follows.
min 2 0.2cPRt
SE P=
− (54)
02
0.2c
c c
SEtMAWPR t
=+
(55)
The minimum required thickness and maximum allowable working pressure for elliptical
heads within the center zone of the head is defined as follows.
min 2 0.2cPD Kt
SE P=
− (56)
02
0.2c
c c
SEtMAWPKD t
=+
(57)
2 30.2535 0.1400 0.1224 0.01530ell ell ellK R R R= + + − (58)
The minimum required thickness and maximum allowable working pressure for torispherical
heads within the center zone of the head is defined as follows.
min 2 0.2rcPCt
SE P=
− (59)
02
0.2c
rc c
SEtMAWPC t
=+
(60)
43
The procedures outlined in Paragraphs 3.5.3.2 and 3.5.3.3 to calculate RSFs for a Level 1
and 2 can be used in conjunction with the above equations to evaluate spherical shells and
formed heads.
3.5.5.3 Conical Shells
The LTA assessment procedures for conical shells are the same as those used for
cylinders. However, in the assessment procedures, the minimum required thickness is based on
the equations in the original construction code for conical shells, and the inside diameter to be
used in the assessment is specified to be the diameter at the center of the LTA. The minimum
required thickness and maximum allowable working pressure for conical shells is defined as
follows.
( )min 2cos 0.6
cPDtSE Pα
=−
(61)
02 cos
1.2 cosc
c c
SEtMAWPD t
αα
=+
(62)
The procedures outlined in Paragraphs 3.5.3.2 and 3.5.3.3 to calculate RSFs for a Level 1
and 2 can be used in conjunction with the above equations to evaluate conical shell sections.
3.5.5.4 Elbows
Bubenik and Rosenfeld [58] studied the effects of an LTA on the strength of an elbow with
analytical and experimental methods. It can be concluded from the results of the study that LTAs
in an elbow can be evaluated using the assessment procedures for a cylindrical shell if the
Lorenz factor is included in the analysis. The Lorenz factor is the ratio of the elastic membrane
stress at a point on the circumference of an elbow to the membrane stress in a cylindrical shell
with the same inside diameter and thickness. The Lorenz factor is defined as follows.
44
sin2
sin
b L
mf
bL
m
RR
LRR
θ
θ
+
=
+
(63)
In the above equation, θL = 00, 1800 correspond to the crown position on the elbow, θL = 900
corresponds to the extrados of the elbow, and θL = 2700 corresponds to the intrados of the elbow.
Bubenik indicates that a conservative estimate of the failure stress for an LTA in an elbow can be
computed as follows.
1
11
flow olocfail
f
t o
AAt
L t AM A
σσ
− = −
(64)
The term tloc in the above equation is the local wall thickness in the elbow before corrosion
and t is the nominal wall thickness of the elbow. The effects of local variation in the elbow wall
thickness from forming are neglected; therefore, in Equation (64), tloc/t = 1.0. The Lorenz factor is
included in the LTA assessment procedure by using the minimum required thickness as follows.
min
2
o
a c
f
PDt MAE PY
Lσ
= +
+
(65)
3.6 API 579 ADVANCED ASSESSMENT OF METAL LOSS 3.6.1 Overview
A Level 3 assessment is API 579 is considered and advanced assessment of metal loss.
Finite element analysis is the typical method for quantifying stress in a component for a Level 3
assessment; however, other numerical methods may be employed. Linear elastic stress analysis
with appropriate stress classification or non-linear elastic-plastic stress analysis to calculate
45
collapse loads may be used. Non-linear stress analysis will more accurately duplicate actual
behavior like the redistribution of stress due to plasticity or creep which are considered directly in
the analysis. Linear elastic analysis tends to under predict strain ranges at fatigue sensitive
points, while non-linear analysis will more accurately represent actual strain ranges and the
accumulation of inelastic strains.
Components that are subject to external pressure or large compressive stresses should also
be evaluated for structural stability and buckling. Additional procedures for components subject
to cyclic loading are also provided in API 579, Appendix B.
When formulating a finite element model for a Level 3 assessment, thickness data can be
mapped directly onto two or three dimensional continuum elements as applicable. Alternately,
shell elements with different thicknesses may be used to approximate an LTA. Mesh densities
and application of loads and boundary conditions vary between applications and must be applied
using engineering experience. Special considerations must be taken into account if there are
significant supplemental loads and structural discontinuities affecting the region containing the
flaw. Flexibility and stress distribution in these locations may be affected by the location and
distribution of metal loss, may cause a reduction in calculated plastic collapse loads, and cause
difficulty in relating to the original design specifications
3.6.2 Assessment with Numerical Analysis
For a non-linear stress analysis, structural integrity can establish for a component by taking
two-thirds of the plastic collapse load. The plastic collapse load can be determined using the
following two criteria taken directly from API 579.
• Global Criteria: A global plastic collapse load is established by performing an elastic-
plastic analysis of the component subject to the specified loading conditions. The plastic
collapse load is the load which causes overall structural instability.
• Local Criteria: A local plastic collapse load is a measure of the local failure in the vicinity
of the flaw as a function of the specified loading conditions. Local failure can be defined
46
in terms of a maximum peak strain in the remaining ligament of the flaw. One
recommendation is to limit the peak strains at any point in the model to 5%. Alternatively,
a measure of local failure can also be established by placing a limit on the net section
stress in the remaining ligament of the flaw when material strain hardening is included in
the analysis. In addition, the operational requirements of the component (i.e. local
deformation); constraint effects related to the hydrostatic stress, material ductility, the
effects of the environment; and the effects of localized strain which can result in zones of
material hardness that may be subject to damage from the environment should be
considered.
An alternate method to determine structural integrity of a component may be used in place
of calculating plastic collapse loads. Applied loads in a finite element analysis may be increased
by a multiplier, and the stability of the component with respect to the loads can be determined
with non-linear elastic-plastic FEA and the global and local criteria. This procedure is referred to
as Load and Resistance Factor Design (LRFD).
3.6.3 API 579, Level 3 Assessment (Lower Bound Limit Load)
The following procedure for performing a Level 3 assessment using LRFD for a volumetric
flaw is provided in API 579 and is also known as the lower bound limit load. The procedure may
be modified based on specific application, component configuration, material properties, and
loading conditions. It is not applicable to cyclic loading conditions.
• Step 1: Develop a finite element model of the component including all relevant geometry
characteristics. The mesh used for the finite element analysis should be designed to
accurately model the component and flaw geometry. In addition, mesh refinement
around areas of stress and strain concentrations should be included. Based on the
experience of the Engineer performing the analysis, the analysis of one or more finite
element models may be required to ensure that an accurate description of the stress and
47
strains in the component is achieved. This type of model evaluation is particularly
important for non-linear analysis.
• Step 2: Define all relevant loading conditions including pressure, supplemental loads and
temperature distributions.
• Step 3: An accurate representation of material properties should be included in the finite
element model. An elastic-plastic material model with large displacement theory should
be used in the analysis. The Von Mises yield function and associated flow rule should be
used if plasticity is anticipated. Material hardening or softening may be included in the
analysis if the material stress-strain curve is available. If hardening is included in the
plastic collapse load analysis, it should be based upon the kinematic hardening model, or
a combined kinematic and isotropic model.
• Step 4: Determine the load to be used in the analysis by applying a load multiplier of 1.5
to the actual load. If the component is subject to multiple loads, all of the actual loads
should be proportionally scaled with the same multiplier.
• Step 5: Perform an elastic-plastic analysis. If convergence is achieved in the solution,
the component is stable under the applied loads, and the global criteria described above
is satisfied. Otherwise, the load as determined in Step 4 should be reduced and the
analysis repeated. Note that if the applied loading results in a compressive stress field
within the component, buckling may occur, and the effects of imperfections, especially for
shell structures, should be considered in the analysis.
• Step 6: Review the results of the analysis in the areas of high strain concentrations and
check the failure parameter chosen to categorize local failure. If the local criteria are not
satisfied, the applied loads should be reduced accordingly.
• Step 7: If the global and local criteria are satisfied, the component is suitable for
continued operation subject to the actual loads used in the assessment.
• Step 8: A check for shakedown should be made if the component is to remain in-service
during multiple start-up and shutdowns. This check can be made by removal and re-
48
application of the actual load. A few cycles of this load reversal may be necessary to
demonstrate shakedown. If significant incremental plastic strains occur during this load
cycling (ratcheting), the permissible operating load should be reduced; otherwise,
shakedown has occurred.
3.6.4 Plastic Collapse Load
An alternate Level 3 procedure for analyzing a LTA is by using FEA to directly calculate a
RSF. The method is known as the plastic collapse load and can be calculated with the following
procedure.
• Step1: Develop a FEA model as described in Step 1 of Paragraph 3.6.3 for both the
undamaged and damaged geometry of the component.
• Step 2: Define all relevant loading conditions including pressure, supplemental loads and
temperature distributions.
• Step 3: Include elastic-plastic material properties with kinematic hardening in the FEA
models.
• Step 4: Perform an elastic-plastic analysis for each model with increasing load
increments. The load increment that causes instability (no convergence) in the analysis
is the plastic collapse load for the component.
• Step 5: Compare the plastic collapse load of the damaged component to the undamaged
component to determine the RSF. The RSF can be used with Equations (5) and (6) to
calculate a safe operating pressure or loading condition.
• Step 6: Rerun the analysis of the damaged component at the safe operating pressure or
loading condition and performs Steps 6 – 8 in Paragraph 3.6.3.
49
3.7 COMPARISON OF GENERAL AND LOCAL METAL LOSS
The differences between the API 579 assessment procedures for general and local metal
loss can be summarized as follows:
The general metal loss rules for Level 1 and Level 2 assessments are based on establishing
an average thickness. The average thickness is then used with Code rules to determine
acceptability for continued operation. Rerates, if required, are based on the Code rules using the
average thickness.
The local metal loss rules for Level 1 and Level 2 assessments are based on establishing a
Remaining Strength Factor. The RSF is then used to determine acceptability for continued
operation. Rerates, if required, are based on the Code rules for determining the MAWP and the
RSF.
The general metal loss rules for Level 1 and Level 2 assessments can be based on point
thickness readings (subject to a restriction on the variability in the thickness reading data) or
critical thickness profiles.
The local metal loss rules for Level 1 and Level 2 assessments are based on critical
thickness profiles.
• The Level 2 assessment procedures for general and local metal loss when applied to
corrosion and/or erosion at local structural discontinuities are currently the same and use
the general metal loss rules. New Level 2 local metal loss assessment procedures are
currently being developed.
• The Level 3 assessment procedures for general and local metal loss are currently the
same. Numerical analysis using elastic-plastic stress analysis techniques is
recommended for the assessment.
As previously stated, the general and local metal loss rules have been structured to provide
consistent results. If the general metal loss rules are applied to an LTA and the assessment
results produce a conservative answer, the same LTA can be re-evaluated with the local metal
loss rules. The resulting answer will typically be less conservative. Therefore, it is recommended
50
by API 579 that regions of corrosion/erosion be evaluated initially with the general metal loss
rules, followed by an assessment using the local metal loss rules.
3.8 REMAINING LIFE EVALUATION 3.8.1 Overview
API 579 includes procedures for estimating the remaining life for components subject to
continued corrosion or degradation. Rules to evaluate the current integrity of a component are
provided by general and local metal loss assessments. However, a remaining life assessment
can be used to calculate a rough estimate to actual time of failure. This type of assessment is
valuable in determining an inspection interval, in service monitoring, or urgency of repair. Two
procedures can be used to evaluate reaming life, one based on component thickness and the
other based on maximum allowable working pressure.
3.8.2 Thickness Approach
Minimum required thickness based on in service conditions, thickness data from inspection,
and an estimated corrosion rate can be used to estimate remaining life of a component. This
method is applicable for components that do not have thickness interdependency and may be
non-conservative when applied to components with this configuration. The remaining life can be
estimated as follows:
am amlife
rate
t KtRC−
= (66)
for components with interdependent thickness, the MAWP approach should be used.
51
3.8.3 MAWP Approach
The MAWP approach for determining remaining life was proposed by Osage [59] and is
applicable to all types of pressurized components, including those with thickness
interdependency. It also ensures that design pressure is not exceeded during operation as long
as the future corrosion rate is correctly estimated. The following procedure for the MAWP
approach is taken directly from API 579.
• Step 1: Determine the metal loss of the component, tloss, by subtracting the average
measured thickness at the time of the last inspection, tam, from the nominal thickness,
tnom.
• Step 2: Determine the MAWP for a series of increasing time increments using an
effective corrosion allowance and the nominal thickness in the computation. The
effective corrosion allowance is determined as follows:
e loss rateCA t C time= + ⋅ (67)
• Step 3: Determine the remaining life from a plot of MAWP versus time. The time at which
the MAWP curve intersects the design MAWP for the component is the remaining life of
the component.
• Step 4: Repeat the Steps 1, 2 and 3 for each component. The equipment remaining life
is taken as the smallest value of the remaining lives computed for each of the individual
components.
52
CHAPTER IV
LTA ASSESSMENT PROCEDURES FOR CIRCUMFERENTIAL STRESS
4.1 INTRODUCTION
This section contains a compilation of the LTA assessment methods published in the public
domain for evaluating the circumferential stress direction in cylindrical shells. All the methods in
this section will be used in the statistical validation to determine the most reliable method. A
complete summary of all the methods provided in Table 5. Each method is assigned a number,
and the method number will be used to identify each in the statistical analysis results.
Where possible, the methods have been converted to a standard calculation format for ease
of comparison. Methods are presented in their original form and then recast into the standard
calculation form whenever possible. For assessment of flaws governed by the circumferential
stress direction only, methods for assessment include the original and modified B31.G methods,
the Battelle method, the API 579 methods and hybrids, the Chell based methods, the British Gas
methods, and the BS 7910 methods. The modified API 510 and API 653 thickness averaging
methods and the Kanninen method are included, but are applicable to both the circumferential
and longitudinal stress direction.
4.2 CALCULATION OF UNDAMAGED MAWP
For the calculation of MAWP of an undamaged component, the following general equation is
used unless otherwise specified:
0 0.6atMAWP
R tσ
=+
(68)
53
Different design codes may use different design equations for the MAWP, but the
differences result in a negligible change in the MAWP calculation. Where a specific design code
has the largest impact on calculated MAWP is in the allowable stress basis. The allowable stress
can be significantly different for different design codes, leading to a large variation in the safety
margin between the calculated MAWP and the calculated failure pressure. The non-uniform
margin on calculated MAWP is addressed in later sections by varying the allowable remaining
strength factor.
4.3 CALCULATION OF UNDAMAGED FAILURE PRESSURE
The estimated undamaged failure pressure is calculated using methodology developed and
validated by Svensson [60]. The method is an internal pressure to inner and outer bore strain
relationship for a material that has the following stress-strain relationship.
0nσ σ ε= (69)
The variables n and σ0 are parameters to define the true stress – true strain curve for the
material. For a thick wall cylinder, the following relationship between pressure and the material
stress-strain curve is as follows. The 1 and 2 locations are the inner radius and outer radius,
respectively.
2
1
0 31
n
P de
ε
εε
εσ ε=−∫ (70)
The formulation for a thick walled sphere is as follows.
2
1
0 1.51
n
P de
ε
εε
εσ ε=−∫ (71)
For the condition where the pressure is at the strain based failure pressure, the following
conditions must be satisfied.
54
1
0dPdε
=
(72)
( )
1
1
31
22 31 1
n
o
i
e
ReR
ε
ε
εε −
= − −
(73)
( )1
23
21 log 1 13
oe
i
ReR
εε−
= − −
(74)
For a given true stress-strain curve, the above equations can be solved using various
numerical techniques to calculate the inner and outer strain values and evaluate the integral to
determine burst pressure. The following simplified solution can be derived for a thin wall cylinder,
but for the calculations in this study, the thick wall solution is always used.
( )0 1
2
3
n
f ni
t nPR e
σ + =
(75)
For spheres, the simplified solution is as follows.
1
023
n n
f ni
t nPR e
σ+ =
(76)
The thick walled formulation for a cylindrical shell was compared to FEA to validate the
accuracy. The FEA models were run with non-linear geometry and an elastic-plastic true stress-
strain curve. The results from the FEA and the above methodology are almost identical. The
validation cases and results are shown in Table 6.
55
4.4 CALCULATION OF DAMAGED MAWP AND DAMAGED FAILURE PRESSURE
All the analysis methods presented here have been recast in terms of a standard calculation
format where applicable in order to provide a standard means for comparison of the methods.
Conversion to the format does not change the values calculated by each method; it only
rearranges the variables to be consistent between all the methods. The standard format consists
of evaluating an LTA by calculating certain factors with the following steps:
• Step 1: Calculate flaw area and original area. The procedure for calculating the flaw
area will vary from method to method. The original area is always the undamaged
component thickness times the length of the LTA. For methods that have an incremental
approach, the area calculation will be referred to as the effective area. The effective area
involves subdividing a LTA into sections centered on the deepest point on the critical
thickness profile in order to prevent an un-conservative result for highly irregular profiles
(See Figures 11 and 12). For a LTA that is very long, but with only one very deep
location, this prevents the severity of the damage from being averaged out over the
length of the flaw. The following equations are used to calculate the areas for the
different methods.
0A t l= ⋅ (undamaged area) (77)
A d l= ⋅ (rectangular area) (78)
23
A d l= ⋅ (parabolic area) (79)
0.85A d l= ⋅ (equivalent area) (80)
( )0
l
A d x dx= ∫ (exact area) (81)
56
( )i i ie sA t l l= − (effective undamaged area) (82)
( )i i ie sA d l l= − (effective rectangular area) (83)
( )ie
is
li
l
A d x dx= ∫ (effective area) (84)
• Step 2: Calculate the lambda (λ) non-dimensional geometry factor and the Folias factor,
Mt. The Folias factor is based on lambda and both vary between methods.
• Step 3: Calculate the surface correction factor, Ms based on area ratio and the Folias
factor. There are two forms of Ms as shown below.
0
0
11
1
ts
AA M
MAA
− =
−
(B31.G) (85)
0 0
111
s
t
MA AA A M
=
− +
(Chell) (86)
• Step 4: Calculate an RSF. The RSF is usually calculated as follows.
1
s
RSFM
= (87)
• Step 5: Calculate the final MAWP for the corroded component using Equations (5) and
(6). The failure pressure for the corroded component can be calculated with the following
equation.
( )0fP P RSF= (88)
57
This procedure is used with every method presented in this chapter where applicable. Each
method is presented in its original format and the standard format whenever possible.
4.5 THICKNESS AVERAGING ASSESSMENT 4.5.1 Overview
Thickness averaging is the simplest method used to evaluate LTAs and was developed to
provide a reasonable result for areas of general metal loss based on the average thickness of the
region. The method is not accurate for complex areas of metal loss and will produce the most
conservative results of all the methods. The thickness averaging methods do not conform to the
standard calculation format described in Paragraph 4.4.
4.5.2 API 510 Assessment (Method 8)
The API 510 assessment methodology consists of averaging thickness readings over a
specified length and comparing the average thickness to limiting thickness. The average
measured thickness, tam, is determined by averaging the thickness readings over the following
lengths:
min , 20 60
2DL inches when D inches = ≤
(89)
min , 40 60
3DL inches when D inches = >
(90)
The required strength check is as follows:
minamt CA t− ≥ (91)
An additional check is made on the minimum measured thickness:
58
min0.5mmt CA t− ≥ (92)
A MAWP and failure pressure can be calculated using the design equations and average
measured thickness over the specified region as follows.
0.6a am
am
tMAWPR tσ
=+
(93)
0.6
uts amf
am
tPR tσ
=+
(94)
4.5.3 API 653 Assessment (Method 9)
The API 653 assessment methodology consists of averaging thickness readings over a
specified length and comparing the average thickness to limiting thickness. The average
measured thickness, tam, is determined by averaging the thickness readings over the following
length:
max 3.7 , 40.0mmL Dt inches = (95)
The required strength check is as follows:
minamt CA t− ≥ (96)
An additional check is made on the minimum measured thickness:
min0.6mmt CA t− ≥ (97)
A MAWP and failure pressure can be calculated using the design equations and average
measured thickness over the specified region with Equations (93) and (94).
59
4.5.4 API 579, Section 4 Level 1 and 2 Assessment (Methods 25 and 26)
The API 579, Section 4 Level 1 and Level 2 assessment for general regions of metal loss is
also a variation of the thickness averaging methodology and is presented in Paragraphs 3.4.3.1
and III.4.3.2 respectively. These methods are used as screening criteria for a local metal loss
assessment. They were never meant to actually be used in the assessment of local metal loss,
but are still included in the statistical comparison of the LTA assessment methods. Like the other
thickness averaging methods, a MAWP and failure pressure can be calculated using the design
equations and average measured thickness over the specified region with Equations (93) and
(94)
4.6 ASME B31.G ASSESSMENT 4.6.1 Overview
The B31.G assessment method was designed to more accurately assess corrosion in pipe
lines and is included in ASME B31 Codes for Pressure Piping. The procedure was developed
based on full-scale burst tests of defected pipes. Mathematical expressions were developed
semi-empirically and based on fracture mechanics principles. The original method is a
combination of a Dugdale plastic zone size model, a Folias analysis of an axial crack in a
pressurized cylinder, and an empirically established flaw depth to pipe thickness relationship.
The original B31.G method has evolved over time with the addition of new burst tests and data.
Methods 4, 5, 6, and 7 in are the original B31.G method and its modifications including the
RSTRENG method.
4.6.2 Original ASME B31-G Assessment (Method 7)
The original B31-G LTA assessment method was first presented in the following form.
60
213' 1.1
2 113
dtP P
dt M
− = −
for 2
20lDt
≤ (98)
' 1.1 1 dP Pt
= − for
2
20lDt
> (99)
By inspection, it is evident that the remaining strength factor and allowable remaining
strength factor can be written as follows.
1 1.1
aRSF= (100)
213
2 113
dtRSF
dt M
− = −
for 2
20lDt
≤ (101)
1 dRSFt
= − for
2
20lDt
> (102)
From this, an original allowable RSF of 0.909 (1/1.1) is specified. Since the surface
correction factor defined in the standard format is equal to one over the RSF, the surface
correction factor can be written as follows.
2 113
213
s
dt MM
dt
− = −
for 2
20lDt
≤ (103)
1
1sM d
t
= −
for 2
20lDt
> (104)
61
The surface correction factor can be converted to areas by multiplying the LTA depth and
original thickness by the length of the LTA. The area of metal loss is assumed to be rectangular
with respect to the maximum depth and length of the LTA. The surface correction factor can be
rewritten as follows.
0
0
11
1s
AA MM A
A
− = −
for 2
20lDt
≤ (105)
In Equation (105), the undamaged area and parabolic damaged area are calculated using
Equations (77) and (79).
0
1
1sM A
A
= −
for 2
20lDt
> (106)
In Equation (106), the undamaged area and rectangular damaged area are calculated using
Equations (77) and (78). The original form of the Folias factor was presented as follows.
1/ 22
1 0.8 lMDt
= +
(107)
The Folias factor and the dimensional limits can be converted to the non-dimensional
parameter, lambda, as follows.
1.285 lDt
λ = (108)
2 2
21.285lDt
λ= (109)
21 0.48449tM λ= + (110)
62
2
20lDt
≤ becomes 5.75λ ≤ (111)
2
20lDt
> becomes 5.75λ > (112)
The original B31.G equations can be recast in terms of the standard format and calculated
with the following steps.
• Step 1: Calculate the undamaged area and parabolic damaged area using Equations
(77) and (79). The defect area is a parabolic estimate based on the maximum depth and
total length of the defect.
• Step 2: Calculate λ and the Folias factor, Mt.
1.285o
lD t
λ = (115)
21.0 0.48449tM λ= + for 5.75λ ≤ (116)
• Step 3: Calculate the B31.G surface correction factor, Ms.
0
0
11
1
ts
AA M
MAA
− =
−
for 5.75λ ≤ (117)
0
1
1sM A
A
= −
for 5.75λ > (118)
• Step 4: Calculate the RSF as described in Paragraph 4.4.
• Step 5: Calculate new MAWP and failure pressure as described in Paragraph 4.4.
63
4.6.3 Modified B31-G Assessment, 0.85dl Area (Method 4)
The modified B31-G, 0.85 dl Area method is essentially the same as the original. The
difference between the two methods is in estimation of defect area and calculation of the Folias
factor. The Folias factor for this method was developed by the American Gas Association (AGA).
The original presentation of this method is as follows:
1 0.8510000' 1
11 0.85ys
dtP P
dt M
σ
−
= + −
(119)
By inspection, the following is apparent from the above equation.
1 100001
a ysRSF σ
= +
(120)
1 0.85
11 0.85
dtRSF
dt M
−
= −
(121)
The RSF can be written in terms of a surface correction factor and areas in the same
manner as the original B31.G method. In the modified B31.G method, the Folias factor is slightly
different and is written as follows.
1/ 22 4
2 2
1.255 0.013512 4
l lMDt D t
= + −
for 2
50lDt
≤ (122)
2
0.032 3.3lMDt
= + for 2
50lDt
> (123)
The Folias factor equations can be rewritten using lambda in place of l2/Dt as follows.
64
2 2
21.285lDt
λ= (124)
2 41.0 0.3797 0.001936tM λ λ= + − for 9.1λ ≤ (125)
20.01936 3.3tM λ= + for 9.1λ > (126)
The allowable remaining strength factor is different from the original B31.G method and is
dependant on the material properties. It can be written as follows.
10000ys
ays
RSFσ
σ=
+ (127)
The Modified B31.G, 0.85 dl area method can be calculated in terms of the standard format
as follows.
• Step 1: Calculate the undamaged area and equivalent damaged area using Equations
(77) and (80).
• Step 2: Calculate λ and the Folias factor, Mt.
1.285o
lD t
λ = (128)
2 41.0 0.3797 0.001936tM λ λ= + − for 9.1λ ≤ (129)
20.01936 3.3tM λ= + for 9.1λ > (130)
• Step 3: Calculate the B31.G surface correction factor, Ms, using Equation (85) in
Paragraph 4.4.
• Step 4: Calculate the RSF as described in Paragraph 4.4.
• Step 5: Calculate new MAWP and failure pressure as described in Paragraph 4.4.
65
4.6.4 Modified B31-G Assessment, Exact Area (Method 6)
The exact area modified B31.G method is exactly the same as the 0.85dl method, except for
the defect area calculation. The defect area is more accurately calculated by numerically
integrating the defect profile. The same procedure detailed in Modified B31.G Assessment,
0.85dl Area can be used with the following modifications.
• Step 1: Calculate the undamaged area and exact damaged area by numerically
integrating the defect profile using Equations (77) and (81).
• Step 2: Calculate λ and the Folias factor, Mt, with equations (128), (129), and (130).
• Step 3: Calculate the B31.G surface correction factor, Ms, using Equation (85) in
Paragraph 4.4.
• Step 4: Calculate the RSF as described in Paragraph 4.4.
• Step 5: Calculate new MAWP and failure pressure as described in Paragraph 4.4.
4.7 RSTRENG METHOD (METHOD 5)
The RSTRENG method differs from other B31.G methods in that it is an iterative calculation.
The flaw profile is divided into sections as described in Step 1 and an RSF is calculated based on
the current section. The advantage of the iterative approach is that very deep locations in an
otherwise shallow flaw are not averaged out over the length of the defect. The final RSF is equal
to the lowest value calculated for all the section iterations. The lambda and Folias factors along
with the surface correction factor are the same as described for the B31.G modified 0.85dl
assessment. The current API 579 Level 2 assessment method is based on the RSTRENG
iterative procedure.
• Step 1: Starting with the deepest location in the critical thickness profile, partition the LTA
into i sections. Calculate the effective undamaged area and effective damaged area for
each section using Equations (82) and (84).
• Step 2: Calculate λ and the Folias factor, Mt for each section.
66
( )
1.285i ie si
o
l l
D tλ
−= (131)
( ) ( )2 41.0 0.3797 0.001936i i i
tM λ λ= + − for 9.1iλ ≤ (132)
( )20.01936 3.3i i
tM λ= + for 9.1iλ > (133)
• Step 3: Calculate the B31.G surface correction factor, Ms, for each section.
0
0
11
1
i
i iti
s i
i
AA M
MAA
− =
−
(134)
• Step 4: Determine the minimum remaining strength factor as follows for all the sections:
1i
is
RSFM
= (135)
1 2min , , ...., iRSF RSF RSF RSF = (136)
• Step 5: Calculate new MAWP and failure pressure as shown in Paragraph 4.4.
4.8 PCORR ASSESSMENT (METHOD 20)
The PCORR method was developed by Battelle as part of ongoing research into the
fundamental mechanisms driving failure of pipeline corrosion defects. The focus was to derive a
more analytical, as opposed to empirical, method for predicting failure of general and complex
LTAs. A finite element analysis tool called PCORR was developed to aid in the research. The
procedure presented here is the final closed form model for the failure of blunt defects in
pipelines that are general in nature and that can be applied to critical defect problems in the
67
pipeline industry. The method is only applicable to high toughness steels, so its flexibility is
limited.
The original Battelle method was designed to predict the failure pressure of damaged pipe
and was originally presented as follows.
*
2 1 1 exp 0.157d utst d lP
D t Rtσ
= − − −
(137)
By inspection, the failure pressure for an undamaged component, and the RSF can be
separated as follows.
02
utstP
Dσ= and
*1 1 exp 0.157d lRSF
t Rt
= − − −
(138)
Since this method is designed to calculate a failure pressure, no allowable RSF is needed.
This method does not use the Folias factor or surface correction factor in the calculation, but an
equivalent Folias factor can be derived using the definition of the surface correction factor in
terms of rectangular area and the definition of lambda as follows.
( )
1.285i
lD t d
λ =−
or *
21.285
lRt
λ= (139)
*
111 1
1 1 1 exp 0.157
ts
dt MM dRSF d l
t t Rt
−= = =
− − − −
(140)
Substituting lambda in the above equation and solving for the Folias factor yields the
following equation.
( )
( )
1 1 exp 0.1728
exp 0.1728t
dtM
λ
λ
− − − =
− (141)
68
The Battelle assessment method can be calculated in the API 579 format with the following
steps:
• Step 1: Calculate the undamaged area and rectangular damaged area using Equations
(77) and (78).
• Step 2: Calculate λ and the Folias factor, Mt.
( )
1.285i
lD t d
λ =−
(142)
( )
( )
1 1 exp 0.1728
exp 0.1728t
dtM
λ
λ
− − − =
− (143)
• Step 3: Calculate the B31.G surface correction factor, Ms, using Equation (85) in
Paragraph 4.4.
• Step 4: Calculate the RSF as described in Paragraph 4.4.
• Step 5: Calculate new MAWP and failure pressure as described in Paragraph 4.4.
4.9 API 579 ASSESSMENT 4.9.1 Overview
The current API 579 Level 1 and 2 assessments for regions of local metal loss are
presented in Paragraphs 3.5.3.2 and 3.5.3.3. These assessments are shown below in the
standard calculation format as methods 1 and 2. Method 3, as shown in Paragraph 4.9.4, is a
modified version of the API 579 Section 5, Level 2 assessment that calculates the exact area of
metal loss instead of using the effective area iterative procedure. Three hybrid assessments
based on API 579 assessment methodology are also included in this section. All of the Level 1
assessments use the rectangular area formulation.
69
4.9.2 API 579 Section 5, Level 1 Analysis (Method 1)
• Step 1: Calculate the undamaged area and rectangular damaged area using Equations
(77) and (78).
• Step 2: Calculate λ and the Modified B31.G Folias factor, Mt.
1.285i
lD t
λ = (144)
21.0 0.48tM λ= + (145)
• Step 3: Calculate the B31.G surface correction factor, Ms, using Equation (85) in
Paragraph 4.4.
• Step 4: Calculate the RSF as described in Paragraph 4.4.
• Step 5: Calculate new MAWP and failure pressure as described in Paragraph 4.4.
4.9.3 API 579 Section 5, Level 2 Assessment, Effective Area (Method 2)
The API 579, Level 2 effective area method is identical to RSTRENG (method 5) except the
Folias factor has been modified. The level 2 assessment differs from level 1 by the area
calculation and Folias factor.
• Step 1: Starting with the deepest location in the critical thickness profile, partition the LTA
into i sections. Calculate the effective undamaged area and effective damaged area for
each section using Equations (82) and (84).
• Step 2: Calculate λ and the Folias factor, Mt.
( )
1.285i ie si
i
l l
D tλ
−= (146)
70
( ) ( )( ) ( )( )
2 4
2 46
1.02 0.4411 0.006124
1.0 0.02642 1.533 10
i i
t i iM
λ λ
λ λ−
+ +=
+ + (147)
• Step 3 – Step 5: See the Modified B31-G Assessment, Effective Area – RSTRENG
method, Steps 3 through 5 in Paragraph 4.7.
4.9.4 API 579 Section 5, Level 2 Assessment, Exact Area (Method 3)
The same procedure detailed in 2.3.4.3. can be used with the following modifications in
steps:
• Step 1: Calculate the undamaged area and exact damaged area by numerically
integrating the defect profile using Equations (77) and (81).
• Step 2: Calculate λ and the Folias factor, Mt.
1.285i
lD t
λ = (148)
( )
2 4
2 6 4
1.02 0.4411 0.0061241.0 0.02642 1.533 10tM λ λ
λ λ−
+ +=
+ + (149)
• Step 3: Calculate the B31.G surface correction factor, Ms, using Equation (85) in
Paragraph 4.4.
• Step 4: Calculate the RSF as described in Paragraph 4.4.
• Step 5: Calculate new MAWP and failure pressure as described in Paragraph 4.4.
4.9.5 API 579 Hybrid 1, Level 1 Assessment (Method 14)
The API 579 Hybrid 1 assessment follows the same procedure as the current API 579
assessments. The λ factor and surface correction factor calculation from the Chell method in
Paragraph 4.10.2 have been substituted into the assessment as well as the B31.G Folias factor.
71
• Step 1: Calculate the undamaged area and rectangular damaged area using Equations
(77) and (78).
• Step 2: Calculate the Chell λ and B31.G Folias Factor, Mt.
1.2854 i
lD dπλ = (150)
21.0 0.48tM λ= + (151)
• Step 3: Calculate the Chell surface correction factor, Ms, using Equation (86) in
Paragraph 4.4.
• Step 4: Calculate the RSF as described in Paragraph 4.4.
• Step 5: Calculate new MAWP and failure pressure as described in Paragraph 4.4.
4.9.6 API 579 Hybrid 1, Level 2 Assessment (Method 15) The Level 2 Hybrid 1 assessment is identical to the Level 1 assessment except the effective area
procedure is used.
• Step 1: Starting with the deepest location in the critical thickness profile, partition the LTA
into i sections. Calculate the effective undamaged area and effective rectangular
damaged area for each section using Equations (82) and (83).
• Step 2: Calculate the Chell λ and Folias Factor, Mt, for each increment.
( )
1.2854
i ie si
i
l l
D d
πλ
−= (152)
( )21.0 0.48i i
tM λ= + (153)
• Step 3: Calculate the Chell surface correction factor, Ms, for each increment.
72
0 0
111
is i i
i i it
MA AA A M
=
− +
(154)
• Step 4 – Step 5: See the Modified B31-G Assessment, Effective Area – RSTRENG
method, Steps 4 and 5 in Paragraph 4.7.
4.9.7 API 579 Hybrid 2, Level 1 Assessment (Method 16)
Hybrid 2 is identical to Hybrid 1 except that a depth dependant lambda and the BG Folias
factor is used. The Level 1 assessment is as follows.
• Step 1: Calculate the undamaged area and rectangular damaged area using Equations
(77) and (78).
• Step 2: Calculate λ and British Gas Folias factor, Mt.
1.285i
lD d
λ = (155)
21.0 0.18774tM λ= + (156)
• Step 3: Calculate the Chell surface correction factor, Ms, using Equation (86) in
Paragraph 4.4.
• Step 4: Calculate the RSF as described in Paragraph 4.4.
• Step 5: Calculate new MAWP and failure pressure as described in Paragraph 4.4.
4.9.8 API 579 Hybrid 2, Level 2 Assessment (Method 17) The Level 2 Hybrid 2 assessment is identical to the Level 1 assessment except the effective area
procedure is used.
73
• Step 1: Starting with the deepest location in the critical thickness profile, partition the LTA
into i sections. Calculate the effective undamaged area and effective damaged area for
each section using Equations (82) and (84).
• Step 2: Calculate λ and the British Gas Folias factor, Mt, for each increment
( )
1.285i ie si
i
l l
D dλ
−= (157)
( )21.0 0.18774i i
tM λ= + (158)
• Step 3: See API 579 Hybrid 1, Level 2 Assessment, Step 3 in Paragraph 4.9.6.
• Step 4 – Step 5: See the Modified B31-G Assessment, Effective Area – RSTRENG
method, Steps 4 and 5 in Paragraph 4.7.
4.9.9 API 579 Hybrid 3, Level 1 Assessment (Methods 18)
Hybrid 3, like hybrid 2, uses different equations for λ, Mt, and Ms. The depth dependant
lambda and Chell surface correction factors are used. A new Folias factor has been developed
based on actual test data and is incorporated into the method. The details of the new JO Folias
factor are presented in Paragraph 5.3.2.
• Step 1: Calculate the undamaged area and rectangular damaged area using Equations
(77) and (78).
• Step 2: Calculate λ using Equation (155) and the JO Folias factor, Mt.
1.5
0.51.0 0.5753 1.7593tdMt
λ λ = − +
(159)
• Step 3 – Step 5: See API 579 Hybrid 1, Level 1 Assessment, Steps 3 through 5.
74
4.9.10 API 579 Hybrid 3, Level 2 Assessment (Method 19) The Level 2 Hybrid 3 assessment is identical to the Level 1 assessment except the effective area
procedure is used.
• Step 1: Starting with the deepest location in the critical thickness profile, partition the LTA
into i sections. Calculate the effective undamaged area and effective damaged area for
each section using Equations (82) and (84).
• Step 2: Calculate λ using Equation (157) and the JO Folias factor, Mt, for each increment
( )1.5
0.51.0 0.5753 1.7593i i
tdMt
λ λ λ = − +
(160)
• Step 3: See API 579 Hybrid 1, Level 2 Assessment, Step 3 in Paragraph 4.9.6.
• Step 4 – Step 5: See the Modified B31-G Assessment, Effective Area – RSTRENG
method, Steps 4 and 5 in Paragraph 4.7.
4.9.11 API 579 Modified, Level 1 Assessment (Method 27)
The modified API 579 methods are identical to the current API 579 methods except that the
Folias factor has been modified to include very long flaws (no lambda limitation). The details of
the modified API 579 Folias factor are presented in Paragraph 5.3.3. The Level 1 assessment
can be calculated as follows.
• Step 1: Calculate the undamaged area and rectangular damaged area using Equations
(77) and (78).
• Step 2: Calculate λ and the Janelle Folias factor, Mt.
1.285i
lD t
λ = (161)
75
( )
( ) ( ) ( )( )
2 3
4 5 4 6
5 7 7 8 8 9
10 10
1.0010 0.014196 0.29090 0.096420
0.020890 0.0030540 2.9570 10
1.8462 10 7.1553 10 1.5631 10
1.4656 10
tM λ λ λ
λ λ λ
λ λ λ
λ
−
− − −
−
= − + − +
− + −
+ − + (162)
• Step 3: Calculate the B31.G surface correction factor, Ms, using Equation (85) in
Paragraph 4.4.
• Step 4: Calculate the RSF as described in Paragraph 4.4.
• Step 5: Calculate new MAWP and failure pressure as described in Paragraph 4.4.
4.9.12 API 579 Modified, Level 2 Assessment (Method 28)
The API 579 Modified Level 2 assessment uses the effective area instead of the rectangular
area and can be calculated as follows.
• Step 1: Starting with the deepest location in the critical thickness profile, partition the LTA
into i sections. Calculate the effective undamaged area and effective damaged area for
each section using Equations (82) and (84).
• Step 2: Calculate λ and the Janelle Folias factor, Mt.
( )
1.285i ie si
i
l l
D tλ
−= (163)
( ) ( ) ( )( ) ( ) ( )( )
( )( ) ( )( ) ( )( )( )( )
2 3
4 5 64
7 8 95 7 8
1010
1.0010 0.014196 0.29090 0.096420
0.020890 0.0030540 2.9570 10
1.8462 10 7.1553 10 1.5631 10
1.4656 10
i i it
i i i
i i i
i
M λ λ λ
λ λ λ
λ λ λ
λ
−
− − −
−
= − + − +
− + −
+ − + (164)
• Step 3 – Step 5: See the Modified B31-G Assessment, Effective Area – RSTRENG
method, Steps 3 through 5 in Paragraph 4.7.
76
4.10 CHELL ASSESSMENT 4.10.1 Overview
In the Chell method, a different surface correction factor is introduced into the original B31.G
assessment method. Like the original B31.G method, the Chell surface correction factor was
originally developed to analyze crack like flaws. The Chell surface correction factor behaves
better for deep flaws than the surface correction factor introduced in B31.G. The surface
correction factors differ as follows:
11
1
ts
dt M
Mdt
− =
−
(B31.G) (165)
1
11s
t
Md dt t M
= − +
(Chell) (166)
The Chell surface correction factor is a more analytical solution than the empirically based
original surface correction factor and is derived by treating a cylinder with metal loss as two
separate cylinders. The area of metal is assumed to be a rectangle encompassing the area of
metal loss. Cylinder 1 is equal to the undamaged cylinder. Cylinder 2 has the radius of cylinder
1 with thickness equal to the depth of the area of metal loss. The failure pressures of cylinders 1
and 2 are calculated as follows.
1cylinder utsf
RPt
σ= (167)
2cylinder utsf
R dPt t
σ =
(168)
77
Subtracting the failure pressures for cylinder 2 from cylinder 1 will yield the failure pressure
for a cylinder with thickness equal to the minimum measured thickness of the original cylinder
containing the flaw as follows:
mmt uts utsf
R R dPt t t
σ σ = −
(169)
The failure pressure for cylinder 2 containing the flaw is calculated based on the Folias
factor as follows:
1flaw uts
ft
R dPt t M
σ =
(170)
By adding the failure pressure for the cylinder with minimum measured thickness and the
failure pressure for cylinder 2 containing the flaw, the failure pressure for the original cylinder with
the flaw can be calculated as follows.
mmt flawf f fP P P= + (171)
1uts uts uts
ft
R R Rd dPt t t t t M
σ σ σ = − +
(172)
0 utsf
RPt
σ= (173)
0 11f ft
d dP Pt t M
= − +
(174)
By definition, the failure pressure for a cylinder containing a flaw is equal to the undamaged
failure pressure multiplied by a remaining strength factor.
11
t
d dRSFt t M
= − +
(175)
78
1
s
RSFM
= (176)
1
11s
t
Md dt t M
= − +
(177)
It can be shown that as the solution approaches a through wall flaw (d = t), the Chell surface
correction factor goes to infinity while the B31.G surface correction factor is simply equal to the
Folias factor. This causes better behavior with the Chell surface correction factor for deep flaws.
Also, an alternate lambda parameter has been derived from the Chell work.
4.10.2 Chell Assessment (Method 12)
The Chell assessment method can be calculated with the following steps:
• Step 1: Calculate the undamaged area and exact damaged area by numerically
integrating the defect profile using Equations (77) and (81).
• Step 2: Calculate the Chell λ and the B31.G Folias factor, Mt.
1.2854 i
lD dπλ = (178)
21.0 0.48449tM λ= + (179)
• Step 3: Calculate the Chell surface correction factor, Ms, using Equation (86) in
Paragraph 4.4.
• Step 4: Calculate the RSF as described in Paragraph 4.4.
• Step 5: Calculate new MAWP and failure pressure as described in Paragraph 4.4.
79
4.10.3 Modified Chell Assessment (Method 13)
The modified Chell uses a D/t dependent Folias factor and an effective area calculation.
The Chell procedure can be used with the following modifications.
• Step 1: Starting with the deepest location in the critical thickness profile, partition the LTA
into i sections. Calculate the effective undamaged area and effective rectangular
damaged area for each section using Equations (82) and (83).
• Step 2: Calculate the Folias factor as follows, where Amm, and Amb are functions that are
defined by the ratio of the diameter to the thickness. The below factors were developed
based on a through wall crack like flaw in a cylinder.
( ) ( ),T mm mb mm mbM Max A A A A= + − (180)
The parameters Amm and Amb are evaluated using the information in Table 7 with λ
computed from the following equation:
1.818
i
lR t
λ = (181)
• Step 3: Calculate the Chell surface correction factor, Ms, using Equation (86) in
Paragraph 4.4.
• Step 4: Calculate the RSF as described in Paragraph 4.4.
• Step 5: Calculate new MAWP and failure pressure as described in Paragraph 4.4.
4.11 BRITISH GAS ASSESSMENT 4.11.1 Overview
LTA defects are separated into two categories in the British Gas methods: single defects
and complex defects. A single defect is defined as an isolated pit or area of general corrosion.
Complex defects are groups of pits or general corrosion. The single defect analysis can be used
80
as a lower bound for complex defect analysis. The same basic equations for assessment are
used by both analysis methods. A Folias factor that was developed based on finite element test
cases is used to calculate the RSF. The finite element test cases of single, semi-elliptical shaped
defects based on varying d/t and lambda were used. The FEA models were then used to
develop a new Folias factor by curve fitting the results. To develop the BG Folias factor, the
following base equation was used.
1B
tlM CDt
= +
(182)
Initially, C and B were allowed to vary in the curve fit, but based on the B31.G form of this
equation, B was set to two. For the final curve fit of the FEA results, a best fit of C=0.31 was
derived and the final equation is as follows:
2
1 0.31tlMDt
= +
(183)
The complex defect analysis uses the same equations to calculate an RSF. The only
difference is the defect is broken into about fifty different depth increments and the geometric
variables are based on all the included defects. An RSF is calculated at each depth increment,
and the worst case RSF is the final result similar to the effective area approach.
Interaction rules are provided to determine whether a flaw can be treated as a single defect
or a complex defect. A flaw can be treated as a single defect if the depth of the flaw is less than
20% of the wall thickness or if the following equations are satisfied.
3360 t
Dφ
π> (184)
2s Dt> (185)
81
Phi is the circumferential spacing between defects, and s is the longitudinal spacing
between defects. If the longitudinal defect spacing is less than the limit, the defects will interact if
the following conditions are satisfied.
1 1 2 21
1 2
1 1 1 2 2
1 12 1 2
111
11 1
d l d ldt l l st
d d l d ltQ tQ l l s
+ − − + + > + − − + +
(186)
1 1 2 22
1 2
2 1 1 2 2
2 12 1 2
111
11 1
d l d ldt l l st
d d l d ltQ tQ l l s
+ − − + + > + − − + +
(187)
2
11 1 0.31 lQ
Dt = +
(188)
2
22 1 0.31 lQ
Dt = +
(189)
2
1 212 1 0.31 l l sQ
Dt+ + = +
(190)
4.11.2 British Gas Single Defect Analysis (Method 10)
The British Gas method for the single defect was originally presented in the following form.
0
1
11f
dtP P d
t Q
−=
− (191)
82
2
1 0.31 lQDt
= +
(192)
Q is the British Gas Folias factor and the RSF is calculated as follows.
1
11
dtRSF d
t Q
−=
− (193)
The RSF is in terms of the surface correction factor and can be simply recast in terms of
rectangular areas. The British Gas Folias factor can be written in terms of lambda with the
following relationship.
2 2
21.285lDt
λ =
(194)
21.0 0.18774tM λ= + (195)
The British Gas single defect analysis can be calculated as follows in terms of the standard
format.
• Step 1: Calculate the undamaged area and rectangular damaged area using Equations
(77) and (78).
• Step 2: Calculate the British Gas Folias factor, Mt, based on λ.
1.285o
lD t
λ = (196)
21.0 0.18774tM λ= + (197)
• Step 3: Calculate the B31.G surface correction factor, Ms, using Equation (85) in
Paragraph 4.4.
• Step 4: Calculate the RSF as described in Paragraph 4.4.
83
• Step 5: Calculate new MAWP and failure pressure as described in Paragraph 4.4.
4.11.3 British Gas Complex Defect Analysis (Method 11)
The British gas complex defect analysis uses an iterative process to calculate failure
pressure. The method divides a complex LTA into several depth increments as shown in Figure
16. At each increment, failure pressure is calculated for the total LTA, each individual LTA that
may be formed based on the depth increment, and the interaction of individual LTAs. A minimum
failure pressure is obtained at each depth increment, and the minimum failure pressure for the
LTA is most limiting result for all the increments. Since the complex defect analysis is iterative, it
is difficult to put it in terms of the standard format. For this reason, it is presented in its original
format, except for the calculation of the Folias factor.
• Step 1: Calculate the failure pressure for a defect free section of pipe and the average
depth of the LTA with numerically integrated area.
( )02 utstPD tσ
=−
(198)
aveAdl
= (exact area) (199)
• Step 2: Calculate the failure pressure for the total defect.
1.285o
lD t
λ = (200)
21.0 0.18774tM λ= + (201)
84
1
11
ave
total oave
t
dtP P
dt M
− =
−
(202)
• Step 3: Select the number of depth increments to partition the LTA and calculate the
incremental depth based on the maximum depth and number of increments.
max
#jdd
inc= (203)
• Step 4: For each depth increment, calculate the average depth of the patch.
patchpatch
total
Ad
l= (exact area) (204)
• Step 5: Calculate the failure pressure of the patch.
1
11
patch
patch opatch
t
dt
P Pd
t M
− =
−
(205)
• Step 6: Determine the number of pits and calculate the average depth of each individual
LTA.
# 'i individual LTA s= (206)
,i LTAi
i
Ad
l= (exact area) (207)
• Step 7: Determine the equivalent thickness for each individual LTA.
( )2patch
euts patch
P Dt
Pσ=
+ for
1
i N
j i patchi
d l A=
=
<∑ (208)
85
et t= for 1
i N
j i patchi
d l A=
=
≥∑ (209)
• Step 8: Determine the equivalent average depth of each individual LTA.
( )ei i ed d t t= − − (210)
• Step 9: Calculate the failure pressure of each individual LTA.
1.285 ii
e
lDt
λ = (211)
21.0 0.18774ti iM λ= + (212)
( )
12
11
ei
ee utsi
e ei
e ti
dttP
D t dt M
σ
− =
− −
(213)
• Step 10: Calculate the overall length of the interacting individual LTAs.
( )1i m
nm m i ii n
l l l s= −
=
= + +∑ (total length of LTAs plus spacing) (214)
• Step 11: Calculate the average depth of the interacting LTAs.
,
i m
ei ii n
e nmnm
d ld
l
=
==∑
(215)
• Step 12: Calculate the failure pressure of the interacting LTAs.
1.285 nmnm
e
lDt
λ = (216)
86
21.0 0.18774nm nmM λ= + (217)
( )
,
,
12
11
e nm
ee utsnm
e nme
e tnm
dttP
dD tt M
σ
− =
− −
(218)
• Step 13: Determine the final failure pressure and RSF for the LTA.
( ), , ,f total patch i nmP MIN P P P P= (219)
0
fPRSF
P= (220)
• Step 14: Repeat Steps 4 through 13 for each depth increment. The failure pressure for
this assessment is the minimum pressure obtained for all the depth increments.
4.12 BS 7910 ASSESSMENT
The BS 7910 flaw assessment guide uses the British Gas research as its basis for the
assessment of local areas of metal loss. Like British Gas, the assessment of local metal loss is
based on classifying a flaw as either a single defect or complex or interacting defect. The
interactions rules are exactly the same as presented in the British Gas method.
4.12.1 BS 7910, Appendix G Assessment, Isolated Defect (Method 21)
The BS 7910 assessment for a single flaw is exactly the same as the British Gas single flaw
assessment procedure presented in Paragraph 4.11.2.
87
4.12.2 BS 7910, Appendix G Assessment, Interacting Flaws (Method 22)
The BS 7910 assessment for interacting defects uses the BS 7910 isolated defect
procedure for each isolated flaw and for all combination of isolated flaw interaction. Unlike the
British Gas complex defect assessment, the BS 7910 procedure is no longer iterative. The BS
7910 flaw assessment procedure is as follows:
• Step 1: Calculate the failure pressure (P1, P2, …, PN) for each of the N isolated defects
using the procedure presented for British Gas Single Defect Analysis.
• Step 2: Calculate the failure pressure for all combinations of the isolated defects using
the procedure presented for British Gas Single Defect Analysis and the following
equations for flaw length and depth.
( )1i m
nm m i ii n
l l l s= −
=
= + +∑ (221)
i m
i ii n
nmnm
d ld
l
=
==∑
(222)
• Step 3: Calculate the failure pressure for the combined defects.
( )1 2, , ..., ,f N nmP MIN P P P P= (223)
• Step 4: Calculate the MAWP. The fc factor is based on the original design factor.
c fMAWP f P= (224)
4.13 KANNINEN ASSESSMENT (METHOD 23)
The Kanninen method was developed by the Southwest Research Institute to analyze
corroded areas in pipes subject to large axial stress. Large longitudinal stresses can be
generated due to end forces and bending moments applied to a pipe in addition to pressure
88
loads. The methods presented above focus on pressure loading only, where failure is a function
of the circumferential stress. In the Kanninen method, large longitudinal stress is accounted for
by computing an equivalent stress based on circumferential and longitudinal stress and
comparing it to material ultimate stress for failure or allowable stress for MAWP. The
Circumferential stress is compute based on the load conditions and increased with an RSF factor
due to the corroded region. The RSF is calculated using a Folias factor derived from shell theory.
The longitudinal stress is calculated based on the load conditions and cross sectional properties
of the corroded region. The Kanninen method can be calculated as follows.
• Step 1: Calculate the undamaged area and exact damaged area by numerically
integrating the defect profile using Equations (77) and (81).
• Step 2: Calculate the shell theory Folias factor, Mt.
1 dt
η = − (225)
( )0.9306 l
D t dα =
− (226)
( )( )( )
( )( )
( )
4
3/ 2 2 2
2
5/ 2 2 2
5/ 2
2
1 cosh sinh sin cos
2 cosh cos
2 cosh sinh sin cos
2 cosh cos
cosh sinsinh cos2 cosh cos
sinh cos cosh sin
tM
η α α α α
η α α
η α α α α
η α α
α αα α
η α α
η α α α α
+ ⋅ + ⋅ + − +
⋅ − ⋅ +
− =⋅ +
⋅ + ⋅ ⋅ + ⋅ − ⋅
(227)
• Step 3: Calculate the B31.G surface correction factor, Ms, using Equation (85) in
Paragraph 4.4.
• Step 4: Calculate the RSF as described in Paragraph 4.4.
89
• Step 5: Calculate the equivalent von Mises stress with the following equations.
2
x
f
IZ D
y=
+ (228)
1 4x
lmMpD
t Zσ = + (229)
2 4x
lmMpD
t Zσ = − (230)
1
2cmpD
RSF tσ = (231)
2 21 1 1eq cm cm lm lmσ σ σ σ σ= − + (232)
2 22 2 2eq cm cm lm lmσ σ σ σ σ= − + (233)
1 2max ,eq eq eqσ σ σ = (234)
• Step 6: Calculated the MAWP and failure pressure by varying the pressure in the above
equations until the calculated equivalent von Mises stress is equal to the material
allowable stress or material ultimate stress, respectively.
4.14 SHELL THEORY ASSESSMENT (METHOD 24)
The shell theory method follows the standard format and uses the shell theory Folias factor
presented in the Kanninen method. The shell theory Folias factor has been curve fit using Table
Curve 3D as shown in Figure 17. The shell theory method can be calculated with the following
steps:
90
• Step 1: Calculate the undamaged area and exact damaged area by numerically
integrating the defect profile using Equations (77) and (81).
• Step 2: Calculate the shell theory Folias factor, Mt.
1 dt
η = − (235)
( )0.9306 l
D t dα =
− (External Flaw) (236)
2 2
2 2
0.9848 0.4582 0.5868 0.006156 0.07628 0.12321 0.4691 0.7484 0.005116 0.2827 0.8853tM η α η α ηα
η α η α ηα− − + + +
=− − − + +
(237)
• Step 3: Calculate the Chell surface correction factor, Ms, using Equation (86) in
Paragraph 4.4.
• Step 4: Calculate the RSF as described in Paragraph 4.4.
• Step 5: Calculate new MAWP and failure pressure as described in Paragraph 4.4.
4.15 JANELLE METHOD
The Janelle method does not involve the calculation of a Folias Factor or surface correction
factor. Instead, the RSF is calculated directly from non-dimensional parameters. The
development of the Janelle method is described in Paragraph 5.3.4. The Level 1 assessment is
based on the rectangular defect area, and the Level 2 assessment is based on the effective area.
4.15.1 Janelle Level 1 Assessment (Method 29)
The Level 1 Janelle assessment can be calculated with the following steps.
• Step 1: Calculate the undamaged area and rectangular damaged area using Equations
(77) and (78).
• Step 2: Compute the Remaining Strength Factor using the following equations.
91
1.285i
lD t
λ = (238)
1 1.0144
0
1.0
1.01006.0
ZAA
= +
(239)
2 1.02321.0
1.01.8753
Zλ
= +
(240)
( )1 2 11200 1.0144 1.0152 1.0141 1RSF Z Z Z= − + + − (241)
• Step 3: Calculate new MAWP and failure pressure as shown in Step 5 of Paragraph 4.4.
4.15.2 Janelle Level 2 Assessment (Method 30)
The Level 2 Janelle assessment can be calculated with the following steps.
• Step 1: Starting with the deepest location in the critical thickness profile, partition the LTA
into i sections. Calculate the effective undamaged area and effective damaged area for
each section using Equations (82) and (84).
• Step 2: For each subsection, compute the Remaining Strength Factor using the following
equations.
( )
1.285i ie si
i
l l
D tλ
−= (242)
92
1 1.0144
0
1.0
1.01006.0
i
i
i
ZAA
= +
(243)
2 1.02321.0
1.01.8753
i
iZ
λ=
+
(244)
( )1 2 11200 1.0144 1.0152 1.0141 1i i i iRSF Z Z Z = − + + − (245)
• Step 3: Determine the minimum remaining strength factor as follows for all the sections:
1 2min , , ...., iRSF RSF RSF RSF = (246)
• Step 4: Calculate new MAWP and failure pressure as shown in Step 5 of Paragraph 4.4.
93
CHAPTER V
VALIDATION OF LTA ASSESSMENT PROCEDURES FOR CIRCUMFERENTIAL STRESS
5.1 INTRODUCTION
This section contains details of the procedures used to validate the LTA analysis methods
presented in Paragraphs 4.5 through 4.15 as well as the theory behind the newly developed
analysis methods. The analysis methods were verified by comparing calculated results for a
given method to full-scale burst tests and non-linear FEA. Close to one thousand full-scale burst
tests and non-linear FEA models were used in the validation. A computer program was used to
evaluate each test case with each analysis method and calculate associated statistics. The most
accurate assessment method was determined based on the statistical analysis.
5.2 VALIDATION DATABASES
There are four separate databases of burst test and FEA cases, which are organized based
on their primary source. The cases in the four databases are assigned by numbering convention.
Database 1 contains cases numbered from 1 to 1999. Similarly, Database 2 cases are
numbered from 2000 to 2999, Database 3 cases are 3000 to 3999, and Database 4 cases are
4000 to 4999. A complete listing of the databases and their sources are shown in Tables 8, 9,
10, and 11.
• LTA Database 1: LTA Database 1 is a collection of burst test cases from two primary
sources. Cases 1-124 and 216-221 are summarized in Kiefner [61], and Cases 1-215
are summarized in Kiefner [62]. There is also a spreadsheet compiled by Battelle that
has a summary of all 222 cases. The cases were compiled and used to develop and
94
validate the RSTRENG analysis method. A case by case summary of LTA Database 1 is
shown in Table 8.
• LTA Database 2: The full scale burst tests in LTA Database 2 are from Connelly [63].
These burst tests were also correlated with finite element analysis by Depadova [64].
The 58 LTA tests were performed using two retired pressure vessels. Approximately 30
LTAs were created in each vessel, and the pressure tests were run until leaks occurred.
Defects included internal and external LTAs in the shell and heads. A case by case
summary of LTA Database 2 is shown in Table 9. The cases in this database were not
used in the LTA validation. The vessels were pressurized to the point of plastic
deformation multiple times and the results obtained from the test are not consistent with
the other databases.
• LTA Database 3: The burst test cases for local thin areas found in LTA Database 3 are
from a British Gas Linepipe Group Sponsored Project reported by Fu [65]. The tests
were designed and performed for the development of the British Gas analysis methods.
These cases are actual burst tests performed for the project. A case by case summary
of LTA Database 3 is shown in Table 10.
• LTA Database 4: LTA Database 4 is composed of the finite element testing done as part
of the British Gas Linepipe Group Sponsored Project performed in conjunction with the
test cases in LTA Database 3. In order to determine a failure or burst pressure for the
FEA cases, the models were run to the ultimate tensile stress for the material. These
cases were reported by Fu [66]. A case by case summary of LTA Database 4 is shown
in Table 11.
5.3 NEW LTA ANALYSIS METHODS
New assessment procedures are incorporated in this study in an attempt to improve
assessment accuracy. Two approaches were taken. The Hybrid methods were developed
based on existing analysis methods. Desirable characteristics were taken from the existing
95
methods and combined to develop hybrid methods. The basis for these hybrids is the API 579
format with alterations to the Folias factor and surface correction factor. Hybrids one and two
have the best attributes of existing methods combined into a new method. Hybrid three is similar,
except that a new Folias factor was derived and included in the method. The new proposed API
579 (Janelle) method was derived directly from actual burst test data and FEA simulation. In the
method, the Folias factor and surface correction factor equations are eliminated. The RSF is
calculated directly based on the area of metal loss and a non-dimensional length parameter.
In addition to developing completely new analysis methods, new Folias factors were
developed for the API 579 method to eliminate the limitation on the length of a flaw that may be
analyzed. Most of the current Folias factors do not behave appropriately for very long flaws and
result in non-conservative evaluations. The new factors were developed based on the original
Folias data and by comparison to FEA.
5.3.1 API 579 Hybrid Assessment Procedures
Methods 14 through 19 presented in Paragraph 4.9.5 through 4.9.10 are newly developed
assessment procedures designed to improve upon existing methods. There are three hybrid
methods, each with a level one and two assessment. Rectangular area calculations are used in
the Level 1 assessment, and the effective area is used in the Level 2 assessment. In all of the
hybrids, the B31.G surface correction factor calculation is replaced with the Chell surface
correction factor. The API Folias factor is used for Hybrid 1, the British Gas Folias factor is used
in Hybrid 2, and a newly developed Folias factor is used in Hybrid 3. The details for development
of the new Folias factor are presented in Paragraph 5.3.2. The hybrid methods were statistically
more accurate than the original API 579 method in the validation process and are not
recommended for use.
96
5.3.2 New Folias Factor Development for Hybrid Methods
The new Folias factor was developed based on a curve fit of the burst test cases. The data
points for all the LTA analysis cases were plotted three dimensionally using d/t, lambda, and RSF
for the axes. The Chell surface correction factor was used for the fit as follows.
11
t
d dRSFt t M
= − +
(247)
The new factor was derived by picking an equation form for the Folias factor Mt, and curve
fitting that equation to the LTA test cases. The first form chosen was similar to the one derived
by British Gas and has the following form.
01.0 ntM C λ= + (248)
1.285i
lD d
λ = (249)
The values of C0 and n were derived based on a curve fit using the Table Curve 3D software
and the resulting equation was as follows.
1.20691.0 0.4497tM λ= + (250)
The accuracy of the above equation was not a significant improvement in the predicted RSF.
A second Folias factor form was chosen with a direct d/t dependence that is lacking in other
forms of the Folias factor. This form was defined as follows.
3
1 20 11.0
nn n
tdM C Ct
λ λ = + +
(251)
The initial curve fit resulted in the following equation.
1.7711
0.3928 0.89071.0 0.6094 2.2361tdMt
λ λ = + − +
(252)
97
Based on the results of the curve fit, n1 was set to 0.5, n2 was set to 1.0, and n3 was set to
1.5. The equation was refit for C0 and C1 with the following final result.
1.5
0.51.0 0.5753 1.7593tdMt
λ λ = − +
(253)
It was determined during the validation process that accuracy was not improved with the
above Folias factor, and it is not recommended for use.
5.3.3 Modified API 579, Level 2 Folias Factor for Long Flaws
One of the limitations with the current API 579 assessment of local metal loss is a restriction
on the length of a LTA that can be analyzed. The current version of the document has the
following length limitation.
5.0 3.891l Dtλ ≤ − > ≤ (254)
The limitation reflects the fact that the Folias factor and corresponding RSF calculation do
not approach the proper bound as a flaw becomes very long. As a flaw increases in length, the
RSF should approach the ratio of the remaining thickness to the undamaged thickness. The
current Folias factor does not approach this limit fast enough, resulting in slightly higher RSFs
and an un-conservative result. The reason this occurs, is because the data for the development
of the original Folias factor only went out to a lambda value of 8. For longer flaws, a linear
extrapolation was used, and the assumption that the function remains linear was not accurate.
The actual trend for the Folias Factor should approach a very large value as the length of the flaw
approaches the following limit based on shell theory.
max 20 15l DT λ= ≈ = (255)
A matrix of axisymmetric and 3D solid FEA models was developed to further investigate the
behavior of long flaws. The models included non-linear geometry effects and an elastic-plastic
98
material model with kinematic hardening. In all cases, the collapse load calculated for a model
containing a flaw was compared to the collapse load of an undamaged model to obtain the RSF
for the flaw. The RSF trend with respect to the flaw length is shown in Figure 18 and the FEA
details and calculated RSF values are shown in Table 12. Typical geometries for the 3D solid
and axisymmetric models are shown in Figures 19 and 20 respectively. In the figure, the current
API 579 Folias factors do not follow the trend of the FEA. The original Folias data (to a lambda of
8) was refit and extrapolated to follow the trend of the FEA results as shown in the figure. For
lambda values greater than 30, a lambda of 30 should be used in the calculation. The curve fit
for the modified Folias factor is shown in Figure 21 and the resulting equation is as follows.
( )
( ) ( ) ( )( )
2 3
4 5 4 6
5 7 7 8 8 9
10 10
1.0010 0.014196 0.29090 0.096420
0.020890 0.0030540 2.9570 10
1.8462 10 7.1553 10 1.5631 10
1.4656 10
tM λ λ λ
λ λ λ
λ λ λ
λ
−
− − −
−
= − + − +
− + −
+ − + (256)
For LTAs that have a lambda less than 8, the results of the analysis are identical when using
the old or new Folias factor (see Figure 22). Almost all of the cases in the LTA database fall into
that category. The results for LTAs with lambda greater than 8 are slightly more conservative
with the new Folias factor and approach the limiting value much quicker than the old Folias
factor. The new Folias factor will be recommended to replace the existing API 579, Level 2
factor, and the length limitation for the analysis will be removed as the results will no longer be
un-conservative for long flaws. A new Level 1 screening curve was also developed with the
modified Folias factor and is shown in Figure 23. A comparison between the new screening
curve and the old screening curve is shown in Figure 24.
The FEA procedure used to investigate long flaws in cylindrical shells was repeated for a
spherical shell. The geometry and RSF calculations for the FEA cases are shown in Table 13. A
typical geometry for the axisymmetric model is shown in Figure 25. The trends of the FEA and
the current API 579 Folias factor for spheres are shown in Figure 26. Based on the trends, the
current API 579 Folias factor is applicable to flaws that extend up to the entire inside
99
circumference of the shell. The API 579 Folias factor for spherical shells is shown in Equation
(53). Tabular data for the cylindrical and spherical shell Folias factors is shown in Table 14.
5.3.4 Janelle Method
The Janelle method is a departure from the previous methodology and does not include the
calculation of the Folias factor or surface correction factor. Instead, the RSF for a given LTA is
calculated directly from a non-dimensional LTA length parameter and metal loss damage factor.
The RSF formulation is a direct data fit of the actual burst tests and FEA simulations. This
method has slightly better scatter statistics than the other methods because it is a curve fit of the
actual database cases, but the greatest advantage is how the function is bounded. The function
approaches and RSF of 1.0 as the length or depth approaches 0.0, and the RSF approaches the
ratio of remaining thickness to undamaged thickness as the length approaches infinity. The
curve fit derived from the Table 3D program is shown in Figure 27. This method will be
recommended to replace the API 579, Level 2 assessment in a future release of the document.
The resulting equations from the fit are as follows.
1 1.014385410
0
1.0
1.01006.013191
ZAA
= +
(257)
2 1.0232170851.0
1.01.875264927
Zλ
= +
(258)
1
2 1 2
1217.299931 1218.2996861216.947150 1216.946241
RSF ZZ Z Z
= − + +−
(259)
100
5.4 STATISTICAL VALIDATION OF LTA METHODOLOGY USING A FAILURE RATIO
In order to validate the analysis methods in this study, comparisons between the methods
and actual test cases are required. Pressure ratio assessment is the main tool for determining
the statistical accuracy of each LTA analysis method. The failure ratio is defined as follows:
Actual Failure PressureFailure Ratio =
Predicted Failure Pressure
(260)
The actual failure pressure can be obtained two ways. Full-scale vessel or pipe specimens
that contain an LTA can be pressurized to failure, or non-linear elastic plastic finite element
models of an LTA can be generated and loaded to failure conditions. The predicted failure
pressure is calculated with the methods provided in this study. For each of the cases in the
database, the ratio is calculated. Statistical analysis based on the calculations is used to quantify
the accuracy of each analysis method at calculating these ratios.
Databases 1, 3, and 4 were used for the validation and omitted cases are shown in Table
15. All the cases in the databases were analyzed using a computer program that included all the
analysis methods and statistics were generated for each method. For the computer program, the
inside diameter, shell or pipe thickness, allowable stress ratios based on yield and ultimate
stress, an allowable RSF, yield and ultimate stresses, actual failure pressure, and the longitudinal
defect profile are required input data. The program output for each method included the
calculated failure pressure, calculated MAWP, ratio of calculated failure to actual failure, ratio of
calculated MAWP to actual failure, and statistics of the ratios based on all the database cases.
The most desirable method is the one with the least amount of scatter in the failure ratio
calculations, or the one with the smallest standard deviation. The analysis methods with
statistical data are shown in Table 16.
Scatter in the data can be attributed to physical phenomenon that can occur with LTAs.
Material toughness plays a major role in determining the failure pressure of a damaged
component. Most of the methods presented here do not directly consider material toughness in
the analysis. Those that make an attempt to include toughness effects, have considered
101
materials with very high toughness which is not applicable to many cases that can be found in
industry. Another phenomenon that affects the failure of corroded components is triaxial
stresses. A high state of triaxiality has been shown to have a significant effect on failure. These
conditions can be generated from jagged or non-uniform profiles of metal loss. Methods like the
British Gas method, which are solely based on cases with smooth metal loss profiles, do not take
this effect into consideration.
5.5 SUMMARY OF VALIDATION RESULTS
Based on the statistical results in Table 16, the new Janelle Method (Method 30) is the most
accurate. It has a mean failure ratio of nearly 1.0 and the lowest standard deviation of any of the
other methods. The most accurate of the old methods are API 579 and modified API 579, Level
2 effective and exact area methods (Methods 2, 3, and 28) and the RSTRENG effective and
exact area methods (Methods 5 and 6). The methods that use the effective area are considered
superior because they protect against highly irregular metal loss profiles. The Janelle and
modified API 579 methods (Methods 28 and 30) do not have a limitation on the length of a flaw
that may be analyzed, so have less limitations than the other methods. The modified API 579,
Level 2 (Method 28) is recommended for current use. The Janelle Method (Method 30) is
recommended to replace the current method in the next release of API 579.
102
CHAPTER VI
ALLOWABLE RSF VALUES FOR DIFFERENT DESIGN CODES
6.1 INTRODUCTION
Local thin areas are phenomena appearing in a wide variety of field equipment, from
pressure vessels to piping to large storage tanks. Based on the type of equipment, different
design codes are used in construction. Since the LTA assessment procedures presented are
meant for use with most types of equipment, effects of the design code must be taken into
consideration. Each design code has different factors to determine allowable material stresses.
Using the different values for allowable stress will have no effect on calculating the failure
pressure or failure ratio. The difference is in calculating the MAWP; some methods may be too
conservative for a certain design code. In this section an allowable RSF vs. MAWP margin will
be developed for various design codes.
6.2 DESIGN CODES FOR PRESSURIZED EQUIPMENT
All of the following design codes provide a maximum allowable stress, which is calculated
from material yield and ultimate stresses as follows:
ysyield stressf
allowable stress= (261)
utsultimate stressf
allowable stress= (262)
103
,a ys ys uts utsMin F Fσ σ σ = (263)
Actual yield and ultimate stresses or minimum values may be used in VCESage, and for the
analysis presented here, actual measured stress values from material testing were used. The
design code will have no effect on the failure ratio calculation, but does contribute to the MAWP
ratio. Some design codes may be over-conservative for calculating the MAWP ratio, allowing for
a reduction in the allowable RSF factor. The objective is to determine which allowable RSF best
matches each design code. A summary of the design codes and their allowable stresses can be
found in Table 17.
• ASME Section VIII, Division I and Division II [67], [68], [69]: ASME Section VIII design
codes cover the fabrication rules for all types of pressure vessels. Section VIII is
subdivided into three divisions. Divisions I and II are addressed in this study and
described below. Division III is alternate rules for high pressure vessels and not
considered in this study. Division I contains the general rules for constructing pressure
vessels or design by rule. Division II is the alternate rules for pressure vessel fabrication.
Division II is more restrictive in the choice of materials than Division I. It also permits
higher design stress intensity values to be used in the range of temperatures over which
the design stress intensity value is controlled by the ultimate or yield strength. More
detailed design procedures and complete examination, testing, and inspection are
required.
• ASME B31.1, B31.3, B31.4, and B31.8 [70], [71], [72], [73], [74]: The ASME B31 design
codes cover all types of piping. ASME B31.1 covers the design, fabrication, and
inspection of power piping associated with steam boilers. This type of piping is usually
found in electrical power generation stations, industrial plants, institutional plants,
geothermal heating systems, and heating and cooling systems. The B31.3 code covers
the design, fabrication, and inspection of process piping that is found in refinery and
petrochemical plants. This code was formerly referred to as the refinery and chemical
plant piping code. It is used in the design of piping that is found in petroleum refineries,
104
chemical, pharmaceutical, textile, paper, semiconductor, and cryogenic plants, and
related processing plants and terminals. The ASME B31.4 design code covers pipeline
transportation systems for liquid hydrocarbons and other hydrocarbons. It is used to
design piping for transporting products which are predominantly liquid between plants
and terminals and within terminals, pumping, regulating, and metering stations. The
B31.8 design code deals with gas transportation and distribution systems. It is used for
the design of piping transporting products which are predominately gas between sources
and terminals including compressor, regulating, and metering stations and gas gathering
pipelines. The code assigns design factors according to pipe classification. The design
factor is selected based on five piping location classes described in B31.8. They are
location class 1, division 1 and division 2, and location class 3, class 4, and class 5. This
code uses yield stress along with the design factor for steel piping system design
requirements. The yield times the design factor, F, is essentially the allowable stress
used in design. The steel pipe design formula presented is written as:
( )2StP F E TD
= ⋅ ⋅ (264)
• API 620 and API 650 [75], [76]: The design and construction of large, welded, low
pressure storage tanks is detailed in API 620. These types of tank include field-
assembled storage tanks that contain petroleum intermediates (gases or vapors) and
finished products including other liquid products commonly handled and stored by the
various branches of industry. Tank temperature must be less than 250 F and tank gas or
vapor space pressure may not exceed 15 psi. API Standard 650 covers the design of
welded steel storage tanks of various sizes and capacities.
• CODAP [77]: CODAP is the French design code for fired or unfired pressure vessels,
similar to the ASME Section VIII Codes.
• AS 1210 [78]: AS 1210 is the Australian design code for fired or unfired pressure vessels,
similar to the ASME Section VIII Codes.
105
• BS 5500 [79]: BS 5500 is the British Standard design code for pressurized vessels,
similar to the ASME Section VIII Codes.
6.3 MARGIN OF MAWP TO FAILURE PRESSURE PER DESIGN CODE
To determine the margin, or safety factor on working pressure compared to failure pressure,
the MAWP ratio is used. The MAWP ratio is defined as:
Actual Failure PressureMAWP Ratio =Predicted MAWP
(265)
The actual failure pressure is determined from a full scale burst test or numeric FEA
simulation. The predicted MAWP for the damaged component is a function of the analysis
methods in Paragraphs 4.5 through 4.15 and the material allowable stress. Since each Code has
a different formulation for allowable stress, the margin between MAWP and failure pressure can
vary. The allowable RSF is used to set a desired margin on MAWP to failure pressure. The
database cases are run with allowable RSFs of 0.7, 0.75, 0.8, 0.85, 0.9, and 0.95, and 1.0 for
each of the design codes in Paragraph 6.2. The lower 95% prediction interval on MAWP ratio is
used to determine the margin on MAWP for each design code. The statistical analysis results for
each method and each design code are shown in Tables 18 through 30.
6.4 ALLOWABLE RSF RESULTS
With the data in Tables 18 through 30, a margin of calculated MAWP to failure pressure can
de derived for any of the methods described in Paragraphs 4.5 through 4.15 and any of the
design codes described in Paragraph 6.2. The allowable RSF vs. the MAWP to failure margin
based on the 95% prediction interval are shown in Figures 28 through 40 for the modified API
579, Level 2 assessment (Method 28). Similar plots can be derived for any assessment method
by graphing the data points in the tables.
106
CHAPTER VII
LTA ASSESSMENT PROCEDURES FOR LONGITUDINAL STRESS
7.1 INTRODUCTION
The LTA assessment procedures for longitudinal stress presented in this section are based
on work done by Southwest Research and Kanninen. The research at Southwest was done to
incorporate effects from thermal expansion and supplemental loads into an LTA assessment.
Full scale burst tests subject to internal pressure and four point bending were performed to
evaluate the increased longitudinal stress. The Kanninen method presented in Chapter 4 was
the conclusion of this research.
7.2 KANNINEN ASSESSMENT METHOD
The Kanninen method is presented in Paragraph 4.13 and was included in the
circumferential stress methods to evaluate its accuracy at predicting failure for flaws dominated
by circumferential stress (internal pressure only).
7.3 THICKNESS AVERAGING
The thickness averaging methods are applicable to both the circumferential and longitudinal
stress directions for evaluating regions of metal loss. The methods are presented in LTA
Assessment Procedures for Circumferential Stress.
107
7.3.1 API 510
This method is presented in Paragraph 4.5.2.
7.3.2 API 653
This method is presented in Paragraph 4.5.3.
7.4 API 579 ASSESSMENT METHODS 7.4.1 API 579 Section 5, Level 1 Analysis
This method is presented in Paragraph 3.5.4.2. The screening curve is shown in Figure 15.
7.4.2 API 579 Section 5, Level 2 Analysis
This method is presented in Paragraph 3.5.4.3.
7.4.3 Modified API 579 Section 5, Level 2 Analysis
The following modifications to the API 579, Section 5, Level 2 longitudinal stress
assessment have been made to improve the assessment. The worst case stress conditions
including effects from both longitudinal and circumferential weld joint efficiency can be calculated
with the following modifications. Equations (266), (267), (268), (269), and (270) should replace
Equation (50) in the original method.
eq ysHσ σ≤ (266)
1 2max ,eq eq eqσ σ σ = (267)
108
2 2
21 3
A Acm cm lm lm
eqc c l lE E E E
σ σ σ σσ τ
= − + +
(268)
2 2
21 3
B Bcm cm lm lm
eqc c l lE E E E
σ σ σ σσ τ
= − + +
(269)
1.0C LE E= = (Corroded region not on a weld) (270)
The shell theory Folias factor presented by Kanninen has been curve fit and incorporated
into the analysis per the following modifications. Equations (271), (272), (273), and (274) replace
the RSF calculation in the original method.
0
0
1
1
AARSF ABA
−=
− (271)
2 2
2 2
0.9848 0.4582 0.5868 0.006156 0.07628 0.12321 0.4691 0.7484 0.005116 0.2827 0.8853
B η α η α ηαη α η α ηα
− − + + +=
− − − + + (272)
1 dt
η = − (273)
( )
0.9306 lD t d
α =−
(274)
7.4.4 Janelle, Level 1 Analysis
The following methodology was used to develop an improved screening curve for the
circumferential extent of a local thin area (LTA). The assumptions used to develop the curve
were:
109
• The LTA must pass the longitudinal extent screening curve. If it does, the worst case
RSF for the longitudinal extent of the LTA is equal to the allowable RSF (typically 0.9).
The longitudinal RSF is set to the allowable RSF for the screening curve.
• The loads on the component are internal pressure plus a supplemental net section
bending moment. All other supplemental loads are assumed to be negligible. If the
component is known to have a negligible supplemental bending moment, the No Bending
Moment screening curve may be used; otherwise, the Maximum Bending Moment
screening curve must be used.
• The equivalent stress criteria must be satisfied for the moment tension and compression
side, an internal or external LTA, and at locations A and B. Location A is the center of
the LTA with respect to the cylinder cross section and point B is the edge of the LTA with
respect to the cylinder cross section.
• The additional longitudinal tension or compression stress is limited to 40% of the material
allowable stress based on a radius to thickness ratio of 10 (see Figure 41).
The following equations from API 579 were used to generate the screening curve:
2 2 23 acm cm lm lm
a
SRSF
σ σ σ σ τ− + + ≤ (275)
In generating the screening curve, the circumferential stress is assumed to be the worst
case that could pass the longitudinal LTA extent screening curve. It is assumed that the
circumferential stress due to pressure is equal to the material allowable stress and the remaining
strength factor for the longitudinal extent of the LTA is equal to the allowable remaining strength
factor. This results in a circumferential stress equal to the allowable stress divided by the
allowable remaining strength factor. The torsion stress is assumed to be zero.
acm
a
SRSF
σ = , 0τ = (276)
110
Substituting the assumptions in (276) into Equation (275) and solving, results in the
acceptance criteria shown in Equation (279).
2
2a a alm lm
a a a
S S SRSF RSF RSF
σ σ
− + ≤
(277)
2 0alm lm
a
SRSF
σ σ
− ≤
(278)
0 1lm a
a
RSFS
σ≤ ≤ (279)
Equation (280) is the formulation for longitudinal stress from API 579 (equations for the
section properties are shown in Table 4).
( )
( )( ),
, ,
w T
Cm f m fA B s
lmA B A Bc
T w x yx y
A FMAWPA A A AMy xE
F y y b MAWP A M MI I
σ
+ + − − = + + + +
(280)
To generate the screening curve it is assumed that the weld joint efficiency, Ec, is equal to 1,
and there is no additional axial force or out of plane bending moment acting on the cylinder. The
maximum allowable working pressure stress is equal to the material allowable stress.
1cE = , 0TF = , 0yM = , 2 aS tMAWP
D= (281)
The stress from the in plane net section bending moment is assumed to be equal to the
allowable stress multiplied by a bending factor, BF.
2
xF a
x
M D B SI
= 2 x a
x FI SM BD
= (282)
111
Substituting in (281) and (282) into Equation (280) results in the final formulation for
longitudinal stress shown in Equation (283).
( ),, 2 2 2A BA B C w a a x alm s w F
m f x
yA S t S t I SM y b A BA A D I D D
σ = + + + −
(283)
Using the acceptance criteria in Equation (279), two conditions for acceptance must be
checked. The first criterion is for the tensile side of the cylinder with respect to the applied
bending moment. Assuming additional tensile longitudinal stress from the moment results in the
acceptance criteria shown in Equation (284).
( ), 22 2 1A BC w xa s w F
m f x
yA It tRSF M y b A BA A D I D D
+ + + ≤ − (284)
The second criterion is for the compressive side of the cylinder with respect to the applied
bending moment. Assuming additional compressive longitudinal stress from the moment results
in the acceptance criteria shown in Equation (285).
( ), 22 2 0A Bw xw F
m f x
yA It ty b A BA A D I D D
+ + − ≥ − (285)
Since the circumferential remaining strength factor cancels out on the compression side, the
acceptance criteria is based more on a bending moment limitation as opposed to limitations on
the LTA dimensions. The bending moment limitation is a function of the radius to thickness ratio
(ROT). The maximum bending factor, BF, was calculated for ROTs varying between 10 and 1000
using an iterative procedure and Equation (285). The ROT of 10 was most limiting, and based on
the calculations, a maximum BF of 0.4 (see Figure 41) was used to generate the screening curve
with a maximum bending moment included.
The screening curve varies based on the ROT for given cylinder. Screening curves using
ROTs of 10 to 500 were generated. The ROT of 10 was the most conservative and used as the
basis for the final screening curves. The screening curve was generated by setting values of
112
lambda ranging from 0 to 18 and solving for the minimum remaining thickness ratio using the
acceptance criteria in Equations (284) and (285). For a cylinder with an ROT of 10, lambda is
equal to 18 for an LTA that extends all the way around the circumference of the cylinder. Two
separate circumferential screening curves are generated to set the bounds for the possible
loading between the no supplemental load case and the maximum permissible bending moment
load case. The two resulting screening curves are shown in Figure 42.
7.4.5 Janelle, Level 2 Analysis
An alternate method for evaluating the longitudinal stress direction of local thin areas has
been developed based on the full-scale tests presented by Kanninen. This method is designed
for use in conjunction with the API 579 circumferential stress assessment for regions of local
metal loss.
This method incorporates the Folias bulging factor into the calculation of circumferential
stress and longitudinal stress and uses a von Mises equivalent stress criteria. The Folias factor
for circumferential stress is taken from the API 579, Section 5, Level 2 assessment. The
equation for the longitudinal stress bulging factor is derived from curve fitting data presented by
Folias for determining bulging effects with circumferentially oriented cracks in cylindrical shells.
The influence of the Folias factor on longitudinal stress is much less than the influence on
circumferential stress, but may have a significant effect on an equivalent stress calculation. The
Folias factor for longitudinal stress is graphically represented in Figure 43.
For flaws with no additional supplemental loads effecting longitudinal stress (pressure only),
longitudinal stress is ignored and equivalent stress is not calculated. In some cases, the addition
of supplement loads may result in equivalent stresses that are less than those that would be
obtained for the pressure only case. For this scenario, supplemental loads may be ignored, as
the circumferential stress solution will be more conservative. This can be used as a screening
technique for determining the influence of supplemental loads on an LTA.
113
The first step in the procedure involves calculating the longitudinal stress in the flawed
region of the cylinder. Longitudinal stress due to an applied bending moment is calculated based
on the damaged cross section of the cylinder. This stress is added to the normal longitudinal
pressure stress. The combined bending and pressure stress is multiplied by a circumferential
bulging factor presented by Folias to determine the total longitudinal stress. An acceptable range
is given for the longitudinal stress. If the calculated longitudinal stress is within the specified
range, it can be ignored and the assessment may be performed per the API 579 Level 2
circumferential stress assessment. If the calculated longitudinal stress is outside the acceptable
range, the assessment must be performed using the von Mises equivalent stress acceptance
criteria. The longitudinal stresses in the given range may be ignored because equivalent von
Mises stresses calculated with these values will be below stresses calculated with the
circumferential assessment method. The alternate longitudinal stress assessment can be
performed as follows (See Figures 13 and 14):
• Step1: Calculate the section properties as shown in Table 4 and the equations in Step 1
of Paragraph 7.4.2.
• Step 2: Calculate the circumferential stress using the following equations:
1.285LlDt
λ = (286)
( )
2 4
2 6 4
1.02 0.4411 0.0061241.0 0.02642 1.533 10
LtM λ λ
λ λ−
+ +=
+ + (287)
11
1
LtL
s
dM t
Mdt
− =
−
(288)
1
L LS
RSFM
= (289)
114
0.6icm
L L o i
DPRSF E D D
σ
= + ⋅ − (290)
• Step 3: Calculate the longitudinal stress with following equations:
1.285CcDt
λ = (291)
( ) ( )( ) ( )
2 4
2 4
1.0 0.1401 0.002046
1.0 0.09556 0.0005024C CC
tC C
Mλ λ
λ λ
+ +=
+ + (292)
11
1
CtC
s
dM t
Mdt
− =
−
(293)
( ),
w TC
m f m fSlm A
C A AT w X Y
X Y
A P FA A A AM
E y xF y y b A P M MI I
σ
+ + − − = + + + +
(294)
( ),
w TC
m f m fSlm B
C B BT w X Y
X Y
A P FA A A AM
E y xF y y b A P M MI I
σ
+ + − − = + + + +
(295)
, ,max ,lm lm A lm Bσ σ σ = (296)
Note: For the validation, TF and YM are set to zero in equations (294) and (295).
• Step 4: Calculate the torsional stress
115
( )2
T
m ft tf mm
M VA AA A t
τ = +−+
(297)
Note: For the validation, TM and V are set to zero in equation (297).
• Step 5: Calculate the von Mises equivalent stress:
2 2 2, , , 3eq A cm cm lm A lm Aσ σ σ σ σ τ= − + + (298)
2 2 2, , , 3eq B cm cm lm B lm Bσ σ σ σ σ τ= − + + (299)
, ,max ,eq eq A eq Bσ σ σ = (300)
• Step 5: The following conditions indicate failure or acceptability:
eq utsσ σ≥ (failure) (301)
eq aσ σ≤ (acceptable) (302)
Failure pressure and MAWP can also be calculated by setting the equivalent stress equal to
the ultimate stress or allowable stress respectively, and solving for the pressure. The maximum
allowable moment can also be calculated in the same fashion as follows. These equations are
valid if net section bending is the only supplemental load.
( ) ( )
22 2
2 21 12 4
Cs
eq x
L L C Cs s s s
MMZtP
R M M M M
σ
− =
− +
(303)
( ) ( )2
2 22 1 12 4
L L C Cx eq s s s sC
s
Z PRM M M M MM t
σ = − − + (304)
116
CHAPTER VIII
VALIDATION OF LTA ASSESSMENT PROCEDURES FOR LONGITUDINAL STRESS
8.1 INTRODUCTION
The Janelle assessment methodology for the longitudinal stress direction of an LTA
described in Paragraph 7.4.5 was validated with full scale burst tests. The full scale tests cases
were pressurized to a fixed value, then four point bending was applied until the pipe failed. The
loads at failure were used to calculate an equivalent stress at failure using the assessment
methodology. The calculated stress was compared to actual measured ultimate stress for the
pipe material. For the test cases available, there was only a small amount of error between
calculated stress at failure and the material ultimate stress.
8.2 VALIDATION DATABASES
Unfortunately, data for only five full scale burst tests was available to validate the
assessment methodology. The tests were performed by Southwest Research on 48 inch
diameter X65 pipe and have properties that are shown in Table 31. The flaws in the pipe were
machined patches on the pipe OD used to simulate metal loss. Each pipe contained 2 machined
flaws, one on the tension side from bending, and one on the compression side. Additional tests
were performed by Southwest for 20 inch diameter X52 pipe, but complete data for use in
validation was unable to be obtained. Additional test cases should be used to further validate the
methodology whether they are actual test cases or Finite Element Analysis simulations.
117
8.3 SUMMARY OF VALIDATION RESULTS
The assessment methodology was used to calculate the equivalent stress for the flaws on
the tension and compression sides of the pipe tests. The equivalent stress that was calculated
for the side that actually experienced failure was compared to material actual ultimate stress to
verify the accuracy of the methodology. The actual failures occurred on the compression side
when the calculated equivalent stresses were significantly higher on that side than the tension
side and vice versa. The actual calculated values are shown in Table 32.
For the five test cases, calculated equivalent stresses at failure were very close to the
material ultimate strength. It can be concluded that the von Mises equivalent stress criteria with
the presented method for calculating stresses in local thin areas is a good predictor of actual
behavior. If this is true, stresses caused by other forms of supplemental loading should be able
to be handled the same way as an applied bending moment. Additional tests should be
performed to confirm these findings.
118
CHAPTER IX
LTA PROCEDURES FOR HIC DAMAGE
9.1 INTRODUCTION
HIC damage is characterized by stepwise internal cracks that connect adjacent hydrogen
blisters on different planes in the metal, or to the metal surface. Externally applied stress is not
required for the formation of HIC. In steels, the development of internal cracks (sometimes
referred to as blister cracks) tends to link with other cracks by a transgranular plastic shear
mechanism because of internal pressure resulting from the accumulation of hydrogen. The link-
up of these cracks on different planes in steels has been referred to as stepwise cracking to
characterize the nature of the crack appearance. HIC is commonly found in steels with high
impurity levels that have a high density of large planar inclusions, and/or regions of anomalous
microstructure produced by segregation of impurity and alloying elements in the steel.
The effect of HIC damage is to produce a weakened zone within a plate. This weakening
effect can be characterized by using an RSF factor. RSF factors need to be developed for both
subsurface and surface breaking HIC damage. In the case of surface breaking HIC damage, the
Folias bulging factor needs to be included in the RSF solution.
9.2 SUBSURFACE HIC DAMAGE
The RSF for subsurface HIC damage (see Figure 44) can be derived from the definition of
the remaining strength factor, or
119
D
UD
L Collapse Load Of The Damaged ComponentRSFL Collapse Load Of The Undamaged Component
= = (305)
The collapse loads of the damaged and undamaged plate can be estimated using lower
bound limit load theory. The lower bound limit load for the damaged plate section is given by the
following equations where DH is a measure of HIC damage:
( )2D H H H ysL L t A A D σ= + − (306)
or
( )2D H H H ysL L t st A D σ= + − (307)
2 HD H H ys
AL t L s Dt
σ = + −
(308)
Finally
2 1 HD H H ys
AL t L s Dst
σ = + − (309)
The lower bound limit load for the undamaged plate section is referenced to the minimum
required wall thickness per the applicable code is:
( )min 2D H ysL t L s σ= + (310)
Combining Equations (309) and (310):
( )min
2 1min , 1.0
2
HH H
H
At L s DstRSF
t L s
+ − = +
(311)
If the actual area is approximated as a rectangle with dimensions s and wH, the expression
for the RSF becomes:
120
( )min
2 1min , 1.0
2
HH H
H
wt L s DtRSF
t L s
+ − = +
(312)
In the above equations for the RSF, the region of the undamaged plate that is assumed to
strengthen the HIC damaged area is:
8HL t= (313)
The minimum function in the above equations is required because the RSF is indexed to tmin.
Therefore, if tmin is small relative to the plate thickness t, and the reduced strength of the HIC
damaged area approaches the strength of undamaged plate, the RSF can be computed to be
greater than 1.0 indicating that the plate thickness above tmin can adequately reinforce the
damaged area located below tmin. If the RSF is indexed to the full plate thickness, then the
expressions for the RSFs shown above become:
( )
2 1
2
HH H
H
AL s DstRSF
L s
+ − =+
(314)
or
( )
2 1
2
hh H
h
wL s DtRSF
L s
+ − =+
(315)
9.3 SURFACE BREAKING HIC DAMAGE
For surface breaking HIC damage (see Figure 45), the bulging factor needs to be
considered in the RSF. By inspection of Equation (311), the RSF factor can directly be written
as:
121
min
min
1
11
HH
HH
t
w DtRSF
w DM t
−=
−
(316)
or in terms of a damaged area:
0
1
11
HH
HH
t o
A DARSF
A DM A
−=
−
(317)
where
minoA st= (318)
Note that when there 100% HIC damage, then DH = 1.0, and the RSF factor becomes:
min
min
1
11
H
H
t
wtRSF
wM t
−=
−
(319)
The remaining thickness ratio, Rt, is:
min
min min min
1mm H Ht
t t w wRt t t
−= = = − (320)
then
[ ]11 1t
tt
RRSFR
M
=− −
(321)
which is the expression used for an LTA.
122
Note that in the above formulation, the parameter, HL , is set to zero. This is consistent with
current LTA assessment methodologies. The modified API Folias factor as shown in Equation
(256) should be used in the above equations.
123
CHAPTER X
LTA PROCEDURES FOR EXTERNAL PRESSURE
The methodology for this analysis is presented by Rajagopalan [80] and supported by
Esslinger [81]. It utilizes a step-wise approach for shells that have abrupt changes in
thicknesses. The overall buckling pressure of a cylinder made of lengths at varying thicknesses
can be calculated from the following equation:
31 2
1 2 3
... ne e e e e
n
L LL L LP P P P P
= + + + + (322)
The parameters L and Pe
n are the unsupported length and buckling pressures of the overall
vessel, respectively, and Ln and Pen represent the unsupported lengths and the buckling
pressures of each of the individual shell courses in the vessel, respectively.
The following assessment procedure can be used to evaluate cylindrical shells subject to
external pressure. If the flaw is found to be unacceptable, the procedure can be used to
establish a new MAWP.
• STEP 1: Determine the CTP and the parameters in Paragraph 3.3.3.2.
• STEP 2: Subdivide the CTP in the longitudinal direction using a series of cylindrical shells
that approximate the actual metal loss (see Figure 46). Determine the length and
thickness of each of these cylindrical shells and designate them ti and Li.
• STEP 3: Determine the allowable external pressure of each of the cylindrical shells
defined in STEP 2 using (ti – FCA) and Li, designate this pressure as Pei. Methods for
determining the allowable external pressure are provided in Appendix A.
124
• STEP 4: Determine the allowable external pressure of the actual cylinder using the
following equation:
1
1
n
ii
r nie
i i
LMAWP
LP
=
=
=∑
∑ (323)
• STEP 5: If MAWPr > MAWP, then the component is acceptable for continued operation.
If MAWPr < MAWP, then the component is not acceptable for continued operation and
the allowable MAWP is MAWPr.
125
CHAPTER XI
CONCLUSIONS AND RECOMMENDATIONS
11.1 INTRODUCTION
This section contains a summary of the validation results for existing and new methods for
evaluating the longitudinal and circumferential extent of an LTA. Recommendations for use are
made for the methods that correlate the most accurately with actual full scale burst tests of
damaged shells. In addition, data is provided so that a margin on MAWP to failure pressure can
be calculated based on various design codes. Finally, additional areas requiring more research
and validation are outlined.
11.2 LTA ASSESSMENT PROCEDURES FOR CIRCUMFERENTIAL STRESS 11.2.1 Recommended Methods for Circumferential Stress
Of the existing methods for analyzing LTAs that are currently in use, the API 579, Level 2
and RSTRENG methods based on an effective area procedure correlate the best to actual test
data. The statistical analysis is presented in Table 16, and those two methods most accurately
predict the burst pressure of a damaged shell with the least amount of scatter in the results. The
drawback with these methods is that they do not approach the proper limits. For example, as the
length of an LTA becomes very long, the RSF is not necessarily calculated to be the ratio of
remaining thickness to undamaged thickness. To correct the problem, the modified Folias factor
should be used in conjunction with these methods. The new Folias factor does not change the
results of the analysis for LTAs that have a lambda value less than 8 (see Figures 21 and 22).
126
However, for longer flaws it is more conservative and approaches the proper bound. The
modified Folias factor is incorporated into Methods 27 and 28. It is recommended that Method 27
replace the current API 579, Level 1 assessment and Method 28 replace the current API 579
Level 2 assessment.
The new Janelle method was developed based on the actual test data and correlates even
better with full scale test results than any of the other methods. It also mathematically
approaches the bounds of the problem with the proper trends (see Figure 27). It is
recommended that the method eventually replace the current methods in API 579 in a future
release of the document.
11.2.2 Allowable Remaining Strength Factors
Any desired margin of calculated MAWP to failure pressure can de derived for the methods
described in Paragraphs 4.5 through 4.15 and the design codes described in Paragraph 6.2 with
the data presented in Tables 18 through 30. It is recommended that the tables which correlate to
the method published in the current or future releases of API 579 be included and referenced in
the document. This will allow a user to calculate whatever safety margin of MAWP to actual
failure is desired for the API 579 methodology.
11.3 RECOMMENDED METHODS FOR LONGITUDINAL STRESS
The Kanninen method, and similarly the API 579 modified method for evaluating flaws with
longitudinal stress do not give accurate results for cases where circumferential stress is
dominant. However, these methods do address loading conditions that result in flaws dominated
by longitudinal stresses. For local thin areas where supplemental loads or thermal expansion
may cause larger longitudinal stress, it is recommended that the LTA be first evaluated using an
assessment method for circumferential stress. If the flaw is acceptable for the circumferential
stress assessment, then it should be evaluated using a method that addresses flaws dominated
by longitudinal stresses.
127
The Janelle method, which is a modified version of the Kanninen and API 579 methodology
is recommended for use when evaluating the circumferential extent of an LTA. The method
correlates much better to actual full scale burst tests as described in Paragraph 8.3 and is
recommended for use in future releases of API 579.
11.4 FURTHER LTA ASSESSMENT DEVELOPMENT 11.4.1 Material Toughness Effects
The material toughness of a shell with a LTA can influence the load carrying capacity of the
component for medium and low toughness steels. A LTA is a natural stress concentration site
and may have large triaxial stresses. The stress concentration in combination with the irregular
geometry of the LTA may result in fracture before plastic collapse. For high toughness steels,
this is likely not an issue as most failures due to a LTA type defect will be mostly a ductile failure.
However, for low toughness steels, the stress concentration at the deepest point of a LTA may
cause micro cracks to form and result in brittle fracture contributing to the failure. This type of
failure occurs at a lower stress level than a purely ductile failure. A criterion to evaluate the
susceptibility of a damaged component to experience a fracture failure should be developed for
LTA type defects. A criterion for crack extension in a cylindrical shell has been developed by
Hahn [82]. A similar procedure for LTAs should be developed for inclusion in a later release of
API 579. In terms of stress, a modified stress calculation could be developed to include the
material fracture toughness and the remaining strength factor to account for susceptibility of low
toughness steels to brittle fracture. The calculation would include a factor based on toughness
as follows.
( )cal mat mRSF f Kσ σ= ⋅ ⋅ (324)
128
11.4.2 Stress Triaxiality from LTAs
The current analysis methods do not directly take into account the magnitude of triaxial
stress that can result from a local defect like an LTA. Typically, as the triaxiality increases the
toughness of the material decreases. This can result in a greater chance of fracture for highly
triaxial stress fields. The new proposed Section VIII, Division 2 Code will have a check and
limitation on the magnitude of triaxial stress fields to reduce the chance of fracture. This type of
criteria could be a good additional screening check for LTAs to help avoid that failure mode.
11.4.3 Rules for LTAs Near Structural Discontinuities
By far the most limiting criteria that must be satisfied in order to perform a FFS assessment
of a LTA is the distance to the nearest structural discontinuity. This distance is based on the
shell theory attenuation distance that stresses due to a global discontinuity die out along the shell
length. In API 579, the limiting distance is set to the following value.
1.8msdL Dt= (325)
In API 579, any attachment or change in shell geometry that creates a local stress field is
classified as a structural discontinuity. In reality there are two different types of discontinuity.
The first type is a global discontinuity, like a conical shell transition. The distance required for the
additional stress to die out along the shell for this type of discontinuity is on the order of
magnitude calculated by Equation (325). The other type of discontinuity is a local structural
discontinuity, like a nozzle attachment. The distance required for the additional stress to die out
along the shell for this type of discontinuity is on the order of plate thicknesses, not the length
specified in Equation (325). For local discontinuities, the limiting distance is extremely
conservative. Research is currently underway to modify this limitation in API 579.
129
CHAPTER XII
NOMENCLATURE
Unless otherwise cited in the text, the variables used in this report are shown below: A = Area of metal loss
oA = Original metal area
aA = Effective cross-sectional area for a cylinder with metal loss
fA = Cross-sectional area of the region of local metal loss
mA = Cylinder or pipe metal cross-section
tA = Mean area to compute torsion stress for the region of the cross section without
metal loss
tfA = Mean area to compute torsion stress for the region of the cross section with
metal loss
wA = Effective area of cylinder or pipe cross section on which pressure acts
FB = Bending Factor. This value is used to determine the additional longitudinal
compression or tension stress caused by the net section bending moment as a
factor of the material allowable stress. i.e. a bending factor of 0.4 results in
addition longitudinal stress equal to 40% of the material allowable stress.
b = Location of the centroid of area Aw, measured from the x x− axis
c = Circumferential extent of the flaw
rateC = Corrosion or metal loss rate
130
eCA = Equivalent corrosion allowance
d = Depth of metal loss damage
D = Mean diameter
iD = Inside diameter of the cylinder
oD = Outside diameter of the cylinder
CE = Weld joint efficiency for circumferential stress (longitudinal weld joints)
LE = Weld joint efficiency for longitudinal stress (circumferential weld joints)
F = Applied section axial force determined for the weight or weight plus thermal load
case
dF = Design factor
ysF = Yield stress factor
utsF = Ultimate tensile stress factor
FCA = Future corrosion allowance
H = Load factor. For the weight case, H=0.75, and for the weight plus thermal case
H=1.5. The H factor is based on an allowable RSF of 0.9, a Fys of 2/3, and a
factor of two for the weight plus thermal load case
xI = Moment of inertia of the cross section with the region of local metal loss about
the y axis
yI = Moment of inertia of the cross section with the region of local metal loss about
the y axis
XI = Moment of inertia of inertia of the cross section with the region of local metal loss
about the x -axis
YI = Moment of inertia of inertia of the cross section with the region of local metal loss
about the y -axis
131
K = Fracture toughness
l = LTA length
L = Length for thickness averaging
fL = Lorenz factor
msdL = Distance from the flaw to the nearest structural discontinuity
bM = Net-section bending moment
sM = Surface correction factor
tM = Folias through-wall bulging factor for a crack-like flaw
TM = Applied net-section torsion determined for the weight or weight plus thermal load
case
xM = Applied section bending moment determined for the weight or weight plus
thermal load case about the x-axis
yM = Applied section bending moment determined for the weight or weight plus
thermal load case about the y-axis
MA = Mechanical allowances
MAWP = Maximum allowable working pressure of damaged component
0MAWP = Maximum allowable working pressure of undamaged component
P = Pressure
0P = Failure pressure of undamaged component
fP = Failure pressure of damage component
Q = Shape factor to determine the length for thickness averaging
bR = Radius of the pipe bend
iR = Inside radius
lifeR = Component remaining life
132
mR = Mean Radius
tR = Remaining thickness ratio
RSF = Calculated Remaining Strength Factor for a given flaw
aRSF = Allowable Remaining Strength Factor
s = Spacing between flaws
t = Current wall thickness of the component
amt = Average measured thickness
Camt = Average measured thickness in the circumferential direction
Lamt = Average measured thickness in the longitudinal direction
limt = Minimum permissible thickness
losst = Metal loss computed as the difference between the furnished thickness and the
thickness at the time of an inspection
mint = Minimum required wall thickness of the shell containing a flaw
minCt = Minimum required wall thickness based on applied circumferential stresses
minLt = Minimum required wall thickness based on applied longitudinal stresses
mmt = Minimum measured wall thickness
nomt = Nominal thickness
T = temperature derating factor
V = Applied net-section shear force determined for the weight or weight plus thermal
load case
x = Distance along the x-axis to a point on the cross section where the bending
stress is to be computed
y = Distance from the x x− axis to a point on the cross section where the bending
stress is to be computed
133
y = Location of the neutral axis
Y = ASME B31 y-factor adjustment for temperature
cZ = Section modulus of the corroded pipe cross section
λ = Shell metal loss damage parameter
aσ = Allowable stress
cmσ = Maximum circumferential stress, typically the hoop stress from pressure loading
for the weight and weight plus thermal load case, as applicable
failσ = Failure stress
flowσ = Material flow stress
lmσ = Maximum longitudinal membrane stress computed for both the weight and
weight plus thermal load cases
utsσ = Material ultimate tensile stress
ysσ = Material yield stress
τ = Maximum shear stress in the region of local metal loss for the weight and weight
plus thermal load case
Lθ = Circumferential position on an elbow where the stress is to be computed
134
CHAPTER XIII
TABLES
Table 1 – Stress Classification
Stress Category Description Value
General Primary Membrane Stress Intensity, (Pm)
• Average value across the thickness of a section • Produced by internal pressure and other mechanical
loads • Excludes all secondary and peak stresses
kSm
Local Primary Membrane Stress Intensity, (PL)
• Average value across the thickness of a section • Produced by internal pressure and other mechanical
loads • Excludes all secondary and peak stresses • Stress intensities exceeding 1.1Sm do not extend in the
meridional direction more than Rt
1.5kSm
Primary Membrane (general or local) Plus Primary Bending Stress Intensity, (PL + Pb)
• Highest value across the thickness of a section • Produced by internal pressure and other mechanical
loads • Excludes all secondary and peak stresses
1.5kSm
Primary Plus Secondary Stress Intensity, (PL + Pb + Q)
• Highest value at any point across the thickness of a section
• Produced by internal pressure and other mechanical loads and general thermal effects
• Effects of gross structural discontinuities but not local discontinuities are included
3Sm
Primary Plus Secondary Plus Peak Stress Intensity, (PL + Pb + Q + F)
• Highest value at any point across the thickness of a section
• Produced by internal pressure and other mechanical loads and general and local thermal effects
• Effects of gross structural discontinuities and local discontinuities are included
• Used in fatigue calculation
Sa
Notes 1. Sm is the allowable stress. 2. k is equal to 1.0 for design loads and equal to 1.2 for design loads plus wind or pressure loads. 3. Sa is the allowable alternating stress established from a design fatigue curve based on a specified
number of cycles. 4. In addition to the stress classification acceptance criteria, a triaxial stress limit,
( )1 2 3 4 mSσ σ σ+ + ≤ , is applied to prevent ductile fracture. This limit is based on primary
loads.
135
Table 2 – Examples of Stress Classification
Vessel Component Location Origin of Stress Type of Stress Classification
Internal pressure General membrane
Gradient through plate thickness
Pm Q Shell plate
remote from discontinuities 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 Temp. difference. Between shell and
head
Membrane Bending
Q Q
Shell distortions such as out-of-roundness and
dents
Internal pressure Membrane Bending
Pm Q
LTA – Center region Internal pressure Membrane
Bending Pm Pb
LTA – Periphery Internal pressure Membrane
Bending PL
Q (2)
Any shell including cylinders, cones,
spheres and formed heads
LTA 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
Membrane stress averaged through
the thickness; stress component perpendicular to
cross section
Pm
Any section across entire
vessel
Net-section axial force, bending
moment applied to the cylinder or cone,
and/or internal pressure
Bending stress through the
thickness; stress component
perpendicular to cross section
Pb
Junction with head or flange Internal pressure Membrane
Bending PL Q
Cylindrical or conical shell
LTA – Tank bottom course-to-shell junction
Liquid Head Membrane Bending
PL Q
136
Table 2 – Examples of Stress Classification (Continued)
Crown Internal pressure Membrane Bending
Pm Pb Dished head or
conical head Knuckle or junction to shell Internal pressure Membrane
Bending PL (1)
Q
Center region Internal pressure Membrane Bending
Pm Pb Flat head
Junction to shell Internal pressure Membrane Bending
PL Q (2)
Typical ligament in a
uniform pattern Pressure
Membrane (average through cross
section) Bending (average
through width of ligament., but
gradient through plate)
Peak
Pm
Pb
F
Perforated head or shell
Isolated or atypical ligament
Pressure Membrane Bending
Peak
Q F F
Internal pressure or external load or
moment
General membrane (average. across
full section). Stress component perpendicular to
section
Pm Cross section perpendicular to
nozzle axis
External load or moment
Bending across nozzle section Pm
Internal pressure
General membrane Local membrane
Bending Peak
Pm PL Q F Nozzle wall
Differential expansion
Membrane Bending
Peak
Q Q F
Nozzle
LTA – Nozzle wall Internal pressure
General membrane Local membrane
Bending Peak
Pm PL Q F
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
137
Table 2 – Examples of Stress Classification (Cont.)
Notes: 1. Consideration must also 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 which has the same net
bending moment as the actual stress distribution.
138
Table 3 – Thickness Averaging for In-Service Inspection Codes
In-Service Inspection Codes
Summary Of Metal Loss Rules
API 510 The average measured thickness, amt , is determined by averaging the thickness readings over the following lengths:
min , 20 602DL inches when D inches = ≤
min , 40 603DL inches when D inches = >
The required
strength check is as follows: minamt CA t− ≥
An additional check is made the minimum measured thickness: min0.5mmt CA t− ≥
An alternative, the corrosion and/or erosion can be analyzed using stress analysis techniques with the results evaluated using principles of the ASME Boiler and Pressure Vessel Code, Section VIII, Division 2, Appendix IV is permitted
API 570 • ASME B31G • Stress analysis evaluated using the principles of the ASME Boiler and
Pressure Vessel Code, Section VIII, Division 2, Appendix IV • Methodology included in API 510
API 653 The average measured thickness, amt , is determined by averaging the thickness readings over the following length:
max 3.7 , 40.0mmL Dt inches =
The required strength check is as follows: minamt CA t− ≥
An additional check is made the minimum measured thickness: min0.6mmt CA t− ≥
An alternative, the corrosion and/or erosion can be analyzed using stress analysis techniques with the results evaluated using principles of the ASME Boiler and Pressure Vessel Code, Section VIII, Division 2, Appendix IV is permitted
NBIC The assessment is the same as that required by API 510
139
Table 4 – Section Properties for Computation of Longitudinal Stress in a Cylinder with an LTA
( )22X m LX f LXXI I A y I A y y= + − − +
Y LYYI I I= −
( )4 4
64X y o iI I D Dπ= = −
( )
2 3 2
2 33
2 2 2
2 2
3 2sin1 sin cos2 4
sin 13 2 6
LX
d d dR R R
I R dd d d
R d R R R
θθ θ θθ
θθ
− + − + − +
= − + −
( )2 3
32 3
31 sin cos2 4LY
d d dI R dR R R
θ θ θ
= − + − −
2 sin 113 2LX
R dyR d R
θθ
= − + −
( ) ( )0.58
i o i ot
D D c D DA
π + − + =
2
4a iA Dπ=
( )2 2
4m o iA D Dπ= −
140
Table 4 – Section Properties for Computation of Longitudinal Stress in a Cylinder with an LTA (Continued)
For A Region of Local Metal Loss Located on the Inside Surface
For A Region of Local Metal Loss Located on the Outside Surface
( )2 2
4f f iA D Dθ= −
w a fA A A= +
( )3 3sin112
f i
m f
D Dy
A Aθ −
=−
0.0Ax =
2o
ADy y= +
sin2
oB
Dx θ=
cos2
oB
Dy y θ= +
( )3 3sin112
f i
a f
D Db
A Aθ −
=+
2fD
R =
( )2
f iD Dd
−=
( )2
o fD Dt
−=
( )8
o ftf
c D DA
+=
( )2 2
4f o fA D Dθ= −
w aA A=
( )3 3sin112
o f
m f
D Dy
A Aθ −
=−
0.0Ax =
2f
A
Dy y= +
sin2
fB
Dx θ=
cos2
fB
Dy y θ= +
0b =
2oDR =
( )2
o fD Dd
−=
( )2
f iD Dt
−=
( )8
i ftf
c D DA
+=
141
Table 5 – LTA Assessment Methods
Method Description 1 API-579 Section 5, Level 1 Analysis – B31.G surface correction,
rectangular area, API level 1 Folias factor 2 API-579 Section 5, Level 2 Analysis – B31.G surface correction, effective
area, API level 2 Folias factor 3 API-579 Section 5, Level 2 Analysis – B31.G surface correction, exact
area, API level 2 Folias factor 4 Modified B31-G Method – B31.G surface correction, 0.85dl area, AGA
Folias factor 5 Modified B31-G Method (RSTRENG) – B31.G surface correction, effective
area, AGA Folias factor 6 Modified B31-G Method – B31.G surface correction, exact area, AGA
Folias factor 7 Original B31-G Method – B31.G surface correction, parabolic area, B31-G
Folias factor 8 Thickness Averaging – API 510, 8th Edition
9 Thickness Averaging – API 653, 2nd Edition
10 British Gas Single Defect Method – B31.G surface correction, exact area, BG Folias factor
11 British Gas Complex Defect Method – B31.G surface correction, exact area, BG Folias factor
12 Chell Method – Chell surface correction, exact area, B31-G Folias factor
13 Osage Method – Chell surface correction, effective area, D/t dependent Folias factor
14 API-579, Level 1, Hybrid 1 Analysis – Chell surface correction, rectangular area, API level 1 Folias factor
15 API-579, Level 2, Hybrid 1 Analysis – Chell surface correction, effective area, API level 2 Folias factor
16 API-579, Level 1, Hybrid 2 Analysis – Chell surface correction, rectangular area, BG Folias factor
17 API-579, Level 2, Hybrid 2 Analysis – Chell surface correction, effective area, BG Folias factor
18 API-579, Level 1, Hybrid 3 Analysis – Chell surface correction, rectangular area, JO Folias factor
19 API-579, Level 2, Hybrid 3 Analysis – Chell surface correction, effective area, JO Folias factor
20 Battelle Method – B31.G surface correction, rectangular area, Battelle Folias factor
21 BS 7910, Appendix G (Isolated Defect) – B31.G surface correction, rectangular area, BG Folias factor
22 BS 7910, Appendix G (Grouped Defects) – B31.G surface correction, rectangular area, BG Folias factor
23 Kanninen Equivalent Stress – B31.G surface correction, rectangular area, shell theory Folias factor
24 Shell Theory Method – Chell surface correction, exact area, shell theory Folias factor
142
Table 5 – LTA Assessment Methods (Continued)
25 Thickness Averaging – API 579, Level 1
26 Thickness Averaging – API 579, Level 2
27 Modified API-579 Section 5, Level 2 Analysis – B31.G surface correction, rectangular area, Modified API Folias factor
28 API-579 Section 5, Level 2 Analysis – B31.G surface correction, effective area, Modified API Folias factor
29 Janelle Method – rectangular area
30 Janelle Method – effective area
143
Table 6 – Validation Cases for the Undamaged Failure Pressure Calculation Method
Outside Diameter (in)
Thickness (in)
Failure Pressure from FEA
(psi)
Failure Pressure from Svensson
Method (psi)
Error Between Methods
6.625 0.28 5064.6 5121.1 1.1%
12.75 0.375 3478.4 3515.9 1.1%
24.0 0.375 1822.4 1841.5 1.0%
36.0 0.375 1204.8 1221.2 1.4%
Outside Diameter (in)
ID Equivalent Plastic Strain
from FEA
ID Equivalent Plastic Strain
from Svensson Method
OD Equivalent Plastic Strain
from FEA
OD Equivalent Plastic Strain
from Svensson Method
6.625 0.1792 0.1811 0.1536 0.1529
12.75 0.1795 0.1765 0.1616 0.1571
24.0 0.1786 0.1717 0.1691 0.1616
36.0 0.1731 0.1700 0.1669 0.1633
Notes: Table 118 The yield stress for the material model used in the FEA and Svensson
method was 34135 psi. Table 118 The ultimate stress and corresponding plastic strain for the material was
82889 psi and 0.3213 in/in. 3. The strain hardening coefficient for the material was 0.3233
144
Table 7 – Parameters for a Through-Wall Longitudinal Crack in a Cylinder Subject to a Through-Wall Membrane and Bending Stress
Rt
i Parameter C0 C1 C2 C3 C4 C5
3.0 Amm 1.0073E+00 8.3839E-01 1.5071E-01 5.4466E-02 -7.5887E-03 2.5248E-04
Amb -5.7070E-03 8.1803E-02 -2.3171E-02 -1.5258E-01 2.4677E-02 -3.0187E-04
5.0 Amm 1.0048E+00 1.8860E-01 7.3172E-01 -8.4972E-02 6.1289E-03 -1.7729E-04
Amb -2.3257E-03 1.4261E-01 -3.6873E-02 2.1666E-03 4.8189E-03 1.4505E-04
10.0 Amm 9.9652E-01 1.3041E-01 3.3780E-01 4.7232E-03 -2.7829E-03 1.3064E-04
Amb -4.7919E-03 1.6845E-01 -3.8474E-02 8.8191E-02 -9.8223E-04 9.9173E-05
20.0 Amm 1.0011E+00 1.2212E-01 4.4068E-01 -2.5824E-02 1.1045E-03 -2.3964E-05
Amb -2.9633E-04 1.5835E-01 -3.2881E-02 -8.9569E-03 1.1153E-02 -4.4610E-04
50.0 Amm 1.0010E+00 2.2135E-01 3.8500E-01 -9.8415E-03 -3.2277E-04 2.3126E-05
Amb -1.3263E-04 1.7173E-01 -3.2485E-02 -3.4733E-03 9.5691E-03 -3.3192E-04
100.0 Amm 1.0115E+00 9.2952E-02 5.6457E-01 -5.7580E-02 4.4685E-03 -1.3837E-04
Amb -4.0142E-04 1.8879E-01 -3.3723E-02 -1.6795E-02 1.3916E-02 -5.4210E-04
Notes: Table 118 The equations to determine the coefficients are shown below.
A C C C C C Cmm = + + + + +0 1 22
33
44
55 0 5
λ λ λ λ λ.
A C C CC C Cmb =
+ ++ + +
0 1 22
3 42
5310
λ λλ λ λ.
Table 118 Interpolation may be used for intermediate values of R ti .
Table 118 The solutions can be used for cylinders with 3 100≤ ≤R ti ; for R ti < 3 use the solution for
R ti = 3 and for R ti > 100 use the solution for R ti = 100 . Interpolation for values of
R ti other than those provided is recommended.
Table 118 Crack and geometry dimensional limits: λ ≤ 12 5. . If 12.5λ > , then use the following
solutions. If λ exceeds the permissible limit, then the following equations can be used:
Amm =+ +
+ +LNM
OQP
−
−
10202 0 44108 61244 1010 0 026421 15329 10
2 3 4
2 6 4
0 5. . . ( )
. . . ( )
.λ λ
λ λ
Amb =− + −
+ +
− −
− −
6 6351 10 0 049633 8 7408 10
10 19046 10 57868 10
3 2 3 4
3 2 3 4
. . . ( )
. . ( ) .c h
c hλ λ
λ λ
145
Table 8 – LTA Database 1 Case Descriptions
Case Number Description
1-25
These tests were performed by the Texas Eastern Transmission Corporation and are described in Reference 1-3. This group of tests involved burst tests of corroded pipe samples removed from service and fabricated into end-capped vessels. Only six different specimens were used to generate the 25 cases; leaks were repaired and the vessel tested again.
26-31
These cases are another group of tests performed for the Texas Eastern Transmission Company. Details and discussion of these tests can be found in References 1-4, 1-5, and 1-6. The six pressure vessel tests were fabricated from samples of corroded pipe.
32-42 These cases are burst tests conducted with PRC funding. All the cases are pressure vessel tests fabricated from line-pipe samples contributed by several pipeline operators.
43-47, 52-78, 83 These cases are burst test results produced by independent pipeline operators. The tests are corroded pipes fabricated into end-capped vessels.
48-51, 79-81, 86 These cases are investigations of service failures by pipeline operators. As such, the longitudinal stress in the pipe is unknown.
87-92
These cases represent burst tests performed by various pipeline operators. The specimens are corroded pipe removed from service and fabricated in pressure vessels. Case 89 involves internal corrosion; the rest have external corrosion.
93-105
These cases are burst tests of end-capped pipe samples performed for Nova. The defects in these test are machined, corrosion simulating, notches of significant width (>1”). Cases 93-96 and 102 were spirally oriented notches. Cases 97-99 were single longitudinally oriented notches. Cases 100 and 101 had pairs of longitudinally oriented notches on the same axial line, separated by different amounts. Cases 103 and 104 involved pairs of parallel, overlapping, longitudinally oriented notches, separated circumferentially by small multiples of the wall thickness. Case 105 is a defect free control case pressurized to failure. More details of these cases can be found in References1-7 and 1-8. There are some discrepancies between the original data and the data found in Reference 1-1 and 1-2. Original values were used.
106-117
Cases 106-117 are pipe samples removed from service that had internal pitting. Testing on these cases was performed in a special rig that allowed pressurization of the pipe without axial stress. Defects were mostly isolated pits less than 3” in axial length. Case 107 gave an anomalous result as it was discovered that a fatigue crack had extended the pit. Cases can be found in Reference 1-9. There are some discrepancies between the original data and the data found in Reference 1-1 and 1-2. Original values were used.
118-124
These cases are a variety of machined, corrosion simulating notches. Case 118 is a defect free control case. Cases 119 and 124 contain long, single, longitudinally oriented notches. Case 120 contains two longitudinally oriented slots of different lengths and depths; one on the side of the pipe and one on the other side of the pipe. Cases 121 and 122 had bands of material of differing sizes removed around the complete circumference in two locations along the axis of the sample. Case 123 contains two different sized rectangular patches of removed metal each on opposite sides of the pipe. All cases were pressurized to failure. Failures were all ruptures
146
Case Number Description occurring at one defect.
Table 8 – LTA Database 1 Case Descriptions (Continued)
Case Number Description
125-157
These cases were presented by British Gas researchers and can be found also in Reference 1-10. They include various machined defects to simulate corroded pipe. Cases 125-129 are a series of single notch defects designed to evaluate the effect of flaw length. The flaws were narrow, behaving more like a crack than a pit-like flaw. Cases 130-133 involve tests with closely spaced notches to monitor defect interaction. Cases 134-142 involve tests with closely spaced round pits. Cases 143-152 are tests to address the behavior of patches of missing metal and their interactions with each other and with rounded pits. Cases 153-157 contain short flaws within longer flaws or areas of reduced wall thickness. Cases 132, 141, and 143 are omitted from the statistical analysis due to lack of information.
158-162
These cases are part of an experiment carried out at Southwest Research Institute and reported in Reference 1-11. Metal loss in these cases was simulated by machining away 25-50% of the wall thickness over rectangular areas of various sizes. Two identical areas of metal loss were created with 180 degrees of circumferential separation between the two. This was done so that one defect would be in compression while the other was in tension for an applied bending moment. The tests were subjected to various combinations of internal pressure and bending moments.
163-187
These cases were performed at the University of Waterloo and can be found in References 1-12, 1-13, and 1-14. These burst tests were conducted on pipes containing various arrays of electrochemically machined pits. Longitudinal, circumferential, and spiral defect arrays were used. Some tests were run using a special apparatus that eliminated axial stress in the test case.
188-215
Most of these cases are failures and burst tests of corroded pipe in and removed from service. Cases 188 and 190 are hydrostatic failures of corroded pipe. Cases 189, 191, 195, and 214 are ductile mode in-service failures of corroded pipe. Cases 192-194, 198-213, and 215 are burst tests of corroded pipe samples previously removed from service. Cases 196 and 197 are brittle mode in-service failures of corroded pipe. Cases 192-194 and 196-197 are omitted from the statistical analysis due to lack of information.
216-221 These cases are additional cases found in Reference 1-1 and on the compiled spreadsheet. Case 217 is omitted from the statistical analysis due to lack of information.
147
Table 9 – LTA Database 2 Case Descriptions
Case Number Description 2000-2025 These cases are from test vessel #1. Cases 2000-2003 are longitudinal
defects in the shell. Case 2004 is a circumferential defect in the shell. Case 2005 is a defect in the shell to head weld. Cases 2006-2013 are defects located in the elliptical heads of the vessel. Cases 2014-2015 are defects in and around the nozzles of the vessel. Cases 2016-2019 are axial defects in the shell. Cases 2020-2025 are external axial defects in the shell.
2026-2057 These cases are from test vessel #2. Cases 2026-2029, 2043-2046, and 2052-2053 are longitudinal defects in the shell. Case 2030 is a circumferential defect in the shell. Case 2031 is a defect in the shell to head weld. Cases 2032-2039 are defects in the elliptical heads of the vessel. Cases 2040-2042 and 2054-2057 are defects around the nozzles of the vessel. Cases 2047-2051 are external axial defects in the shell. Cases 2054-2057 are omitted from the statistical analysis due to lack of information.
Table 10 – LTA Database 3 Case Descriptions
Case Number Description
3000-3006 These cases are machined isolated pit defects. Cases 3000-3003 are external pits and cases 3004-3006 are internal pits.
3007-3035 These cases contain machined groove defects. Cases 3007-3013 and 3017-3035 are external grooves and cases 3014-3016 are internal grooves.
3036-3045, 3047-3057
These cases contain machined patches that simulate areas of general corrosion. Cases 3036-3042 and 3047-3057 are external general defects and cases 3043-3045 are patches of internal corrosion.
3046 This case is a defect free control case.
3058-3063 These cases are machined circumferential defects. Cases 3058 and 3061 are areas of external general corrosion. Cases 3059 and 3062 are external grooves. Cases 3060 and 3063 are external slots.
3064-3068 These cases contain adjacent deep pit defects.
3069-3070 These cases have multiple adjacent deep pit defects. Case 3069 has 4 connected pits, and case 3070 has 3 adjacent pits.
3071-3074 These cases contain adjacent areas of machined general corrosion patches.
3075-3080 These cases contain machined pits in areas of machined general corrosion. Cases 3075 and 3076 have two pits in an area of general corrosion. Cases 3077 and 3078 have one pit in an area of general corrosion.
148
Table 11 – LTA Database 4 Case Descriptions
Case Number Description
4000-4187 These cases are FEA models of corroded pipe. Diameter, thickness, defect length, depth, and width have all been varied.
4188-4198 These cases are defect free FEA control cases.
4199-4220 These cases are FEA models of corroded pipe with decreased material yield stress.
4221-4242 These cases are FEA models of corroded pipe with increased material yield stress.
4243-2251 These cases are FEA models of deep corrosion pits.
4252-4347 These cases are FEA models of axially adjacent corrosion pits of various dimensions.
4348-4441 These cases are FEA models of axially adjacent general areas of corrosion of varying parameters.
4442-4459 These cases are repeats of cases 4415-4442, except that the defect length has been changed.
4460-4504 These cases are FEA models of corrosion pits contained within an area of general corrosion.
4505- These cases are FEA models of undamaged validation cases.
149
Table 12 – FEA Results for a Cylindrical Shell with a LTA
FEA Model Type LTA Length (in)
Lambda, λ Failure Pressure (psi)
RSF
0.0 0 1823.2 1.0 11.4893 5 1431.8 0.785 22.9784 10 1236.0 0.678 34.468 15 1183.4 0.649
45.9572 20 1147.6 0.629 57.4466 25 1127.2 0.618 68.9358 30 1114.0 0.611
3D Solid
Infinite Infinite 1090.8 0.598 0.0 0 1822.2 1.0
11.4893 5 1385.4 0.760 22.9784 10 1138.4 0.625 34.468 15 1017.8 0.559
45.9572 20 966.4 0.530 57.4466 25 943.6 0.518 68.9358 30 932.0 0.511
Axisymmetric Solid
Infinite Infinite 911.1 0.500 Notes 1. The FEA models were run with non-linear geometry and elastic-plastic material properties. 2. The geometry used for the models was a standard 24 inch pipe (inside diameter of 23.25
inches and thickness of 0.375 inches) 3. The LTA is a rectangular area of metal loss with depth of 0.1875 inches. 4. For the 3D models, the flaw length in the circumferential direction was a 60 degree arc.
150
Table 13 – FEA Results for a Spherical Shell with a LTA
FEA Model Type LTA Length (in)
Lambda, λ Failure Pressure (psi)
RSF
0.0 0 1650.2 1.0 5.7447 2.5 1620.4 0.982 11.4893 5 1466.2 0.889 17.2340 7.5 1341.4 0.813 22.9784 10 1212.6 0.735 34.468 15 1081.2 0.655 45.9572 20 1001.4 0.607 57.4466 25 943.4 0.572 68.9358 30 905.6 0.549
Axisymmetric Solid
Infinite (148.44) Infinite (63.6) 825.2 0.500 Notes 1. The FEA models were run with non-linear geometry and elastic-plastic material properties. 2. The geometry used for the models was a sphere with inside diameter of 47.25 inches and
thickness of 0.375 inches. 3. The LTA was modeled as a circular area of metal loss with diameter equal to the LTA
Length and uniform depth of 0.1875 inches.
151
Table 14 – API 579 Folias Factor Values for a Cylinder and Sphere
Lambda, λ Folias Factor, Mt, for a Cylindrical Shell
Folias Factor, Mt, for a Spherical Shell
0.0 1.001 1.001
0.5 1.056 1.063
1.0 1.199 1.218
1.5 1.394 1.427
2.0 1.618 1.673
2.5 1.857 1.946
3.0 2.103 2.240
3.5 2.351 2.552
4.0 2.600 2.880
4.5 2.847 3.221
5.0 3.091 3.576
5.5 3.331 3.944
6.0 3.568 4.323
6.5 3.802 4.715
7.0 4.032 5.119
7.5 4.262 5.535
8.0 4.493 5.964
8.5 4.728 6.405
9.0 4.972 6.858
9.5 5.227 7.325
10.0 5.500 7.806
10.5 5.794 8.301
11.0 6.117 8.810
11.5 6.474 9.334
12.0 6.872 9.873
12.5 7.316 10.429
13.0 7.815 11.002
13.5 8.375 11.592
14.0 9.004 12.200
14.5 9.710 12.827
15.0 10.500 13.474
15.5 11.382 14.142
16.0 12.361 14.832
16.5 13.446 15.544
152
Table 14 – API 579 Folias Factor Values for a Cylinder and Sphere (Continued)
Lambda, λ Folias Factor, Mt, for a Cylindrical Shell
Folias Factor, Mt, for a Spherical Shell
17.0 14.638 16.281
17.5 15.941 17.042
18.0 17.355 17.830
18.5 18.876 18.645
19.0 20.496 19.489
19.5 22.208 20.364
20.0 23.999 21.272
Notes 1. The equation for the cylindrical shell is as follows. If λ is greater than 30, use a λ value of 30
in the calculation.
( )( ) ( )( ) ( )
2 3
4 5 4 6
5 7 7 8
8 9 10 10
1.0010 0.014195 0.29090 0.096420
0.020890 0.0030540 2.9570 10
1.8462 10 7.1553 10
1.5631 10 1.4656 10
tM λ λ λ
λ λ λ
λ λ
λ λ
−
− −
− −
= − + − +
− + −
+ −
+
2. The equation for the spherical shell is as follows. The λ value is only limited by the inside circumference of the shell.
( ) ( )( ) ( )
2
2
1.0005 0.49001 0.324091.0 0.50144 0.011067tM
λ λ
λ λ
+ +=
+ −
153
Table 15 – Cases Omitted from Statistics
Case Numbers Reason
132, 141, 143 The length of the flaw is unknown.
192-194 The failure pressure or bending moment of the test is unknown.
196-197, 217 No information is known regarding these cases.
2054-2057 The defect depth is unknown.
26, 36-37, 40-41, 45, 49-50, 52, 62, 79, 83,
85, 189, 195, 200-201,
2010, 2019, 3001-3002, 3005-3006,
3023, 3032-3033, 3064-3070, 4248-4251
These cases have a remaining thickness over original thickness ratio of less than 0.2. The statistical analysis results obtained from these cases will skew the data as cases with less than 20% of the original wall thickness are not practical applications for the various analysis methods presented here.
107 Case 107 gave an anomalous result as it was discovered that a fatigue crack had extended the pit.
Database 2 The cases in this database were not used in the LTA validation. The vessels were pressurized to the point of plastic deformation multiple times and the results obtained from the test are not consistent with the other databases.
105, 118, 1005,
4188-4198
These cases are defect free control cases, and are not included in the statistical analysis.
154
Table 16 – Failure Ratio Statistics for Method Validation
Method Mean Failure Ratio
Failure Ratio Standard Deviation
Failure Ratio Upper 95% Prediction
Limit
Failure Ratio Lower 95% Prediction
Limit 1 - API 579 Section 5, Level 1 Analysis - B31.G surface correction, rectangular area, API level 1 Folias factor
1.2184 0.3134 1.8341 0.6027
2 - API 579 Section 5, Level 2 Analysis - B31.G surface correction, effective area, API level 2 Folias factor
1.0397 0.1514 1.337 0.7423
3 - API-579 Section 5, Level 2 Analysis - B31.G surface correction, exact area, API level 2 Folias factor
1.015 0.1495 1.3088 0.7213
4 - Modified B31.G Method - B31.G surface correction, 0.85dl area, AGA Folias factor
1.0035 0.1976 1.3916 0.6154
5 - Modified B31.G Method (RSTRENG) - B31.G surface correction, effective area, AGA Folias factor
1.0284 0.1465 1.3161 0.7408
6 - Modified B31.G Method - B31.G surface correction, exact area, AGA Folias factor
1.006 0.1457 1.2922 0.7198
7 - Original B31.G Method - B31.G surface correction, parabolic area, B31-G Folias factor
1.0317 0.2937 1.6087 0.4547
8 - Thickness Averaging - API 510, 8th Edition 1.1225 0.2597 1.6326 0.6124
9 - Thickness Averaging - API 653, 2nd Edition 1.217 0.2962 1.7988 0.6351
10 - British Gas Single Defect Method - B31.G surface correction, exact area, BG Folias factor
1.0782 0.2413 1.5522 0.6042
11 - British Gas Complex Defect Method - B31.G surface correction, exact area, BG Folias factor
1.0953 0.1978 1.4838 0.7067
12 - Chell Method - Chell surface correction, exact area, B31-G Folias factor
1.0142 0.2099 1.4264 0.6019
155
Table 16 – Failure Ratio Statistics for Method Validation (Continued)
Method Mean Failure Ratio
Failure Ratio Standard Deviation
Failure Ratio Upper 95% Prediction
Limit
Failure Ratio Lower 95% Prediction
Limit 13 - Osage Method - Chell surface correction, effective area, D/t dependent Folias factor
0.9361 0.1677 1.2656 0.6067
14 - API 579, Level 1, Hybrid 1 Analysis - Chell surface correction, rectangular area, API level 1 Folias factor
1.0132 0.2098 1.4253 0.601
15 - API 579, Level 2, Hybrid 1 Analysis - Chell surface correction, effective area, API level 2 Folias factor
0.9204 0.1717 1.2576 0.5832
16 - API 579, Level 1, Hybrid 2 Analysis - Chell surface correction, rectangular area, BG Folias factor
0.9658 0.2068 1.3719 0.5596
17 - API 579, Level 2, Hybrid 2 Analysis - Chell surface correction, effective area, BG Folias factor
0.9079 0.1752 1.252 0.5638
18 - API 579, Level 1, Hybrid 3 Analysis - Chell surface correction, rectangular area, JO Folias factor
0.8963 0.1747 1.2393 0.5532
19 - API 579, Level 2, Hybrid 3 Analysis - Chell surface correction, effective area, JO Folias factor
0.8537 0.1446 1.1377 0.5697
20 - Battelle Method - B31.G surface correction, rectangular area, Battelle Folias factor
1.078 0.2421 1.5536 0.6025
21 - BS 7910, Appendix G (Isolated Defect) - B31.G surface correction, rectangular area, BG Folias factor
1.0782 0.2413 1.5522 0.6042
22 - BS 7910, Appendix G (Grouped Defects) - B31.G surface correction, rectangular area, BG Folias factor
1.0105 0.1906 1.385 0.6361
23 - Kanninen Equivalent Stress - B31.G surface correction, rectangular area, shell theory Folias factor
1.3862 0.5358 2.4387 0.3337
156
Table 16 – Failure Ratio Statistics for Method Validation (Continued)
Method Mean Failure Ratio
Failure Ratio Standard Deviation
Failure Ratio Upper 95% Prediction
Limit
Failure Ratio Lower 95% Prediction
Limit 24 - Shell Theory Method - Chell surface correction, exact area, shell theory Folias factor
1.168 0.3156 1.7879 0.5481
25 - Thickness Averaging - API 579, Level 1 1.3599 0.445 2.234 0.4858
26 - Thickness Averaging - API 579, Level 2 1.0391 0.299 1.6264 0.4518
27 - Modified API 579 Section 5, Level 1 Analysis - B31.G surface correction, rectangular area, Modified API Folias factor
1.1896 0.2939 1.767 0.6122
28 - Modified API 579 Section 5, Level 2 Analysis - B31.G surface correction, effective area, Modified API Folias factor
1.0415 0.1509 1.3408 0.7422
29 - Janelle Method, Level 1 - rectangular area 1.1166 0.2253 1.5591 0.674
30 - Janelle Method, Level 1 - effective area 1.0128 0.1433 1.2942 0.7314
157
Table 17 – Stress Limits Based on Design Codes
Design Code Equipment ysF utsF
ASME Section VIII, Divison 1 (pre 1999) Pressure Vessels 2/3 1/4
ASME Section VIII, Divison 1 (post 1999) Pressure Vessels 2/3 1/3.5
ASME Section VIII, Division 2 Pressure Vessels 2/3 1/3
New Proposed ASME Section VIII, Division 2
Pressure Vessels 2/3 1/2.4
EN13445 Pressure Vessels 2/3 1/2.4
CODAP Pressure Vessels 1 1/3
AS 1210 Pressure Vessels 2/3 1/2.35
BS 5500 Pressure Vessels 2/3 1/2.35
ASME B31.1 (pre 1999) Power Piping 2/3 1/4
ASME B31.1 (post 1999) Power Piping 2/3 1/3.5
ASME B31.3 Process Piping 2/3 1/3
ASME B31.4 Liquid Piping 0.72 1
ASME B31.8, Class 1, Division I Gas Piping 4/5 1
ASME B31.8, Class 1, Division II Gas Piping 0.72 1
ASME B31.8, Class 2 Gas Piping 3/5 1
ASME B31.8, Class 3 Gas Piping 1/2 1
ASME B31.8, Class 4 Gas Piping 2/5 1
API 620 Atmospheric Storage Tanks
3/5 3/10
API 650 Low-Pressure Storage Tanks
2/3 2/5
158
Table 18 – MAWP Ratio vs. Allowable RSF for ASME Section VIII, Division 1 (pre 1999) and ASME B31.1 (pre 1999)
Method Allowable RSF
Mean MAWP Ratio
MAWP Ratio
Standard Deviation
MAWP Ratio Upper 95% Prediction
Limit
MAWP Ratio Lower 95% Prediction
Limit 0.7 3.8496 0.8788 5.5758 2.1235 0.75 4.0301 0.9478 5.8919 2.1683 0.8 4.2236 1.0253 6.2375 2.2096 0.85 4.4319 1.1069 6.6061 2.2576 0.9 4.6610 1.1858 6.9902 2.3317 0.95 4.9079 1.2575 7.3780 2.4378
1 - API 579 Section 5, Level 1 Analysis - B31.G surface correction, rectangular area, API level 1 Folias factor 1.0 5.1641 1.3249 7.7666 2.5616
0.7 3.4419 0.5716 4.5646 2.3191 0.75 3.5509 0.5560 4.6431 2.4587 0.8 3.6780 0.5564 4.7709 2.5850 0.85 3.8218 0.5751 4.9513 2.6922 0.9 3.9952 0.6075 5.1885 2.8019 0.95 4.1939 0.6435 5.4580 2.9299
2 - API 579 Section 5, Level 2 Analysis - B31.G surface correction, effective area, API level 2 Folias factor 1.0 4.4107 0.6778 5.7422 3.0793
0.7 3.3769 0.6030 4.5614 2.1924 0.75 3.4780 0.5792 4.6157 2.3403 0.8 3.5978 0.5687 4.7150 2.4806 0.85 3.7349 0.5766 4.8675 2.6024 0.9 3.9011 0.6017 5.0830 2.7192 0.95 4.0944 0.6339 5.3396 2.8493
3 - API-579 Section 5, Level 2 Analysis - B31.G surface correction, exact area, API level 2 Folias factor 1.0 4.3060 0.6671 5.6163 2.9957
0.7 3.3822 0.7606 4.8761 1.8883 0.75 3.4912 0.7449 4.9544 2.0281 0.8 3.6227 0.7425 5.0812 2.1641 0.85 3.7702 0.7574 5.2578 2.2826 0.9 3.9405 0.7861 5.4846 2.3964 0.95 4.1336 0.8264 5.7568 2.5104
4 - Modified B31.G Method - B31.G surface correction, 0.85dl area, AGA Folias factor
1.0 4.3468 0.8693 6.0542 2.6393 0.7 3.5014 0.5976 4.6753 2.3275 0.75 3.6079 0.5791 4.7455 2.4703 0.8 3.7322 0.5750 4.8616 2.6028 0.85 3.8744 0.5896 5.0325 2.7163 0.9 4.0453 0.6194 5.2621 2.8286 0.95 4.2417 0.6564 5.5310 2.9524
5 - Modified B31.G Method (RSTRENG) - B31.G surface correction, effective area, AGA Folias factor 1.0 4.4595 0.6915 5.8177 3.1012
0.7 3.4404 0.6306 4.6791 2.2016 0.75 3.5396 0.6049 4.7277 2.3515 0.8 3.6574 0.5912 4.8187 2.4961 0.85 3.7932 0.5958 4.9634 2.6230 0.9 3.9577 0.6184 5.1724 2.7430 0.95 4.1490 0.6514 5.4284 2.8696
6 - Modified B31.G Method - B31.G surface correction, exact area, AGA Folias factor
1.0 4.3619 0.6854 5.7083 3.0156
159
Table 18 – MAWP Ratio vs. Allowable RSF for ASME Section VIII, Division 1 (pre 1999) and ASME B31.1 (pre 1999) (Continued)
Method Allowable RSF
Mean MAWP Ratio
MAWP Ratio
Standard Deviation
MAWP Ratio Upper 95% Prediction
Limit
MAWP Ratio Lower 95% Prediction
Limit 0.7 3.4403 0.9192 5.2460 1.6347 0.75 3.5408 0.9572 5.4209 1.6607 0.8 3.6565 1.0039 5.6284 1.6847 0.85 3.8052 1.0572 5.8819 1.7285 0.9 3.9715 1.1168 6.1651 1.7780 0.95 4.1600 1.1801 6.4781 1.8419
7 – Original B31.G Method – B31.G surface correction, parabolic area, B31-G Folias factor
1.0 4.3732 1.2426 6.8141 1.9324 0.7 4.7645 1.1374 6.9987 2.5304 0.75 4.7645 1.1374 6.9987 2.5304 0.8 4.7645 1.1374 6.9987 2.5304 0.85 4.7645 1.1374 6.9987 2.5304 0.9 4.7645 1.1374 6.9987 2.5304 0.95 4.7645 1.1374 6.9987 2.5304
8 – Thickness Averaging – API 510, 8th Edition
1.0 4.7645 1.1374 6.9987 2.5304 0.7 5.1635 1.2870 7.6915 2.6355 0.75 5.1635 1.2870 7.6915 2.6355 0.8 5.1635 1.2870 7.6915 2.6355 0.85 5.1635 1.2870 7.6915 2.6355 0.9 5.1635 1.2870 7.6915 2.6355 0.95 5.1635 1.2870 7.6915 2.6355
9 – Thickness Averaging – API 653, 2nd Edition
1.0 5.1635 1.2870 7.6915 2.6355 0.7 3.5369 0.7360 4.9827 2.0912 0.75 3.6652 0.7619 5.1617 2.1687 0.8 3.8086 0.8011 5.3822 2.2350 0.85 3.9678 0.8513 5.6400 2.2955 0.9 4.1490 0.9070 5.9306 2.3674 0.95 4.3489 0.9646 6.2436 2.4541
10 – British Gas Single Defect Method – B31.G surface correction, exact area, BG Folias factor
1.0 4.5701 1.0177 6.5691 2.5710 0.7 3.6074 0.5867 4.7598 2.4550 0.75 3.7334 0.6129 4.9372 2.5296 0.8 3.8730 0.6549 5.1593 2.5867 0.85 4.0335 0.7085 5.4253 2.6418 0.9 4.2180 0.7681 5.7268 2.7093 0.95 4.4220 0.8256 6.0438 2.8003
11 – British Gas Complex Defect Method – B31.G surface correction, exact area, BG Folias factor
1.0 4.6475 0.8728 6.3620 2.9330 0.7 3.3119 0.7394 4.7643 1.8595 0.75 3.4208 0.7304 4.8554 1.9861 0.8 3.5504 0.7370 4.9980 2.1028 0.85 3.7057 0.7615 5.2016 2.2099 0.9 3.8890 0.8014 5.4632 2.3148 0.95 4.0863 0.8496 5.7551 2.4176
12 – Chell Method – Chell surface correction, exact area, B31-G Folias factor
1.0 4.2996 0.8949 6.0574 2.5418
160
Table 18 – MAWP Ratio vs. Allowable RSF for ASME Section VIII, Division 1 (pre 1999) and ASME B31.1 (pre 1999) (Continued)
Method Allowable RSF
Mean MAWP Ratio
MAWP Ratio
Standard Deviation
MAWP Ratio Upper 95% Prediction
Limit
MAWP Ratio Lower 95% Prediction
Limit 0.7 3.1684 0.7459 4.6335 1.7032 0.75 3.2398 0.7048 4.6242 1.8553 0.8 3.3292 0.6722 4.6496 2.0089 0.85 3.4431 0.6550 4.7297 2.1566 0.9 3.5945 0.6664 4.9035 2.2856 0.95 3.7728 0.6971 5.1420 2.4036
13 - Osage Method - Chell surface correction, effective area, D/t dependent Folias factor
1.0 3.9707 0.7334 5.4114 2.5300 0.7 3.3101 0.7400 4.7637 1.8566 0.75 3.4185 0.7307 4.8538 1.9832 0.8 3.5476 0.7371 4.9954 2.0997 0.85 3.7025 0.7614 5.1981 2.2068 0.9 3.8854 0.8012 5.4590 2.3117 0.95 4.0824 0.8492 5.7504 2.4143
14 - API 579, Level 1, Hybrid 1 Analysis - Chell surface correction, rectangular area, API level 1 Folias factor 1.0 4.2953 0.8946 6.0525 2.5382
0.7 3.1530 0.7621 4.6500 1.6561 0.75 3.2180 0.7227 4.6375 1.7985 0.8 3.2990 0.6911 4.6565 1.9416 0.85 3.4044 0.6726 4.7255 2.0833 0.9 3.5449 0.6819 4.8844 2.2054 0.95 3.7128 0.7121 5.1116 2.3140
15 - API 579, Level 2, Hybrid 1 Analysis - Chell surface correction, effective area, API level 2 Folias factor 1.0 3.9040 0.7493 5.3758 2.4322
0.7 3.2316 0.7718 4.7477 1.7155 0.75 3.3177 0.7537 4.7983 1.8372 0.8 3.4213 0.7497 4.8939 1.9488 0.85 3.5518 0.7626 5.0498 2.0539 0.9 3.7137 0.7948 5.2748 2.1526 0.95 3.8958 0.8378 5.5415 2.2502
16 - API 579, Level 1, Hybrid 2 Analysis - Chell surface correction, rectangular area, BG Folias factor
1.0 4.0946 0.8832 5.8294 2.3598 0.7 3.1445 0.7741 4.6651 1.6240 0.75 3.2053 0.7371 4.6531 1.7576 0.8 3.2801 0.7070 4.6687 1.8914 0.85 3.3766 0.6900 4.7319 2.0212 0.9 3.5069 0.6970 4.8760 2.1377 0.95 3.6667 0.7252 5.0912 2.2423
17 - API 579, Level 2, Hybrid 2 Analysis - Chell surface correction, effective area, BG Folias factor
1.0 3.8510 0.7632 5.3501 2.3519 0.7 3.1584 0.7930 4.7160 1.6007 0.75 3.2260 0.7611 4.7209 1.7311 0.8 3.3104 0.7363 4.7566 1.8642 0.85 3.4142 0.7218 4.8320 1.9964 0.9 3.5365 0.7202 4.9512 2.1218 0.95 3.6738 0.7317 5.1111 2.2366
18 - API 579, Level 1, Hybrid 3 Analysis - Chell surface correction, rectangular area, JO Folias factor
1.0 3.8290 0.7547 5.3114 2.3467
161
Table 18 – MAWP Ratio vs. Allowable RSF for ASME Section VIII, Division 1 (pre 1999) and ASME B31.1 (pre 1999) (Continued)
Method Allowable RSF
Mean MAWP Ratio
MAWP Ratio
Standard Deviation
MAWP Ratio Upper 95% Prediction
Limit
MAWP Ratio Lower 95% Prediction
Limit 0.7 3.0967 0.8083 4.6844 1.5089 0.75 3.1382 0.7660 4.6427 1.6336 0.8 3.1948 0.7219 4.6128 1.7767 0.85 3.2695 0.6817 4.6085 1.9306 0.9 3.3667 0.6507 4.6449 2.0885 0.95 3.4875 0.6363 4.7374 2.2376
19 - API 579, Level 2, Hybrid 3 Analysis - Chell surface correction, effective area, JO Folias factor
1.0 3.6304 0.6391 4.8858 2.3750 0.7 3.5181 0.7547 5.0006 2.0357 0.75 3.6420 0.7805 5.1751 2.1089 0.8 3.7845 0.8179 5.3912 2.1779 0.85 3.9475 0.8655 5.6476 2.2475 0.9 4.1335 0.9178 5.9363 2.3307 0.95 4.3431 0.9703 6.2491 2.4371
20 - Battelle Method - B31.G surface correction, rectangular area, Battelle Folias factor
1.0 4.5694 1.0217 6.5763 2.5624 0.7 3.5369 0.7360 4.9827 2.0912 0.75 3.6652 0.7619 5.1617 2.1687 0.8 3.8086 0.8011 5.3822 2.2350 0.85 3.9678 0.8513 5.6400 2.2955 0.9 4.1490 0.9070 5.9306 2.3674 0.95 4.3489 0.9646 6.2436 2.4541
21 - BS 7910, Appendix G (Isolated Defect) - B31.G surface correction, rectangular area, BG Folias factor 1.0 4.5701 1.0177 6.5691 2.5710
0.7 3.4056 0.6658 4.7135 2.0978 0.75 3.5092 0.6574 4.8006 2.2179 0.8 3.6273 0.6637 4.9309 2.3237 0.85 3.7581 0.6851 5.1038 2.4124 0.9 3.9101 0.7184 5.3212 2.4990 0.95 4.0827 0.7602 5.5759 2.5896
22 - BS 7910, Appendix G (Grouped Defects) - B31.G surface correction, rectangular area, BG Folias factor 1.0 4.2823 0.8021 5.8579 2.7067
0.7 4.3514 1.4718 7.2423 1.4604 0.75 4.5660 1.6113 7.7310 1.4010 0.8 4.7931 1.7515 8.2334 1.3527 0.85 5.0393 1.8860 8.7439 1.3347 0.9 5.3005 2.0150 9.2585 1.3425 0.95 5.5782 2.1360 9.7739 1.3825
23 - Kanninen Equivalent Stress - B31.G surface correction, rectangular area, shell theory Folias factor 1.0 5.8690 2.2501 10.2887 1.4493
0.7 3.8278 0.8540 5.5053 2.1504 0.75 3.9704 0.9346 5.8063 2.1345 0.8 4.1254 1.0229 6.1348 2.1161 0.85 4.3002 1.1121 6.4847 2.1156 0.9 4.4953 1.1982 6.8489 2.1416 0.95 4.7108 1.2788 7.2227 2.1989
24 - Shell Theory Method - Chell surface correction, exact area, shell theory Folias factor
1.0 4.9518 1.3491 7.6017 2.3018
162
Table 18 – MAWP Ratio vs. Allowable RSF for ASME Section VIII, Division 1 (pre 1999) and ASME B31.1 (pre 1999) (Continued)
Method Allowable RSF
Mean MAWP Ratio
MAWP Ratio
Standard Deviation
MAWP Ratio Upper 95% Prediction
Limit
MAWP Ratio Lower 95% Prediction
Limit 0.7 4.8300 1.5839 7.9412 1.7188 0.75 5.0507 1.7875 8.5618 1.5395 0.8 5.3068 2.0618 9.3566 1.2569 0.85 5.6841 2.3371 10.2749 1.0934 0.9 6.1443 2.6847 11.4178 0.8707 0.95 6.6748 2.9860 12.5401 0.8095
25 - Thickness Averaging - API 579, Level 1
1.0 7.4340 3.2858 13.8882 0.9799 0.7 3.6916 1.0691 5.7914 1.5917 0.75 3.9833 1.2852 6.5078 1.4588 0.8 4.3724 1.5932 7.5019 1.2430 0.85 4.8674 1.9639 8.7250 1.0098 0.9 5.5303 2.4109 10.2659 0.7947 0.95 6.3377 2.8362 11.9087 0.7666
26 - Thickness Averaging - API 579, Level 2
1.0 7.4340 3.2858 13.8882 0.9799 0.7 3.7722 0.8347 5.4118 2.1327 0.75 3.9433 0.8932 5.6978 2.1888 0.8 4.1278 0.9621 6.0177 2.2379 0.85 4.3271 1.0366 6.3632 2.2910 0.9 4.5471 1.1103 6.7281 2.3661 0.95 4.7860 1.1778 7.0996 2.4725
27 - Modified API 579 Section 5, Level 1 Analysis - B31.G surface correction, rectangular area, Modified API Folias factor 1.0 5.0356 1.2410 7.4733 2.5979
0.7 3.4450 0.5711 4.5668 2.3232 0.75 3.5544 0.5562 4.6469 2.4619 0.8 3.6820 0.5572 4.7765 2.5874 0.85 3.8265 0.5765 4.9590 2.6940 0.9 4.0001 0.6096 5.1974 2.8028 0.95 4.1989 0.6461 5.4681 2.9298
28 - Modified API 579 Section 5, Level 2 Analysis - B31.G surface correction, effective area, Modified API Folias factor 1.0 4.4160 0.6806 5.7529 3.0790
0.7 3.5308 0.7205 4.9460 2.1155 0.75 3.6844 0.7366 5.1313 2.2375 0.8 3.8548 0.7689 5.3651 2.3444 0.85 4.0461 0.8133 5.6436 2.4485 0.9 4.2642 0.8596 5.9526 2.5757 0.95 4.4963 0.9078 6.2796 2.7131
29 - Janelle Method, Level 1 - rectangular area
1.0 4.7329 0.9556 6.6100 2.8558 0.7 3.3159 0.6239 4.5414 2.0904 0.75 3.4184 0.5860 4.5694 2.2673 0.8 3.5426 0.5630 4.6486 2.4367 0.85 3.6909 0.5617 4.7942 2.5877 0.9 3.8761 0.5790 5.0134 2.7389 0.95 4.0816 0.6070 5.2739 2.8894
30 - Janelle Method, Level 1 - effective area
1.0 4.2960 0.6389 5.5510 3.0411
163
Table 19 – MAWP Ratio vs. Allowable RSF for ASME Section VIII, Division 1 (post 1999) and ASME B31.1 (post 1999)
Method Allowable RSF
Mean MAWP Ratio
MAWP Ratio
Standard Deviation
MAWP Ratio Upper 95% Prediction
Limit
MAWP Ratio Lower 95% Prediction
Limit 0.7 3.3684 0.7689 4.8788 1.8580 0.75 3.5263 0.8294 5.1554 1.8972 0.8 3.6956 0.8972 5.4579 1.9334 0.85 3.8779 0.9685 5.7803 1.9754 0.9 4.0783 1.0376 6.1164 2.0403 0.95 4.2944 1.1003 6.4557 2.1331
1 - API 579 Section 5, Level 1 Analysis - B31.G surface correction, rectangular area, API level 1 Folias factor 1.0 4.5186 1.1593 6.7958 2.2414
0.7 3.0116 0.5001 3.9940 2.0293 0.75 3.1070 0.4865 4.0627 2.1514 0.8 3.2182 0.4869 4.1746 2.2618 0.85 3.3440 0.5032 4.3324 2.3556 0.9 3.4958 0.5316 4.5399 2.4517 0.95 3.6697 0.5631 4.7758 2.5636
2 - API 579 Section 5, Level 2 Analysis - B31.G surface correction, effective area, API level 2 Folias factor 1.0 3.8594 0.5931 5.0244 2.6944
0.7 2.9548 0.5276 3.9913 1.9184 0.75 3.0432 0.5068 4.0387 2.0478 0.8 3.1481 0.4977 4.1256 2.1705 0.85 3.2681 0.5045 4.2590 2.2771 0.9 3.4135 0.5265 4.4476 2.3793 0.95 3.5826 0.5547 4.6722 2.4931
3 - API-579 Section 5, Level 2 Analysis - B31.G surface correction, exact area, API level 2 Folias factor 1.0 3.7677 0.5837 4.9143 2.6212
0.7 2.9594 0.6655 4.2666 1.6522 0.75 3.0548 0.6518 4.3351 1.7746 0.8 3.1698 0.6497 4.4461 1.8936 0.85 3.2989 0.6627 4.6006 1.9972 0.9 3.4480 0.6878 4.7991 2.0969 0.95 3.6169 0.7231 5.0372 2.1966
4 - Modified B31.G Method - B31.G surface correction, 0.85dl area, AGA Folias factor
1.0 3.8034 0.7606 5.2975 2.3094 0.7 3.0637 0.5229 4.0909 2.0365 0.75 3.1569 0.5067 4.1523 2.1615 0.8 3.2657 0.5031 4.2539 2.2775 0.85 3.3901 0.5159 4.4034 2.3768 0.9 3.5397 0.5420 4.6043 2.4750 0.95 3.7115 0.5743 4.8396 2.5833
5 - Modified B31.G Method (RSTRENG) - B31.G surface correction, effective area, AGA Folias factor 1.0 3.9020 0.6050 5.0905 2.7136
0.7 3.0103 0.5518 4.0942 1.9264 0.75 3.0972 0.5293 4.1368 2.0576 0.8 3.2002 0.5173 4.2164 2.1841 0.85 3.3191 0.5213 4.3430 2.2951 0.9 3.4630 0.5411 4.5259 2.4001 0.95 3.6304 0.5699 4.7499 2.5109
6 - Modified B31.G Method - B31.G surface correction, exact area, AGA Folias factor
1.0 3.8167 0.5997 4.9947 2.6386
164
Table 19 – MAWP Ratio vs. Allowable RSF for ASME Section VIII, Division 1 (post 1999) and ASME B31.1 (post 1999) (Continued)
Method Allowable RSF
Mean MAWP Ratio
MAWP Ratio
Standard Deviation
MAWP Ratio Upper 95% Prediction
Limit
MAWP Ratio Lower 95% Prediction
Limit 0.7 3.0103 0.8043 4.5902 1.4304 0.75 3.0982 0.8375 4.7433 1.4531 0.8 3.1995 0.8784 4.9249 1.4741 0.85 3.3296 0.9251 5.1467 1.5124 0.9 3.4751 0.9772 5.3945 1.5557 0.95 3.6400 1.0326 5.6683 1.6117
7 - Original B31.G Method - B31.G surface correction, parabolic area, B31-G Folias factor
1.0 3.8266 1.0873 5.9624 1.6908 0.7 4.1690 0.9952 6.1238 2.2141 0.75 4.1690 0.9952 6.1238 2.2141 0.8 4.1690 0.9952 6.1238 2.2141 0.85 4.1690 0.9952 6.1238 2.2141 0.9 4.1690 0.9952 6.1238 2.2141 0.95 4.1690 0.9952 6.1238 2.2141
8 - Thickness Averaging - API 510, 8th Edition
1.0 4.1690 0.9952 6.1238 2.2141 0.7 4.5181 1.1261 6.7301 2.3061 0.75 4.5181 1.1261 6.7301 2.3061 0.8 4.5181 1.1261 6.7301 2.3061 0.85 4.5181 1.1261 6.7301 2.3061 0.9 4.5181 1.1261 6.7301 2.3061 0.95 4.5181 1.1261 6.7301 2.3061
9 - Thickness Averaging - API 653, 2nd Edition
1.0 4.5181 1.1261 6.7301 2.3061 0.7 3.0948 0.6440 4.3599 1.8298 0.75 3.2071 0.6666 4.5165 1.8976 0.8 3.3325 0.7010 4.7094 1.9556 0.85 3.4718 0.7449 4.9350 2.0086 0.9 3.6304 0.7936 5.1893 2.0715 0.95 3.8053 0.8440 5.4632 2.1474
10 - British Gas Single Defect Method - B31.G surface correction, exact area, BG Folias factor
1.0 3.9988 0.8905 5.7480 2.2496 0.7 3.1565 0.5134 4.1649 2.1481 0.75 3.2668 0.5362 4.3201 2.2134 0.8 3.3889 0.5730 4.5144 2.2634 0.85 3.5294 0.6200 4.7471 2.3116 0.9 3.6908 0.6721 5.0109 2.3706 0.95 3.8693 0.7224 5.2883 2.4503
11 - British Gas Complex Defect Method - B31.G surface correction, exact area, BG Folias factor
1.0 4.0666 0.7637 5.5667 2.5664 0.7 2.8979 0.6470 4.1688 1.6271 0.75 2.9932 0.6391 4.2485 1.7378 0.8 3.1066 0.6449 4.3733 1.8399 0.85 3.2425 0.6664 4.5514 1.9336 0.9 3.4029 0.7012 4.7803 2.0255 0.95 3.5755 0.7434 5.0357 2.1154
12 - Chell Method - Chell surface correction, exact area, B31-G Folias factor
1.0 3.7622 0.7830 5.3002 2.2241
165
Table 19 – MAWP Ratio vs. Allowable RSF for ASME Section VIII, Division 1 (post 1999) and ASME B31.1 (post 1999) (Continued)
Method Allowable RSF
Mean MAWP Ratio
MAWP Ratio
Standard Deviation
MAWP Ratio Upper 95% Prediction
Limit
MAWP Ratio Lower 95% Prediction
Limit 0.7 2.7723 0.6527 4.0543 1.4903 0.75 2.8348 0.6167 4.0462 1.6234 0.8 2.9131 0.5881 4.0684 1.7578 0.85 3.0127 0.5731 4.1385 1.8870 0.9 3.1452 0.5831 4.2906 1.9999 0.95 3.3012 0.6099 4.4993 2.1032
13 - Osage Method - Chell surface correction, effective area, D/t dependent Folias factor
1.0 3.4744 0.6418 4.7350 2.2138 0.7 2.8964 0.6475 4.1682 1.6245 0.75 2.9912 0.6394 4.2471 1.7353 0.8 3.1041 0.6450 4.3710 1.8372 0.85 3.2397 0.6663 4.5484 1.9309 0.9 3.3997 0.7010 4.7767 2.0227 0.95 3.5721 0.7431 5.0316 2.1125
14 - API 579, Level 1, Hybrid 1 Analysis - Chell surface correction, rectangular area, API level 1 Folias factor 1.0 3.7584 0.7827 5.2959 2.2209
0.7 2.7589 0.6668 4.0688 1.4490 0.75 2.8157 0.6323 4.0578 1.5737 0.8 2.8867 0.6047 4.0744 1.6989 0.85 2.9789 0.5885 4.1348 1.8229 0.9 3.1018 0.5967 4.2739 1.9297 0.95 3.2487 0.6231 4.4726 2.0248
15 - API 579, Level 2, Hybrid 1 Analysis - Chell surface correction, effective area, API level 2 Folias factor 1.0 3.4160 0.6556 4.7038 2.1281
0.7 2.8277 0.6754 4.1543 1.5011 0.75 2.9030 0.6595 4.1985 1.6076 0.8 2.9937 0.6560 4.2821 1.7052 0.85 3.1078 0.6673 4.4185 1.7971 0.9 3.2495 0.6954 4.6155 1.8835 0.95 3.4089 0.7331 4.8488 1.9689
16 - API 579, Level 1, Hybrid 2 Analysis - Chell surface correction, rectangular area, BG Folias factor
1.0 3.5828 0.7728 5.1007 2.0648 0.7 2.7515 0.6774 4.0820 1.4210 0.75 2.8047 0.6449 4.0715 1.5379 0.8 2.8701 0.6186 4.0851 1.6550 0.85 2.9545 0.6037 4.1404 1.7686 0.9 3.0685 0.6099 4.2665 1.8705 0.95 3.2084 0.6345 4.4548 1.9620
17 - API 579, Level 2, Hybrid 2 Analysis - Chell surface correction, effective area, BG Folias factor
1.0 3.3697 0.6678 4.6814 2.0579 0.7 2.7636 0.6939 4.1265 1.4006 0.75 2.8228 0.6659 4.1308 1.5147 0.8 2.8966 0.6442 4.1621 1.6312 0.85 2.9874 0.6316 4.2280 1.7469 0.9 3.0945 0.6302 4.3323 1.8566 0.95 3.2146 0.6402 4.4722 1.9570
18 - API 579, Level 1, Hybrid 3 Analysis - Chell surface correction, rectangular area, JO Folias factor
1.0 3.3504 0.6603 4.6475 2.0533
166
Table 19 – MAWP Ratio vs. Allowable RSF for ASME Section VIII, Division 1 (post 1999) and ASME B31.1 (post 1999) (Continued)
Method Allowable RSF
Mean MAWP Ratio
MAWP Ratio
Standard Deviation
MAWP Ratio Upper 95% Prediction
Limit
MAWP Ratio Lower 95% Prediction
Limit 0.7 2.7096 0.7073 4.0988 1.3203 0.75 2.7459 0.6702 4.0624 1.4294 0.8 2.7954 0.6317 4.0362 1.5546 0.85 2.8608 0.5965 4.0324 1.6892 0.9 2.9459 0.5694 4.0643 1.8274 0.95 3.0516 0.5568 4.1452 1.9579
19 – API 579, Level 2, Hybrid 3 Analysis – Chell surface correction, effective area, JO Folias factor
1.0 3.1766 0.5592 4.2751 2.0781 0.7 3.0784 0.6604 4.3755 1.7812 0.75 3.1867 0.6829 4.5282 1.8453 0.8 3.3115 0.7157 4.7173 1.9057 0.85 3.4541 0.7573 4.9416 1.9665 0.9 3.6168 0.8031 5.1943 2.0393 0.95 3.8002 0.8491 5.4680 2.1325
20 – Battelle Method – B31.G surface correction, rectangular area, Battelle Folias factor
1.0 3.9982 0.8940 5.7543 2.2421 0.7 3.0948 0.6440 4.3599 1.8298 0.75 3.2071 0.6666 4.5165 1.8976 0.8 3.3325 0.7010 4.7094 1.9556 0.85 3.4718 0.7449 4.9350 2.0086 0.9 3.6304 0.7936 5.1893 2.0715 0.95 3.8053 0.8440 5.4632 2.1474
21 – BS 7910, Appendix G (Isolated Defect) – B31.G surface correction, rectangular area, BG Folias factor 1.0 3.9988 0.8905 5.7480 2.2496
0.7 2.9799 0.5826 4.1243 1.8356 0.75 3.0706 0.5752 4.2005 1.9407 0.8 3.1739 0.5807 4.3146 2.0332 0.85 3.2883 0.5994 4.4658 2.1108 0.9 3.4213 0.6286 4.6561 2.1866 0.95 3.5724 0.6651 4.8789 2.2659
22 – BS 7910, Appendix G (Grouped Defects) – B31.G surface correction, rectangular area, BG Folias factor 1.0 3.7470 0.7019 5.1257 2.3684
0.7 3.8075 1.2878 6.3370 1.2779 0.75 3.9952 1.4099 6.7646 1.2259 0.8 4.1939 1.5325 7.2042 1.1836 0.85 4.4094 1.6502 7.6509 1.1679 0.9 4.6379 1.7631 8.1012 1.1747 0.95 4.8809 1.8690 8.5522 1.2097
23 – Kanninen Equivalent Stress – B31.G surface correction, rectangular area, shell theory Folias factor 1.0 5.1354 1.9688 9.0026 1.2682
0.7 3.3494 0.7472 4.8172 1.8816 0.75 3.4741 0.8178 5.0805 1.8677 0.8 3.6098 0.8951 5.3679 1.8516 0.85 3.7626 0.9731 5.6741 1.8512 0.9 3.9334 1.0485 5.9928 1.8739 0.95 4.1220 1.1189 6.3199 1.9241
24 – Shell Theory Method – Chell surface correction, exact area, shell theory Folias factor
1.0 4.3328 1.1805 6.6515 2.0141
167
Table 19 – MAWP Ratio vs. Allowable RSF for ASME Section VIII, Division 1 (post 1999) and ASME B31.1 (post 1999) (Continued)
Method Allowable RSF
Mean MAWP Ratio
MAWP Ratio
Standard Deviation
MAWP Ratio Upper 95% Prediction
Limit
MAWP Ratio Lower 95% Prediction
Limit 0.7 4.2263 1.3859 6.9486 1.5039 0.75 4.4194 1.5641 7.4916 1.3471 0.8 4.6434 1.8040 8.1870 1.0998 0.85 4.9736 2.0450 8.9905 0.9567 0.9 5.3762 2.3492 9.9906 0.7619 0.95 5.8404 2.6128 10.9726 0.7083
25 - Thickness Averaging - API 579, Level 1
1.0 6.5048 2.8751 12.1521 0.8574 0.7 3.2301 0.9354 5.0675 1.3927 0.75 3.4854 1.1246 5.6944 1.2765 0.8 3.8259 1.3940 6.5641 1.0876 0.85 4.2590 1.7184 7.6343 0.8836 0.9 4.8390 2.1095 8.9827 0.6953 0.95 5.5455 2.4817 10.4202 0.6708
26 - Thickness Averaging - API 579, Level 2
1.0 6.5048 2.8751 12.1521 0.8574 0.7 3.3007 0.7303 4.7353 1.8661 0.75 3.4504 0.7816 4.9855 1.9152 0.8 3.6118 0.8419 5.2655 1.9581 0.85 3.7862 0.9070 5.5678 2.0046 0.9 3.9787 0.9715 5.8871 2.0703 0.95 4.1878 1.0306 6.2122 2.1634
27 - Modified API 579 Section 5, Level 1 Analysis - B31.G surface correction, rectangular area, Modified API Folias factor 1.0 4.4062 1.0859 6.5392 2.2732
0.7 3.0144 0.4997 3.9960 2.0328 0.75 3.1101 0.4867 4.0660 2.1542 0.8 3.2217 0.4876 4.1795 2.2640 0.85 3.3482 0.5045 4.3391 2.3573 0.9 3.5001 0.5334 4.5478 2.4524 0.95 3.6741 0.5654 4.7846 2.5635
28 - Modified API 579 Section 5, Level 2 Analysis - B31.G surface correction, effective area, Modified API Folias factor 1.0 3.8640 0.5955 5.0338 2.6941
0.7 3.0894 0.6304 4.3278 1.8511 0.75 3.2239 0.6445 4.4899 1.9578 0.8 3.3729 0.6728 4.6945 2.0514 0.85 3.5403 0.7116 4.9381 2.1425 0.9 3.7312 0.7521 5.2086 2.2537 0.95 3.9343 0.7944 5.4946 2.3739
29 - Janelle Method, Level 1 - rectangular area
1.0 4.1413 0.8362 5.7838 2.4988 0.7 2.9014 0.5459 3.9737 1.8291 0.75 2.9911 0.5127 3.9982 1.9839 0.8 3.0998 0.4926 4.0675 2.1321 0.85 3.2296 0.4915 4.1949 2.2642 0.9 3.3916 0.5066 4.3867 2.3965 0.95 3.5714 0.5311 4.6146 2.5282
30 - Janelle Method, Level 1 - effective area
1.0 3.7590 0.5590 4.8571 2.6610
168
Table 20 – MAWP Ratio vs. Allowable RSF for ASME Section VIII, Division 2 and B31.3
Method Allowable RSF
Mean MAWP Ratio
MAWP Ratio
Standard Deviation
MAWP Ratio Upper 95% Prediction
Limit
MAWP Ratio Lower 95% Prediction
Limit 0.7 2.8872 0.6591 4.1819 1.5926 0.75 3.0225 0.7109 4.4189 1.6262 0.8 3.1677 0.7690 4.6782 1.6572 0.85 3.3239 0.8302 4.9546 1.6932 0.9 3.4957 0.8894 5.2427 1.7488 0.95 3.6809 0.9431 5.5335 1.8284
1 - API 579 Section 5, Level 1 Analysis - B31.G surface correction, rectangular area, API level 1 Folias factor 1.0 3.8731 0.9937 5.8250 1.9212
0.7 2.5814 0.4287 3.4235 1.7394 0.75 2.6632 0.4170 3.4823 1.8440 0.8 2.7585 0.4173 3.5782 1.9387 0.85 2.8663 0.4313 3.7135 2.0191 0.9 2.9964 0.4556 3.8914 2.1014 0.95 3.1455 0.4827 4.0935 2.1974
2 - API 579 Section 5, Level 2 Analysis - B31.G surface correction, effective area, API level 2 Folias factor 1.0 3.3081 0.5084 4.3066 2.3095
0.7 2.5327 0.4523 3.4211 1.6443 0.75 2.6085 0.4344 3.4618 1.7552 0.8 2.6983 0.4266 3.5362 1.8605 0.85 2.8012 0.4324 3.6506 1.9518 0.9 2.9258 0.4513 3.8122 2.0394 0.95 3.0708 0.4754 4.0047 2.1369
3 - API-579 Section 5, Level 2 Analysis - B31.G surface correction, exact area, API level 2 Folias factor 1.0 3.2295 0.5003 4.2122 2.2467
0.7 2.5367 0.5704 3.6571 1.4162 0.75 2.6184 0.5587 3.7158 1.5211 0.8 2.7170 0.5569 3.8109 1.6231 0.85 2.8276 0.5680 3.9434 1.7119 0.9 2.9554 0.5896 4.1135 1.7973 0.95 3.1002 0.6198 4.3176 1.8828
4 - Modified B31.G Method - B31.G surface correction, 0.85dl area, AGA Folias factor
1.0 3.2601 0.6519 4.5407 1.9795 0.7 2.6260 0.4482 3.5065 1.7456 0.75 2.7059 0.4344 3.5591 1.8528 0.8 2.7992 0.4312 3.6462 1.9521 0.85 2.9058 0.4422 3.7743 2.0373 0.9 3.0340 0.4646 3.9465 2.1215 0.95 3.1812 0.4923 4.1482 2.2143
5 - Modified B31.G Method (RSTRENG) - B31.G surface correction, effective area, AGA Folias factor 1.0 3.3446 0.5186 4.3633 2.3259
0.7 2.5803 0.4730 3.5093 1.6512 0.75 2.6547 0.4536 3.5458 1.7636 0.8 2.7430 0.4434 3.6140 1.8721 0.85 2.8449 0.4468 3.7226 1.9673 0.9 2.9683 0.4638 3.8793 2.0573 0.95 3.1117 0.4885 4.0713 2.1522
6 - Modified B31.G Method - B31.G surface correction, exact area, AGA Folias factor
1.0 3.2714 0.5141 4.2812 2.2617
169
Table 20 – MAWP Ratio vs. Allowable RSF for ASME Section VIII, Division 2 and B31.3 (Continued)
Method Allowable RSF
Mean MAWP Ratio
MAWP Ratio
Standard Deviation
MAWP Ratio Upper 95% Prediction
Limit
MAWP Ratio Lower 95% Prediction
Limit 0.7 2.5803 0.6894 3.9345 1.2260 0.75 2.6556 0.7179 4.0657 1.2455 0.8 2.7424 0.7529 4.2213 1.2635 0.85 2.8539 0.7929 4.4114 1.2964 0.9 2.9787 0.8376 4.6238 1.3335 0.95 3.1200 0.8851 4.8585 1.3815
7 – Original B31.G Method – B31.G surface correction, parabolic area, B31-G Folias factor
1.0 3.2799 0.9320 5.1106 1.4493 0.7 3.5734 0.8530 5.2490 1.8978 0.75 3.5734 0.8530 5.2490 1.8978 0.8 3.5734 0.8530 5.2490 1.8978 0.85 3.5734 0.8530 5.2490 1.8978 0.9 3.5734 0.8530 5.2490 1.8978 0.95 3.5734 0.8530 5.2490 1.8978
8 – Thickness Averaging – API 510, 8th Edition
1.0 3.5734 0.8530 5.2490 1.8978 0.7 3.8726 0.9652 5.7686 1.9767 0.75 3.8726 0.9652 5.7686 1.9767 0.8 3.8726 0.9652 5.7686 1.9767 0.85 3.8726 0.9652 5.7686 1.9767 0.9 3.8726 0.9652 5.7686 1.9767 0.95 3.8726 0.9652 5.7686 1.9767
9 – Thickness Averaging – API 653, 2nd Edition
1.0 3.8726 0.9652 5.7686 1.9767 0.7 2.6527 0.5520 3.7370 1.5684 0.75 2.7489 0.5714 3.8713 1.6265 0.8 2.8565 0.6008 4.0367 1.6763 0.85 2.9758 0.6385 4.2300 1.7216 0.9 3.1118 0.6802 4.4479 1.7756 0.95 3.2617 0.7235 4.6827 1.8406
10 – British Gas Single Defect Method – B31.G surface correction, exact area, BG Folias factor
1.0 3.4276 0.7633 4.9268 1.9283 0.7 2.7056 0.4400 3.5699 1.8412 0.75 2.8001 0.4596 3.7029 1.8972 0.8 2.9048 0.4911 3.8695 1.9401 0.85 3.0252 0.5314 4.0690 1.9813 0.9 3.1635 0.5761 4.2951 2.0320 0.95 3.3165 0.6192 4.5328 2.1002
11 – British Gas Complex Defect Method – B31.G surface correction, exact area, BG Folias factor
1.0 3.4856 0.6546 4.7715 2.1998 0.7 2.4839 0.5546 3.5732 1.3946 0.75 2.5656 0.5478 3.6416 1.4896 0.8 2.6628 0.5527 3.7485 1.5771 0.85 2.7793 0.5712 3.9012 1.6574 0.9 2.9168 0.6011 4.0974 1.7361 0.95 3.0647 0.6372 4.3163 1.8132
12 – Chell Method – Chell surface correction, exact area, B31-G Folias factor
1.0 3.2247 0.6712 4.5431 1.9063
170
Table 20 – MAWP Ratio vs. Allowable RSF for ASME Section VIII, Division 2 and B31.3 (Continued)
Method Allowable RSF
Mean MAWP Ratio
MAWP Ratio
Standard Deviation
MAWP Ratio Upper 95% Prediction
Limit
MAWP Ratio Lower 95% Prediction
Limit 0.7 2.3763 0.5594 3.4751 1.2774 0.75 2.4298 0.5286 3.4682 1.3915 0.8 2.4969 0.5041 3.4872 1.5067 0.85 2.5824 0.4912 3.5473 1.6175 0.9 2.6959 0.4998 3.6776 1.7142 0.95 2.8296 0.5228 3.8565 1.8027
13 - Osage Method - Chell surface correction, effective area, D/t dependent Folias factor
1.0 2.9780 0.5501 4.0585 1.8975 0.7 2.4826 0.5550 3.5728 1.3924 0.75 2.5639 0.5480 3.6404 1.4874 0.8 2.6607 0.5528 3.7466 1.5748 0.85 2.7768 0.5711 3.8986 1.6551 0.9 2.9140 0.6009 4.0943 1.7338 0.95 3.0618 0.6369 4.3128 1.8107
14 - API 579, Level 1, Hybrid 1 Analysis - Chell surface correction, rectangular area, API level 1 Folias factor 1.0 3.2215 0.6709 4.5394 1.9036
0.7 2.3648 0.5716 3.4875 1.2420 0.75 2.4135 0.5420 3.4781 1.3489 0.8 2.4743 0.5183 3.4924 1.4562 0.85 2.5533 0.5044 3.5441 1.5625 0.9 2.6587 0.5115 3.6633 1.6541 0.95 2.7846 0.5341 3.8337 1.7355
15 - API 579, Level 2, Hybrid 1 Analysis - Chell surface correction, effective area, API level 2 Folias factor 1.0 2.9280 0.5620 4.0318 1.8241
0.7 2.4237 0.5789 3.5608 1.2866 0.75 2.4883 0.5653 3.5987 1.3779 0.8 2.5660 0.5622 3.6704 1.4616 0.85 2.6639 0.5720 3.7873 1.5404 0.9 2.7853 0.5961 3.9561 1.6144 0.95 2.9219 0.6284 4.1561 1.6876
16 - API 579, Level 1, Hybrid 2 Analysis - Chell surface correction, rectangular area, BG Folias factor
1.0 3.0709 0.6624 4.3721 1.7698 0.7 2.3584 0.5806 3.4988 1.2180 0.75 2.4040 0.5528 3.4898 1.3182 0.8 2.4601 0.5302 3.5015 1.4186 0.85 2.5324 0.5175 3.5489 1.5159 0.9 2.6301 0.5228 3.6570 1.6033 0.95 2.7501 0.5439 3.8184 1.6817
17 - API 579, Level 2, Hybrid 2 Analysis - Chell surface correction, effective area, BG Folias factor
1.0 2.8883 0.5724 4.0126 1.7640 0.7 2.3688 0.5948 3.5370 1.2005 0.75 2.4195 0.5708 3.5407 1.2983 0.8 2.4828 0.5522 3.5675 1.3982 0.85 2.5607 0.5413 3.6240 1.4973 0.9 2.6524 0.5402 3.7134 1.5914 0.95 2.7554 0.5488 3.8333 1.6774
18 - API 579, Level 1, Hybrid 3 Analysis - Chell surface correction, rectangular area, JO Folias factor
1.0 2.8718 0.5660 3.9836 1.7600
171
Table 20 – MAWP Ratio vs. Allowable RSF for ASME Section VIII, Division 2 and B31.3 (Continued)
Method Allowable RSF
Mean MAWP Ratio
MAWP Ratio
Standard Deviation
MAWP Ratio Upper 95% Prediction
Limit
MAWP Ratio Lower 95% Prediction
Limit 0.7 2.3225 0.6062 3.5133 1.1317 0.75 2.3536 0.5745 3.4820 1.2252 0.8 2.3961 0.5415 3.4596 1.3325 0.85 2.4521 0.5112 3.4564 1.4479 0.9 2.5250 0.4880 3.4837 1.5664 0.95 2.6156 0.4772 3.5531 1.6782
19 - API 579, Level 2, Hybrid 3 Analysis - Chell surface correction, effective area, JO Folias factor
1.0 2.7228 0.4793 3.6643 1.7812 0.7 2.6386 0.5660 3.7504 1.5268 0.75 2.7315 0.5854 3.8813 1.5817 0.8 2.8384 0.6135 4.0434 1.6334 0.85 2.9606 0.6491 4.2357 1.6856 0.9 3.1001 0.6884 4.4523 1.7480 0.95 3.2573 0.7278 4.6869 1.8278
20 - Battelle Method - B31.G surface correction, rectangular area, Battelle Folias factor
1.0 3.4270 0.7663 4.9322 1.9218 0.7 2.6527 0.5520 3.7370 1.5684 0.75 2.7489 0.5714 3.8713 1.6265 0.8 2.8565 0.6008 4.0367 1.6763 0.85 2.9758 0.6385 4.2300 1.7216 0.9 3.1118 0.6802 4.4479 1.7756 0.95 3.2617 0.7235 4.6827 1.8406
21 - BS 7910, Appendix G (Isolated Defect) - B31.G surface correction, rectangular area, BG Folias factor 1.0 3.4276 0.7633 4.9268 1.9283
0.7 2.5542 0.4994 3.5351 1.5734 0.75 2.6319 0.4931 3.6004 1.6634 0.8 2.7205 0.4978 3.6982 1.7428 0.85 2.8186 0.5138 3.8278 1.8093 0.9 2.9326 0.5388 3.9909 1.8742 0.95 3.0620 0.5701 4.1819 1.9422
22 - BS 7910, Appendix G (Grouped Defects) - B31.G surface correction, rectangular area, BG Folias factor 1.0 3.2117 0.6016 4.3934 2.0300
0.7 3.2635 1.1038 5.4317 1.0953 0.75 3.4245 1.2085 5.7982 1.0508 0.8 3.5948 1.3136 6.1750 1.0146 0.85 3.7795 1.4145 6.5579 1.0010 0.9 3.9754 1.5113 6.9439 1.0069 0.95 4.1837 1.6020 7.3304 1.0369
23 - Kanninen Equivalent Stress - B31.G surface correction, rectangular area, shell theory Folias factor 1.0 4.4018 1.6875 7.7165 1.0870
0.7 2.8709 0.6405 4.1290 1.6128 0.75 2.9778 0.7010 4.3547 1.6009 0.8 3.0941 0.7672 4.6011 1.5871 0.85 3.2251 0.8341 4.8635 1.5867 0.9 3.3714 0.8987 5.1367 1.6062 0.95 3.5331 0.9591 5.4170 1.6492
24 - Shell Theory Method - Chell surface correction, exact area, shell theory Folias factor
1.0 3.7138 1.0118 5.7013 1.7264
172
Table 20 – MAWP Ratio vs. Allowable RSF for ASME Section VIII, Division 2 and B31.3 (Continued)
Method Allowable RSF
Mean MAWP Ratio
MAWP Ratio
Standard Deviation
MAWP Ratio Upper 95% Prediction
Limit
MAWP Ratio Lower 95% Prediction
Limit 0.7 3.6225 1.1879 5.9559 1.2891 0.75 3.7880 1.3406 6.4214 1.1547 0.8 3.9801 1.5463 7.0174 0.9427 0.85 4.2631 1.7529 7.7062 0.8200 0.9 4.6082 2.0136 8.5634 0.6530 0.95 5.0061 2.2395 9.4051 0.6071
25 - Thickness Averaging - API 579, Level 1
1.0 5.5755 2.4643 10.4161 0.7349 0.7 2.7687 0.8018 4.3436 1.1937 0.75 2.9875 0.9639 4.8809 1.0941 0.8 3.2793 1.1949 5.6264 0.9322 0.85 3.6505 1.4729 6.5437 0.7574 0.9 4.1477 1.8082 7.6994 0.5960 0.95 4.7533 2.1272 8.9316 0.5750
26 - Thickness Averaging - API 579, Level 2
1.0 5.5755 2.4643 10.4161 0.7349 0.7 2.8292 0.6260 4.0588 1.5995 0.75 2.9575 0.6699 4.2733 1.6416 0.8 3.0958 0.7216 4.5133 1.6784 0.85 3.2453 0.7774 4.7724 1.7182 0.9 3.4103 0.8328 5.0460 1.7746 0.95 3.5895 0.8834 5.3247 1.8543
27 - Modified API 579 Section 5, Level 1 Analysis - B31.G surface correction, rectangular area, Modified API Folias factor 1.0 3.7767 0.9308 5.6050 1.9484
0.7 2.5837 0.4283 3.4251 1.7424 0.75 2.6658 0.4171 3.4852 1.8464 0.8 2.7615 0.4179 3.5824 1.9406 0.85 2.8699 0.4324 3.7192 2.0205 0.9 3.0001 0.4572 3.8981 2.1021 0.95 3.1492 0.4846 4.1011 2.1973
28 - Modified API 579 Section 5, Level 2 Analysis - B31.G surface correction, effective area, Modified API Folias factor 1.0 3.3120 0.5105 4.3147 2.3093
0.7 2.6481 0.5404 3.7095 1.5866 0.75 2.7633 0.5525 3.8485 1.6781 0.8 2.8911 0.5767 4.0238 1.7583 0.85 3.0345 0.6100 4.2327 1.8364 0.9 3.1981 0.6447 4.4645 1.9318 0.95 3.3722 0.6809 4.7097 2.0348
29 - Janelle Method, Level 1 - rectangular area
1.0 3.5497 0.7167 4.9575 2.1418 0.7 2.4869 0.4679 3.4060 1.5678 0.75 2.5638 0.4395 3.4271 1.7005 0.8 2.6570 0.4223 3.4864 1.8275 0.85 2.7682 0.4212 3.5956 1.9408 0.9 2.9071 0.4342 3.7600 2.0542 0.95 3.0612 0.4552 3.9554 2.1670
30 - Janelle Method, Level 1 - effective area
1.0 3.2220 0.4792 4.1632 2.2808
173
Table 21 – MAWP Ratio vs. Allowable RSF for New Proposed ASME Section VIII, Division 2
Method Allowable RSF
Mean MAWP Ratio
MAWP Ratio
Standard Deviation
MAWP Ratio Upper 95% Prediction
Limit
MAWP Ratio Lower 95% Prediction
Limit 0.7 2.3183 0.5265 3.3525 1.2842 0.75 2.4269 0.5676 3.5419 1.3119 0.8 2.5434 0.6139 3.7492 1.3375 0.85 2.6687 0.6626 3.9703 1.3671 0.9 2.8066 0.7099 4.2010 1.4122 0.95 2.9553 0.7528 4.4340 1.4766
1 - API 579 Section 5, Level 1 Analysis - B31.G surface correction, rectangular area, API level 1 Folias factor 1.0 3.1096 0.7932 4.6675 1.5516
0.7 2.0729 0.3419 2.7445 1.4012 0.75 2.1385 0.3321 2.7908 1.4862 0.8 2.2150 0.3316 2.8664 1.5635 0.85 2.3015 0.3422 2.9736 1.6293 0.9 2.4059 0.3614 3.1158 1.6961 0.95 2.5256 0.3828 3.2775 1.7737
2 - API 579 Section 5, Level 2 Analysis - B31.G surface correction, effective area, API level 2 Folias factor 1.0 2.6561 0.4031 3.4480 1.8643
0.7 2.0338 0.3613 2.7435 1.3241 0.75 2.0946 0.3465 2.7752 1.4140 0.8 2.1667 0.3396 2.8337 1.4997 0.85 2.2493 0.3436 2.9241 1.5744 0.9 2.3493 0.3584 3.0533 1.6453 0.95 2.4657 0.3775 3.2072 1.7242
3 - API-579 Section 5, Level 2 Analysis - B31.G surface correction, exact area, API level 2 Folias factor 1.0 2.5931 0.3972 3.3733 1.8129
0.7 2.0368 0.4561 2.9327 1.1408 0.75 2.1024 0.4462 2.9789 1.2258 0.8 2.1815 0.4443 3.0541 1.3088 0.85 2.2702 0.4525 3.1590 1.3814 0.9 2.3727 0.4692 3.2943 1.4511 0.95 2.4889 0.4931 3.4575 1.5204
4 - Modified B31.G Method - B31.G surface correction, 0.85dl area, AGA Folias factor
1.0 2.6173 0.5186 3.6360 1.5986 0.7 2.1087 0.3575 2.8108 1.4065 0.75 2.1728 0.3458 2.8521 1.4935 0.8 2.2476 0.3427 2.9207 1.5745 0.85 2.3332 0.3507 3.0221 1.6442 0.9 2.4361 0.3684 3.1596 1.7125 0.95 2.5543 0.3903 3.3210 1.7876
5 - Modified B31.G Method (RSTRENG) - B31.G surface correction, effective area, AGA Folias factor 1.0 2.6855 0.4111 3.4931 1.8779
0.7 2.0720 0.3777 2.8139 1.3300 0.75 2.1317 0.3618 2.8423 1.4211 0.8 2.2026 0.3529 2.8958 1.5093 0.85 2.2843 0.3550 2.9815 1.5871 0.9 2.3834 0.3682 3.1066 1.6601 0.95 2.4985 0.3878 3.2602 1.7369
6 - Modified B31.G Method - B31.G surface correction, exact area, AGA Folias factor
1.0 2.6268 0.4080 3.4282 1.8254
174
Table 21 – MAWP Ratio vs. Allowable RSF for New Proposed ASME Section VIII, Division 2 (Continued)
Method Allowable RSF
Mean MAWP Ratio
MAWP Ratio
Standard Deviation
MAWP Ratio Upper 95% Prediction
Limit
MAWP Ratio Lower 95% Prediction
Limit 0.7 2.0717 0.5516 3.1553 0.9882 0.75 2.1322 0.5742 3.2602 1.0042 0.8 2.2019 0.6021 3.3845 1.0192 0.85 2.2913 0.6339 3.5366 1.0461 0.9 2.3914 0.6694 3.7063 1.0766 0.95 2.5049 0.7073 3.8942 1.1156
7 – Original B31.G Method – B31.G surface correction, parabolic area, B31-G Folias factor
1.0 2.6333 0.7447 4.0961 1.1704 0.7 2.8688 0.6792 4.2030 1.5346 0.75 2.8688 0.6792 4.2030 1.5346 0.8 2.8688 0.6792 4.2030 1.5346 0.85 2.8688 0.6792 4.2030 1.5346 0.9 2.8688 0.6792 4.2030 1.5346 0.95 2.8688 0.6792 4.2030 1.5346
8 – Thickness Averaging – API 510, 8th Edition
1.0 2.8688 0.6792 4.2030 1.5346 0.7 3.1096 0.7721 4.6263 1.5930 0.75 3.1096 0.7721 4.6263 1.5930 0.8 3.1096 0.7721 4.6263 1.5930 0.85 3.1096 0.7721 4.6263 1.5930 0.9 3.1096 0.7721 4.6263 1.5930 0.95 3.1096 0.7721 4.6263 1.5930
9 – Thickness Averaging – API 653, 2nd Edition
1.0 3.1096 0.7721 4.6263 1.5930 0.7 2.1300 0.4410 2.9962 1.2639 0.75 2.2072 0.4561 3.1032 1.3113 0.8 2.2935 0.4793 3.2351 1.3520 0.85 2.3893 0.5091 3.3893 1.3893 0.9 2.4984 0.5422 3.5634 1.4333 0.95 2.6187 0.5767 3.7514 1.4860
10 – British Gas Single Defect Method – B31.G surface correction, exact area, BG Folias factor
1.0 2.7519 0.6084 3.9469 1.5569 0.7 2.1726 0.3509 2.8619 1.4833 0.75 2.2485 0.3663 2.9679 1.5290 0.8 2.3325 0.3911 3.1008 1.5642 0.85 2.4291 0.4231 3.2603 1.5979 0.9 2.5402 0.4589 3.4415 1.6388 0.95 2.6630 0.4934 3.6321 1.6939
11 – British Gas Complex Defect Method – B31.G surface correction, exact area, BG Folias factor
1.0 2.7988 0.5216 3.8233 1.7743 0.7 1.9943 0.4432 2.8649 1.1237 0.75 2.0598 0.4372 2.9186 1.2010 0.8 2.1378 0.4405 3.0030 1.2725 0.85 2.2312 0.4547 3.1243 1.3381 0.9 2.3416 0.4783 3.2811 1.4020 0.95 2.4603 0.5069 3.4561 1.4646
12 – Chell Method – Chell surface correction, exact area, B31-G Folias factor
1.0 2.5887 0.5340 3.6376 1.5399
175
Table 21 – MAWP Ratio vs. Allowable RSF for New Proposed ASME Section VIII, Division 2 (Continued)
Method Allowable RSF
Mean MAWP Ratio
MAWP Ratio
Standard Deviation
MAWP Ratio Upper 95% Prediction
Limit
MAWP Ratio Lower 95% Prediction
Limit 0.7 1.9079 0.4477 2.7874 1.0285 0.75 1.9509 0.4226 2.7809 1.1208 0.8 2.0047 0.4023 2.7949 1.2145 0.85 2.0732 0.3913 2.8418 1.3046 0.9 2.1644 0.3978 2.9458 1.3830 0.95 2.2717 0.4160 3.0888 1.4547
13 - Osage Method - Chell surface correction, effective area, D/t dependent Folias factor
1.0 2.3909 0.4376 3.2505 1.5312 0.7 1.9932 0.4436 2.8645 1.1219 0.75 2.0584 0.4374 2.9177 1.1992 0.8 2.1361 0.4406 3.0015 1.2706 0.85 2.2293 0.4546 3.1223 1.3363 0.9 2.3394 0.4782 3.2786 1.4001 0.95 2.4580 0.5067 3.4533 1.4626
14 - API 579, Level 1, Hybrid 1 Analysis - Chell surface correction, rectangular area, API level 1 Folias factor 1.0 2.5862 0.5338 3.6346 1.5377
0.7 1.8987 0.4576 2.7975 0.9999 0.75 1.9378 0.4334 2.7892 1.0864 0.8 1.9865 0.4139 2.7995 1.1736 0.85 2.0499 0.4021 2.8397 1.2601 0.9 2.1345 0.4075 2.9349 1.3342 0.95 2.2356 0.4253 3.0710 1.4001
15 - API 579, Level 2, Hybrid 1 Analysis - Chell surface correction, effective area, API level 2 Folias factor 1.0 2.3507 0.4475 3.2296 1.4717
0.7 1.9459 0.4631 2.8555 1.0364 0.75 1.9978 0.4517 2.8850 1.1105 0.8 2.0601 0.4487 2.9414 1.1787 0.85 2.1386 0.4559 3.0340 1.2431 0.9 2.2360 0.4749 3.1689 1.3032 0.95 2.3457 0.5005 3.3288 1.3626
16 - API 579, Level 1, Hybrid 2 Analysis - Chell surface correction, rectangular area, BG Folias factor
1.0 2.4653 0.5275 3.5015 1.4291 0.7 1.8936 0.4648 2.8066 0.9805 0.75 1.9301 0.4422 2.7987 1.0616 0.8 1.9751 0.4236 2.8071 1.1431 0.85 2.0331 0.4128 2.8440 1.2223 0.9 2.1116 0.4168 2.9302 1.2930 0.95 2.2079 0.4335 3.0593 1.3564
17 - API 579, Level 2, Hybrid 2 Analysis - Chell surface correction, effective area, BG Folias factor
1.0 2.3188 0.4561 3.2147 1.4229 0.7 1.9019 0.4763 2.8374 0.9664 0.75 1.9427 0.4568 2.8399 1.0454 0.8 1.9935 0.4415 2.8607 1.1263 0.85 2.0559 0.4323 2.9051 1.2067 0.9 2.1295 0.4308 2.9757 1.2834 0.95 2.2121 0.4370 3.0705 1.3537
18 - API 579, Level 1, Hybrid 3 Analysis - Chell surface correction, rectangular area, JO Folias factor
1.0 2.3055 0.4502 3.1899 1.4211
176
Table 21 – MAWP Ratio vs. Allowable RSF for New Proposed ASME Section VIII, Division 2 (Continued)
Method Allowable RSF
Mean MAWP Ratio
MAWP Ratio
Standard Deviation
MAWP Ratio Upper 95% Prediction
Limit
MAWP Ratio Lower 95% Prediction
Limit 0.7 1.8648 0.4857 2.8187 0.9108 0.75 1.8898 0.4600 2.7933 0.9863 0.8 1.9238 0.4332 2.7748 1.0729 0.85 1.9688 0.4086 2.7713 1.1663 0.9 2.0273 0.3893 2.7921 1.2625 0.95 2.1000 0.3799 2.8463 1.3537
19 – API 579, Level 2, Hybrid 3 Analysis – Chell surface correction, effective area, JO Folias factor
1.0 2.1860 0.3809 2.9341 1.4378 0.7 2.1186 0.4520 3.0065 1.2308 0.75 2.1932 0.4672 3.1108 1.2756 0.8 2.2790 0.4893 3.2400 1.3180 0.85 2.3771 0.5174 3.3933 1.3608 0.9 2.4890 0.5485 3.5663 1.4117 0.95 2.6152 0.5798 3.7540 1.4764
20 – Battelle Method – B31.G surface correction, rectangular area, Battelle Folias factor
1.0 2.7514 0.6104 3.9505 1.5523 0.7 2.1300 0.4410 2.9962 1.2639 0.75 2.2072 0.4561 3.1032 1.3113 0.8 2.2935 0.4793 3.2351 1.3520 0.85 2.3893 0.5091 3.3893 1.3893 0.9 2.4984 0.5422 3.5634 1.4333 0.95 2.6187 0.5767 3.7514 1.4860
21 – BS 7910, Appendix G (Isolated Defect) – B31.G surface correction, rectangular area, BG Folias factor 1.0 2.7519 0.6084 3.9469 1.5569
0.7 2.0512 0.3995 2.8360 1.2664 0.75 2.1136 0.3943 2.8881 1.3391 0.8 2.1847 0.3978 2.9661 1.4033 0.85 2.2634 0.4104 3.0695 1.4573 0.9 2.3549 0.4302 3.2000 1.5099 0.95 2.4589 0.4553 3.3532 1.5646
22 – BS 7910, Appendix G (Grouped Defects) – B31.G surface correction, rectangular area, BG Folias factor 1.0 2.5791 0.4805 3.5228 1.6353
0.7 2.6207 0.8841 4.3573 0.8840 0.75 2.7498 0.9679 4.6511 0.8485 0.8 2.8865 1.0521 4.9532 0.8198 0.85 3.0347 1.1329 5.2601 0.8093 0.9 3.1919 1.2105 5.5696 0.8143 0.95 3.3591 1.2831 5.8796 0.8387
23 – Kanninen Equivalent Stress – B31.G surface correction, rectangular area, shell theory Folias factor 1.0 3.5343 1.3517 6.1893 0.8793
0.7 2.3057 0.5139 3.3152 1.2962 0.75 2.3916 0.5625 3.4965 1.2867 0.8 2.4849 0.6156 3.6941 1.2757 0.85 2.5901 0.6692 3.9047 1.2755 0.9 2.7076 0.7210 4.1239 1.2913 0.95 2.8374 0.7695 4.3489 1.3259
24 – Shell Theory Method – Chell surface correction, exact area, shell theory Folias factor
1.0 2.9825 0.8118 4.5770 1.3880
177
Table 21 – MAWP Ratio vs. Allowable RSF for New Proposed ASME Section VIII, Division 2 (Continued)
Method Allowable RSF
Mean MAWP Ratio
MAWP Ratio
Standard Deviation
MAWP Ratio Upper 95% Prediction
Limit
MAWP Ratio Lower 95% Prediction
Limit 0.7 2.9078 0.9486 4.7711 1.0445 0.75 3.0406 1.0709 5.1441 0.9370 0.8 3.1947 1.2358 5.6221 0.7673 0.85 3.4221 1.4017 6.1754 0.6688 0.9 3.6994 1.6118 6.8655 0.5334 0.95 4.0191 1.7939 7.5428 0.4954
25 - Thickness Averaging - API 579, Level 1
1.0 4.4766 1.9753 8.3567 0.5965 0.7 2.2228 0.6408 3.4814 0.9641 0.75 2.3983 0.7703 3.9114 0.8853 0.8 2.6325 0.9550 4.5084 0.7566 0.85 2.9305 1.1779 5.2441 0.6169 0.9 3.3298 1.4474 6.1729 0.4866 0.95 3.8161 1.7039 7.1631 0.4692
26 - Thickness Averaging - API 579, Level 2
1.0 4.4766 1.9753 8.3567 0.5965 0.7 2.2717 0.4999 3.2537 1.2897 0.75 2.3746 0.5347 3.4250 1.3243 0.8 2.4857 0.5758 3.6167 1.3546 0.85 2.6056 0.6202 3.8239 1.3873 0.9 2.7380 0.6643 4.0429 1.4331 0.95 2.8819 0.7047 4.2661 1.4977
27 - Modified API 579 Section 5, Level 1 Analysis - B31.G surface correction, rectangular area, Modified API Folias factor 1.0 3.0322 0.7425 4.4907 1.5737
0.7 2.0747 0.3416 2.7458 1.4037 0.75 2.1406 0.3321 2.7930 1.4882 0.8 2.2174 0.3321 2.8697 1.5651 0.85 2.3043 0.3430 2.9781 1.6305 0.9 2.4089 0.3626 3.1211 1.6967 0.95 2.5286 0.3843 3.2835 1.7737
28 - Modified API 579 Section 5, Level 2 Analysis - B31.G surface correction, effective area, Modified API Folias factor 1.0 2.6593 0.4048 3.4544 1.8642
0.7 2.1261 0.4310 2.9728 1.2795 0.75 2.2186 0.4400 3.0829 1.3542 0.8 2.3210 0.4587 3.2221 1.4200 0.85 2.4361 0.4848 3.3885 1.4838 0.9 2.5674 0.5123 3.5737 1.5612 0.95 2.7072 0.5410 3.7698 1.6446
29 - Janelle Method, Level 1 - rectangular area
1.0 2.8497 0.5695 3.9682 1.7311 0.7 1.9968 0.3735 2.7304 1.2633 0.75 2.0585 0.3500 2.7459 1.3711 0.8 2.1332 0.3352 2.7916 1.4749 0.85 2.2225 0.3335 2.8775 1.5674 0.9 2.3340 0.3434 3.0084 1.6595 0.95 2.4577 0.3599 3.1645 1.7509
30 - Janelle Method, Level 1 - effective area
1.0 2.5868 0.3788 3.3308 1.8428
178
Table 22 – MAWP Ratio vs. Allowable RSF for CODAP
Method Allowable RSF
Mean MAWP Ratio
MAWP Ratio
Standard Deviation
MAWP Ratio Upper 95% Prediction
Limit
MAWP Ratio Lower 95% Prediction
Limit 0.7 2.8872 0.6591 4.1819 1.5926 0.75 3.0225 0.7109 4.4189 1.6262 0.8 3.1677 0.7690 4.6782 1.6572 0.85 3.3239 0.8302 4.9546 1.6932 0.9 3.4957 0.8894 5.2427 1.7488 0.95 3.6809 0.9431 5.5335 1.8284
1 - API 579 Section 5, Level 1 Analysis - B31.G surface correction, rectangular area, API level 1 Folias factor 1.0 3.8731 0.9937 5.8250 1.9212
0.7 2.5814 0.4287 3.4235 1.7394 0.75 2.6632 0.4170 3.4823 1.8440 0.8 2.7585 0.4173 3.5782 1.9387 0.85 2.8663 0.4313 3.7135 2.0191 0.9 2.9964 0.4556 3.8914 2.1014 0.95 3.1455 0.4827 4.0935 2.1974
2 - API 579 Section 5, Level 2 Analysis - B31.G surface correction, effective area, API level 2 Folias factor 1.0 3.3081 0.5084 4.3066 2.3095
0.7 2.5327 0.4523 3.4211 1.6443 0.75 2.6085 0.4344 3.4618 1.7552 0.8 2.6983 0.4266 3.5362 1.8605 0.85 2.8012 0.4324 3.6506 1.9518 0.9 2.9258 0.4513 3.8122 2.0394 0.95 3.0708 0.4754 4.0047 2.1369
3 - API-579 Section 5, Level 2 Analysis - B31.G surface correction, exact area, API level 2 Folias factor 1.0 3.2295 0.5003 4.2122 2.2467
0.7 2.5367 0.5704 3.6571 1.4162 0.75 2.6184 0.5587 3.7158 1.5211 0.8 2.7170 0.5569 3.8109 1.6231 0.85 2.8276 0.5680 3.9434 1.7119 0.9 2.9554 0.5896 4.1135 1.7973 0.95 3.1002 0.6198 4.3176 1.8828
4 - Modified B31.G Method - B31.G surface correction, 0.85dl area, AGA Folias factor
1.0 3.2601 0.6519 4.5407 1.9795 0.7 2.6260 0.4482 3.5065 1.7456 0.75 2.7059 0.4344 3.5591 1.8528 0.8 2.7992 0.4312 3.6462 1.9521 0.85 2.9058 0.4422 3.7743 2.0373 0.9 3.0340 0.4646 3.9465 2.1215 0.95 3.1812 0.4923 4.1482 2.2143
5 - Modified B31.G Method (RSTRENG) - B31.G surface correction, effective area, AGA Folias factor 1.0 3.3446 0.5186 4.3633 2.3259
0.7 2.5803 0.4730 3.5093 1.6512 0.75 2.6547 0.4536 3.5458 1.7636 0.8 2.7430 0.4434 3.6140 1.8721 0.85 2.8449 0.4468 3.7226 1.9673 0.9 2.9683 0.4638 3.8793 2.0573 0.95 3.1117 0.4885 4.0713 2.1522
6 - Modified B31.G Method - B31.G surface correction, exact area, AGA Folias factor
1.0 3.2714 0.5141 4.2812 2.2617
179
Table 22 – MAWP Ratio vs. Allowable RSF for CODAP (Continued)
Method Allowable RSF
Mean MAWP Ratio
MAWP Ratio
Standard Deviation
MAWP Ratio Upper 95% Prediction
Limit
MAWP Ratio Lower 95% Prediction
Limit 0.7 2.5803 0.6894 3.9345 1.2260 0.75 2.6556 0.7179 4.0657 1.2455 0.8 2.7424 0.7529 4.2213 1.2635 0.85 2.8539 0.7929 4.4114 1.2964 0.9 2.9787 0.8376 4.6238 1.3335 0.95 3.1200 0.8851 4.8585 1.3815
7 - Original B31.G Method - B31.G surface correction, parabolic area, B31-G Folias factor
1.0 3.2799 0.9320 5.1106 1.4493 0.7 3.5734 0.8530 5.2490 1.8978 0.75 3.5734 0.8530 5.2490 1.8978 0.8 3.5734 0.8530 5.2490 1.8978 0.85 3.5734 0.8530 5.2490 1.8978 0.9 3.5734 0.8530 5.2490 1.8978 0.95 3.5734 0.8530 5.2490 1.8978
8 - Thickness Averaging - API 510, 8th Edition
1.0 3.5734 0.8530 5.2490 1.8978 0.7 3.8726 0.9652 5.7686 1.9767 0.75 3.8726 0.9652 5.7686 1.9767 0.8 3.8726 0.9652 5.7686 1.9767 0.85 3.8726 0.9652 5.7686 1.9767 0.9 3.8726 0.9652 5.7686 1.9767 0.95 3.8726 0.9652 5.7686 1.9767
9 - Thickness Averaging - API 653, 2nd Edition
1.0 3.8726 0.9652 5.7686 1.9767 0.7 2.6527 0.5520 3.7370 1.5684 0.75 2.7489 0.5714 3.8713 1.6265 0.8 2.8565 0.6008 4.0367 1.6763 0.85 2.9758 0.6385 4.2300 1.7216 0.9 3.1118 0.6802 4.4479 1.7756 0.95 3.2617 0.7235 4.6827 1.8406
10 - British Gas Single Defect Method - B31.G surface correction, exact area, BG Folias factor
1.0 3.4276 0.7633 4.9268 1.9283 0.7 2.7056 0.4400 3.5699 1.8412 0.75 2.8001 0.4596 3.7029 1.8972 0.8 2.9048 0.4911 3.8695 1.9401 0.85 3.0252 0.5314 4.0690 1.9813 0.9 3.1635 0.5761 4.2951 2.0320 0.95 3.3165 0.6192 4.5328 2.1002
11 - British Gas Complex Defect Method - B31.G surface correction, exact area, BG Folias factor
1.0 3.4856 0.6546 4.7715 2.1998 0.7 2.4839 0.5546 3.5732 1.3946 0.75 2.5656 0.5478 3.6416 1.4896 0.8 2.6628 0.5527 3.7485 1.5771 0.85 2.7793 0.5712 3.9012 1.6574 0.9 2.9168 0.6011 4.0974 1.7361 0.95 3.0647 0.6372 4.3163 1.8132
12 - Chell Method - Chell surface correction, exact area, B31-G Folias factor
1.0 3.2247 0.6712 4.5431 1.9063
180
Table 22 – MAWP Ratio vs. Allowable RSF for CODAP (Continued)
Method Allowable RSF
Mean MAWP Ratio
MAWP Ratio
Standard Deviation
MAWP Ratio Upper 95% Prediction
Limit
MAWP Ratio Lower 95% Prediction
Limit 0.7 2.3763 0.5594 3.4751 1.2774 0.75 2.4298 0.5286 3.4682 1.3915 0.8 2.4969 0.5041 3.4872 1.5067 0.85 2.5824 0.4912 3.5473 1.6175 0.9 2.6959 0.4998 3.6776 1.7142 0.95 2.8296 0.5228 3.8565 1.8027
13 - Osage Method - Chell surface correction, effective area, D/t dependent Folias factor
1.0 2.9780 0.5501 4.0585 1.8975 0.7 2.4826 0.5550 3.5728 1.3924 0.75 2.5639 0.5480 3.6404 1.4874 0.8 2.6607 0.5528 3.7466 1.5748 0.85 2.7768 0.5711 3.8986 1.6551 0.9 2.9140 0.6009 4.0943 1.7338 0.95 3.0618 0.6369 4.3128 1.8107
14 - API 579, Level 1, Hybrid 1 Analysis - Chell surface correction, rectangular area, API level 1 Folias factor 1.0 3.2215 0.6709 4.5394 1.9036
0.7 2.3648 0.5716 3.4875 1.2420 0.75 2.4135 0.5420 3.4781 1.3489 0.8 2.4743 0.5183 3.4924 1.4562 0.85 2.5533 0.5044 3.5441 1.5625 0.9 2.6587 0.5115 3.6633 1.6541 0.95 2.7846 0.5341 3.8337 1.7355
15 - API 579, Level 2, Hybrid 1 Analysis - Chell surface correction, effective area, API level 2 Folias factor 1.0 2.9280 0.5620 4.0318 1.8241
0.7 2.4237 0.5789 3.5608 1.2866 0.75 2.4883 0.5653 3.5987 1.3779 0.8 2.5660 0.5622 3.6704 1.4616 0.85 2.6639 0.5720 3.7873 1.5404 0.9 2.7853 0.5961 3.9561 1.6144 0.95 2.9219 0.6284 4.1561 1.6876
16 - API 579, Level 1, Hybrid 2 Analysis - Chell surface correction, rectangular area, BG Folias factor
1.0 3.0709 0.6624 4.3721 1.7698 0.7 2.3584 0.5806 3.4988 1.2180 0.75 2.4040 0.5528 3.4898 1.3182 0.8 2.4601 0.5302 3.5015 1.4186 0.85 2.5324 0.5175 3.5489 1.5159 0.9 2.6301 0.5228 3.6570 1.6033 0.95 2.7501 0.5439 3.8184 1.6817
17 - API 579, Level 2, Hybrid 2 Analysis - Chell surface correction, effective area, BG Folias factor
1.0 2.8883 0.5724 4.0126 1.7640 0.7 2.3688 0.5948 3.5370 1.2005 0.75 2.4195 0.5708 3.5407 1.2983 0.8 2.4828 0.5522 3.5675 1.3982 0.85 2.5607 0.5413 3.6240 1.4973 0.9 2.6524 0.5402 3.7134 1.5914 0.95 2.7554 0.5488 3.8333 1.6774
18 - API 579, Level 1, Hybrid 3 Analysis - Chell surface correction, rectangular area, JO Folias factor
1.0 2.8718 0.5660 3.9836 1.7600
181
Table 22 – MAWP Ratio vs. Allowable RSF for CODAP (Continued)
Method Allowable RSF
Mean MAWP Ratio
MAWP Ratio
Standard Deviation
MAWP Ratio Upper 95% Prediction
Limit
MAWP Ratio Lower 95% Prediction
Limit 0.7 2.3225 0.6062 3.5133 1.1317 0.75 2.3536 0.5745 3.4820 1.2252 0.8 2.3961 0.5415 3.4596 1.3325 0.85 2.4521 0.5112 3.4564 1.4479 0.9 2.5250 0.4880 3.4837 1.5664 0.95 2.6156 0.4772 3.5531 1.6782
19 – API 579, Level 2, Hybrid 3 Analysis – Chell surface correction, effective area, JO Folias factor
1.0 2.7228 0.4793 3.6643 1.7812 0.7 2.6386 0.5660 3.7504 1.5268 0.75 2.7315 0.5854 3.8813 1.5817 0.8 2.8384 0.6135 4.0434 1.6334 0.85 2.9606 0.6491 4.2357 1.6856 0.9 3.1001 0.6884 4.4523 1.7480 0.95 3.2573 0.7278 4.6869 1.8278
20 – Battelle Method – B31.G surface correction, rectangular area, Battelle Folias factor
1.0 3.4270 0.7663 4.9322 1.9218 0.7 2.6527 0.5520 3.7370 1.5684 0.75 2.7489 0.5714 3.8713 1.6265 0.8 2.8565 0.6008 4.0367 1.6763 0.85 2.9758 0.6385 4.2300 1.7216 0.9 3.1118 0.6802 4.4479 1.7756 0.95 3.2617 0.7235 4.6827 1.8406
21 – BS 7910, Appendix G (Isolated Defect) – B31.G surface correction, rectangular area, BG Folias factor 1.0 3.4276 0.7633 4.9268 1.9283
0.7 2.5542 0.4994 3.5351 1.5734 0.75 2.6319 0.4931 3.6004 1.6634 0.8 2.7205 0.4978 3.6982 1.7428 0.85 2.8186 0.5138 3.8278 1.8093 0.9 2.9326 0.5388 3.9909 1.8742 0.95 3.0620 0.5701 4.1819 1.9422
22 – BS 7910, Appendix G (Grouped Defects) – B31.G surface correction, rectangular area, BG Folias factor 1.0 3.2117 0.6016 4.3934 2.0300
0.7 3.2635 1.1038 5.4317 1.0953 0.75 3.4245 1.2085 5.7982 1.0508 0.8 3.5948 1.3136 6.1750 1.0146 0.85 3.7795 1.4145 6.5579 1.0010 0.9 3.9754 1.5113 6.9439 1.0069 0.95 4.1837 1.6020 7.3304 1.0369
23 – Kanninen Equivalent Stress – B31.G surface correction, rectangular area, shell theory Folias factor 1.0 4.4018 1.6875 7.7165 1.0870
0.7 2.8709 0.6405 4.1290 1.6128 0.75 2.9778 0.7010 4.3547 1.6009 0.8 3.0941 0.7672 4.6011 1.5871 0.85 3.2251 0.8341 4.8635 1.5867 0.9 3.3714 0.8987 5.1367 1.6062 0.95 3.5331 0.9591 5.4170 1.6492
24 – Shell Theory Method – Chell surface correction, exact area, shell theory Folias factor
1.0 3.7138 1.0118 5.7013 1.7264
182
Table 22 – MAWP Ratio vs. Allowable RSF for CODAP (Continued)
Method Allowable RSF
Mean MAWP Ratio
MAWP Ratio
Standard Deviation
MAWP Ratio Upper 95% Prediction
Limit
MAWP Ratio Lower 95% Prediction
Limit 0.7 3.6225 1.1879 5.9559 1.2891 0.75 3.7880 1.3406 6.4214 1.1547 0.8 3.9801 1.5463 7.0174 0.9427 0.85 4.2631 1.7529 7.7062 0.8200 0.9 4.6082 2.0136 8.5634 0.6530 0.95 5.0061 2.2395 9.4051 0.6071
25 - Thickness Averaging - API 579, Level 1
1.0 5.5755 2.4643 10.4161 0.7349 0.7 2.7687 0.8018 4.3436 1.1937 0.75 2.9875 0.9639 4.8809 1.0941 0.8 3.2793 1.1949 5.6264 0.9322 0.85 3.6505 1.4729 6.5437 0.7574 0.9 4.1477 1.8082 7.6994 0.5960 0.95 4.7533 2.1272 8.9316 0.5750
26 - Thickness Averaging - API 579, Level 2
1.0 5.5755 2.4643 10.4161 0.7349 0.7 2.8292 0.6260 4.0588 1.5995 0.75 2.9575 0.6699 4.2733 1.6416 0.8 3.0958 0.7216 4.5133 1.6784 0.85 3.2453 0.7774 4.7724 1.7182 0.9 3.4103 0.8328 5.0460 1.7746 0.95 3.5895 0.8834 5.3247 1.8543
27 - Modified API 579 Section 5, Level 1 Analysis - B31.G surface correction, rectangular area, Modified API Folias factor 1.0 3.7767 0.9308 5.6050 1.9484
0.7 2.5837 0.4283 3.4251 1.7424 0.75 2.6658 0.4171 3.4852 1.8464 0.8 2.7615 0.4179 3.5824 1.9406 0.85 2.8699 0.4324 3.7192 2.0205 0.9 3.0001 0.4572 3.8981 2.1021 0.95 3.1492 0.4846 4.1011 2.1973
28 - Modified API 579 Section 5, Level 2 Analysis - B31.G surface correction, effective area, Modified API Folias factor 1.0 3.3120 0.5105 4.3147 2.3093
0.7 2.6481 0.5404 3.7095 1.5866 0.75 2.7633 0.5525 3.8485 1.6781 0.8 2.8911 0.5767 4.0238 1.7583 0.85 3.0345 0.6100 4.2327 1.8364 0.9 3.1981 0.6447 4.4645 1.9318 0.95 3.3722 0.6809 4.7097 2.0348
29 - Janelle Method, Level 1 - rectangular area
1.0 3.5497 0.7167 4.9575 2.1418 0.7 2.4869 0.4679 3.4060 1.5678 0.75 2.5638 0.4395 3.4271 1.7005 0.8 2.6570 0.4223 3.4864 1.8275 0.85 2.7682 0.4212 3.5956 1.9408 0.9 2.9071 0.4342 3.7600 2.0542 0.95 3.0612 0.4552 3.9554 2.1670
30 - Janelle Method, Level 1 - effective area
1.0 3.2220 0.4792 4.1632 2.2808
183
Table 23 – MAWP Ratio vs. Allowable RSF for AS 1210 and BS5500
Method Allowable RSF
Mean MAWP Ratio
MAWP Ratio
Standard Deviation
MAWP Ratio Upper 95% Prediction
Limit
MAWP Ratio Lower 95% Prediction
Limit 0.7 2.2726 0.5170 3.2880 1.2571 0.75 2.3790 0.5574 3.4738 1.2842 0.8 2.4931 0.6027 3.6770 1.3092 0.85 2.6160 0.6505 3.8939 1.3382 0.9 2.7512 0.6969 4.1201 1.3823 0.95 2.8969 0.7390 4.3486 1.4453
1 - API 579 Section 5, Level 1 Analysis - B31.G surface correction, rectangular area, API level 1 Folias factor 1.0 3.0482 0.7786 4.5776 1.5187
0.7 2.0318 0.3346 2.6890 1.3745 0.75 2.0961 0.3248 2.7340 1.4582 0.8 2.1710 0.3242 2.8077 1.5343 0.85 2.2558 0.3343 2.9125 1.5991 0.9 2.3582 0.3530 3.0516 1.6647 0.95 2.4755 0.3739 3.2100 1.7409
2 - API 579 Section 5, Level 2 Analysis - B31.G surface correction, effective area, API level 2 Folias factor 1.0 2.6034 0.3938 3.3769 1.8299
0.7 1.9935 0.3537 2.6882 1.2987 0.75 2.0531 0.3390 2.7191 1.3871 0.8 2.1237 0.3321 2.7760 1.4715 0.85 2.2046 0.3358 2.8642 1.5450 0.9 2.3027 0.3502 2.9906 1.6148 0.95 2.4168 0.3688 3.1413 1.6923
3 - API-579 Section 5, Level 2 Analysis - B31.G surface correction, exact area, API level 2 Folias factor 1.0 2.5416 0.3881 3.3039 1.7794
0.7 1.9965 0.4472 2.8749 1.1180 0.75 2.0608 0.4376 2.9204 1.2012 0.8 2.1383 0.4357 2.9941 1.2825 0.85 2.2253 0.4437 3.0969 1.3537 0.9 2.3258 0.4601 3.2296 1.4219 0.95 2.4397 0.4836 3.3895 1.4898
4 - Modified B31.G Method - B31.G surface correction, 0.85dl area, AGA Folias factor
1.0 2.5655 0.5086 3.5645 1.5665 0.7 2.0668 0.3498 2.7539 1.3798 0.75 2.1297 0.3382 2.7940 1.4654 0.8 2.2030 0.3349 2.8608 1.5452 0.85 2.2868 0.3426 2.9599 1.6138 0.9 2.3877 0.3598 3.0944 1.6810 0.95 2.5036 0.3812 3.2525 1.7547
5 - Modified B31.G Method (RSTRENG) - B31.G surface correction, effective area, AGA Folias factor 1.0 2.6321 0.4016 3.4209 1.8433
0.7 2.0309 0.3697 2.7571 1.3046 0.75 2.0894 0.3539 2.7847 1.3942 0.8 2.1589 0.3451 2.8368 1.4810 0.85 2.2390 0.3469 2.9204 1.5576 0.9 2.3360 0.3598 3.0427 1.6294 0.95 2.4489 0.3789 3.1931 1.7048
6 - Modified B31.G Method - B31.G surface correction, exact area, AGA Folias factor
1.0 2.5746 0.3986 3.3575 1.7917
184
Table 23 – MAWP Ratio vs. Allowable RSF for AS 1210 and BS5500 (Continued)
Method Allowable RSF
Mean MAWP Ratio
MAWP Ratio
Standard Deviation
MAWP Ratio Upper 95% Prediction
Limit
MAWP Ratio Lower 95% Prediction
Limit 0.7 2.0307 0.5405 3.0923 0.9691 0.75 2.0899 0.5626 3.1950 0.9848 0.8 2.1582 0.5899 3.3169 0.9995 0.85 2.2459 0.6211 3.4659 1.0260 0.9 2.3440 0.6558 3.6322 1.0558 0.95 2.4552 0.6929 3.8163 1.0941
7 – Original B31.G Method – B31.G surface correction, parabolic area, B31-G Folias factor
1.0 2.5811 0.7296 4.0142 1.1479 0.7 2.8117 0.6641 4.1162 1.5072 0.75 2.8117 0.6641 4.1162 1.5072 0.8 2.8117 0.6641 4.1162 1.5072 0.85 2.8117 0.6641 4.1162 1.5072 0.9 2.8117 0.6641 4.1162 1.5072 0.95 2.8117 0.6641 4.1162 1.5072
8 – Thickness Averaging – API 510, 8th Edition
1.0 2.8117 0.6641 4.1162 1.5072 0.7 3.0479 0.7559 4.5327 1.5632 0.75 3.0479 0.7559 4.5327 1.5632 0.8 3.0479 0.7559 4.5327 1.5632 0.85 3.0479 0.7559 4.5327 1.5632 0.9 3.0479 0.7559 4.5327 1.5632 0.95 3.0479 0.7559 4.5327 1.5632
9 – Thickness Averaging – API 653, 2nd Edition
1.0 3.0479 0.7559 4.5327 1.5632 0.7 2.0879 0.4328 2.9382 1.2377 0.75 2.1636 0.4478 3.0433 1.2840 0.8 2.2482 0.4707 3.1727 1.3237 0.85 2.3421 0.4999 3.3240 1.3602 0.9 2.4490 0.5324 3.4947 1.4033 0.95 2.5670 0.5662 3.6791 1.4549
10 – British Gas Single Defect Method - B31.G surface correction, exact area, BG Folias factor
1.0 2.6975 0.5973 3.8707 1.5243 0.7 2.1295 0.3432 2.8037 1.4553 0.75 2.2038 0.3581 2.9073 1.5003 0.8 2.2862 0.3824 3.0373 1.5351 0.85 2.3808 0.4136 3.1933 1.5683 0.9 2.4897 0.4486 3.3709 1.6085 0.95 2.6101 0.4823 3.5576 1.6627
11 - British Gas Complex Defect Method - B31.G surface correction, exact area, BG Folias factor
1.0 2.7432 0.5099 3.7448 1.7416 0.7 1.9548 0.4344 2.8081 1.1015 0.75 2.0190 0.4285 2.8607 1.1773 0.8 2.0954 0.4317 2.9434 1.2474 0.85 2.1870 0.4456 3.0623 1.3118 0.9 2.2952 0.4687 3.2159 1.3745 0.95 2.4116 0.4968 3.3873 1.4358
12 - Chell Method - Chell surface correction, exact area, B31-G Folias factor
1.0 2.5374 0.5233 3.5652 1.5096
185
Table 23 – MAWP Ratio vs. Allowable RSF for AS 1210 and BS5500 (Continued)
Method Allowable RSF
Mean MAWP Ratio
MAWP Ratio
Standard Deviation
MAWP Ratio Upper 95% Prediction
Limit
MAWP Ratio Lower 95% Prediction
Limit 0.7 1.8701 0.4386 2.7315 1.0086 0.75 1.9122 0.4138 2.7250 1.0994 0.8 1.9649 0.3938 2.7384 1.1915 0.85 2.0321 0.3828 2.7840 1.2801 0.9 2.1214 0.3891 2.8857 1.3571 0.95 2.2266 0.4068 3.0257 1.4276
13 – Osage Method – Chell surface correction, effective area, D/t dependent Folias factor
1.0 2.3434 0.4280 3.1841 1.5027 0.7 1.9538 0.4347 2.8077 1.0998 0.75 2.0177 0.4287 2.8598 1.1756 0.8 2.0938 0.4318 2.9419 1.2456 0.85 2.1851 0.4455 3.0602 1.3100 0.9 2.2930 0.4686 3.2134 1.3726 0.95 2.4092 0.4966 3.3846 1.4339
14 – API 579, Level 1, Hybrid 1 Analysis – Chell surface correction, rectangular area, API level 1 Folias factor 1.0 2.5349 0.5231 3.5623 1.5075
0.7 1.8610 0.4482 2.7415 0.9806 0.75 1.8993 0.4245 2.7331 1.0655 0.8 1.9471 0.4052 2.7429 1.1513 0.85 2.0092 0.3935 2.7820 1.2364 0.9 2.0921 0.3986 2.8751 1.3091 0.95 2.1912 0.4160 3.0084 1.3740
15 – API 579, Level 2, Hybrid 1 Analysis – Chell surface correction, effective area, API level 2 Folias factor 1.0 2.3040 0.4377 3.1637 1.4443
0.7 1.9074 0.4538 2.7987 1.0161 0.75 1.9582 0.4426 2.8276 1.0888 0.8 2.0193 0.4397 2.8828 1.1557 0.85 2.0962 0.4467 2.9735 1.2188 0.9 2.1917 0.4653 3.1057 1.2777 0.95 2.2992 0.4903 3.2623 1.3360
16 – API 579, Level 1, Hybrid 2 Analysis – Chell surface correction, rectangular area, BG Folias factor
1.0 2.4164 0.5168 3.4316 1.4012 0.7 1.8560 0.4554 2.7505 0.9616 0.75 1.8919 0.4331 2.7425 1.0412 0.8 1.9359 0.4147 2.7505 1.1213 0.85 1.9928 0.4040 2.7863 1.1993 0.9 2.0697 0.4078 2.8706 1.2687 0.95 2.1640 0.4241 2.9970 1.3310
17 – API 579, Level 2, Hybrid 2 Analysis – Chell surface correction, effective area, BG Folias factor
1.0 2.2727 0.4462 3.1492 1.3963 0.7 1.8643 0.4668 2.7812 0.9474 0.75 1.9042 0.4477 2.7836 1.0248 0.8 1.9540 0.4328 2.8041 1.1039 0.85 2.0152 0.4238 2.8477 1.1828 0.9 2.0874 0.4223 2.9169 1.2579 0.95 2.1683 0.4284 3.0098 1.3269
18 – API 579, Level 1, Hybrid 3 Analysis – Chell surface correction, rectangular area, JO Folias factor
1.0 2.2599 0.4413 3.1268 1.3930
186
Table 23 – MAWP Ratio vs. Allowable RSF for AS 1210 and BS5500 (Continued)
Method Allowable RSF
Mean MAWP Ratio
MAWP Ratio
Standard Deviation
MAWP Ratio Upper 95% Prediction
Limit
MAWP Ratio Lower 95% Prediction
Limit 0.7 1.8278 0.4758 2.7625 0.8932 0.75 1.8523 0.4506 2.7375 0.9672 0.8 1.8857 0.4243 2.7192 1.0522 0.85 1.9298 0.4001 2.7156 1.1440 0.9 1.9871 0.3811 2.7358 1.2385 0.95 2.0583 0.3718 2.7886 1.3281
19 - API 579, Level 2, Hybrid 3 Analysis - Chell surface correction, effective area, JO Folias factor
1.0 2.1426 0.3726 2.8745 1.4107 0.7 2.0768 0.4434 2.9478 1.2057 0.75 2.1498 0.4584 3.0502 1.2495 0.8 2.2339 0.4801 3.1769 1.2910 0.85 2.3300 0.5076 3.3272 1.3329 0.9 2.4398 0.5381 3.4968 1.3827 0.95 2.5635 0.5688 3.6808 1.4461
20 - Battelle Method - B31.G surface correction, rectangular area, Battelle Folias factor
1.0 2.6970 0.5989 3.8735 1.5205 0.7 2.0879 0.4328 2.9382 1.2377 0.75 2.1636 0.4478 3.0433 1.2840 0.8 2.2482 0.4707 3.1727 1.3237 0.85 2.3421 0.4999 3.3240 1.3602 0.9 2.4490 0.5324 3.4947 1.4033 0.95 2.5670 0.5662 3.6791 1.4549
21 - BS 7910, Appendix G (Isolated Defect) - B31.G surface correction, rectangular area, BG Folias factor 1.0 2.6975 0.5973 3.8707 1.5243
0.7 2.0106 0.3916 2.7798 1.2414 0.75 2.0718 0.3865 2.8309 1.3126 0.8 2.1415 0.3899 2.9074 1.3755 0.85 2.2186 0.4023 3.0088 1.4285 0.9 2.3084 0.4217 3.1367 1.4800 0.95 2.4103 0.4463 3.2870 1.5335
22 - BS 7910, Appendix G (Grouped Defects) - B31.G surface correction, rectangular area, BG Folias factor 1.0 2.5281 0.4710 3.4533 1.6029
0.7 2.5691 0.8680 4.2741 0.8641 0.75 2.6957 0.9503 4.5623 0.8292 0.8 2.8297 1.0329 4.8585 0.8009 0.85 2.9750 1.1121 5.1595 0.7904 0.9 3.1291 1.1882 5.4631 0.7952 0.95 3.2931 1.2595 5.7671 0.8190
23 - Kanninen Equivalent Stress - B31.G surface correction, rectangular area, shell theory Folias factor 1.0 3.4647 1.3268 6.0709 0.8586
0.7 2.2601 0.5035 3.2491 1.2710 0.75 2.3442 0.5511 3.4268 1.2617 0.8 2.4357 0.6032 3.6205 1.2510 0.85 2.5388 0.6557 3.8268 1.2508 0.9 2.6540 0.7065 4.0417 1.2663 0.95 2.7812 0.7540 4.2622 1.3002
24 - Shell Theory Method - Chell surface correction, exact area, shell theory Folias factor
1.0 2.9234 0.7954 4.4858 1.3611
187
Table 23 – MAWP Ratio vs. Allowable RSF for AS 1210 and BS5500 (Continued)
Method Allowable RSF
Mean MAWP Ratio
MAWP Ratio
Standard Deviation
MAWP Ratio Upper 95% Prediction
Limit
MAWP Ratio Lower 95% Prediction
Limit 0.7 2.8502 0.9296 4.6761 1.0243 0.75 2.9804 1.0493 5.0415 0.9192 0.8 3.1314 1.2108 5.5097 0.7532 0.85 3.3544 1.3734 6.0521 0.6567 0.9 3.6263 1.5795 6.7288 0.5238 0.95 3.9397 1.7582 7.3934 0.4861
25 - Thickness Averaging - API 579, Level 1
1.0 4.3884 1.9370 8.1932 0.5836 0.7 2.1788 0.6280 3.4122 0.9453 0.75 2.3509 0.7548 3.8335 0.8683 0.8 2.5804 0.9357 4.4185 0.7424 0.85 2.8725 1.1541 5.1394 0.6056 0.9 3.2639 1.4184 6.0500 0.4779 0.95 3.7408 1.6700 7.0211 0.4604
26 - Thickness Averaging - API 579, Level 2
1.0 4.3884 1.9370 8.1932 0.5836 0.7 2.2269 0.4908 3.1910 1.2627 0.75 2.3278 0.5250 3.3590 1.2965 0.8 2.4366 0.5653 3.5470 1.3262 0.85 2.5541 0.6089 3.7501 1.3582 0.9 2.6839 0.6521 3.9649 1.4030 0.95 2.8250 0.6918 4.1838 1.4662
27 - Modified API 579 Section 5, Level 1 Analysis - B31.G surface correction, rectangular area, Modified API Folias factor 1.0 2.9723 0.7289 4.4040 1.5406
0.7 2.0336 0.3343 2.6902 1.3770 0.75 2.0981 0.3248 2.7362 1.4601 0.8 2.1734 0.3246 2.8109 1.5358 0.85 2.2586 0.3351 2.9169 1.6003 0.9 2.3610 0.3542 3.0567 1.6654 0.95 2.4784 0.3754 3.2158 1.7410
28 - Modified API 579 Section 5, Level 2 Analysis - B31.G surface correction, effective area, Modified API Folias factor 1.0 2.6065 0.3954 3.3831 1.8298
0.7 2.0841 0.4227 2.9143 1.2538 0.75 2.1747 0.4315 3.0223 1.3270 0.8 2.2751 0.4498 3.1587 1.3915 0.85 2.3879 0.4754 3.3217 1.4541 0.9 2.5166 0.5023 3.5033 1.5300 0.95 2.6536 0.5304 3.6955 1.6117
29 - Janelle Method, Level 1 - rectangular area
1.0 2.7932 0.5584 3.8900 1.6965 0.7 1.9572 0.3656 2.6753 1.2392 0.75 2.0176 0.3423 2.6901 1.3452 0.8 2.0909 0.3276 2.7344 1.4474 0.85 2.1784 0.3258 2.8183 1.5385 0.9 2.2876 0.3353 2.9462 1.6290 0.95 2.4089 0.3514 3.0991 1.7187
30 - Janelle Method, Level 1 - effective area
1.0 2.5354 0.3698 3.2619 1.8090
188
Table 24 – MAWP Ratio vs. Allowable RSF for ASME B31.4 and ASME B31.8, Class 1, Division 2
Method Allowable RSF
Mean MAWP Ratio
MAWP Ratio
Standard Deviation
MAWP Ratio Upper 95% Prediction
Limit
MAWP Ratio Lower 95% Prediction
Limit 0.7 1.7305 0.4190 2.5535 0.9075 0.75 1.8117 0.4520 2.6995 0.9238 0.8 1.8987 0.4885 2.8582 0.9391 0.85 1.9923 0.5265 3.0265 0.9581 0.9 2.0953 0.5633 3.2017 0.9889 0.95 2.2063 0.5971 3.3792 1.0334
1 - API 579 Section 5, Level 1 Analysis - B31.G surface correction, rectangular area, API level 1 Folias factor 1.0 2.3215 0.6290 3.5571 1.0859
0.7 1.5437 0.2525 2.0396 1.0478 0.75 1.5922 0.2429 2.0693 1.1151 0.8 1.6488 0.2404 2.1210 1.1766 0.85 1.7129 0.2461 2.1963 1.2294 0.9 1.7904 0.2590 2.2991 1.2817 0.95 1.8794 0.2744 2.4185 1.3403
2 - API 579 Section 5, Level 2 Analysis - B31.G surface correction, effective area, API level 2 Folias factor 1.0 1.9766 0.2890 2.5443 1.4088
0.7 1.5152 0.2694 2.0442 0.9861 0.75 1.5601 0.2567 2.0643 1.0559 0.8 1.6134 0.2496 2.1036 1.1232 0.85 1.6745 0.2505 2.1665 1.1825 0.9 1.7487 0.2601 2.2596 1.2379 0.95 1.8354 0.2739 2.3733 1.2974
3 - API-579 Section 5, Level 2 Analysis - B31.G surface correction, exact area, API level 2 Folias factor 1.0 1.9302 0.2882 2.4962 1.3641
0.7 1.5196 0.3523 2.2117 0.8275 0.75 1.5686 0.3478 2.2518 0.8854 0.8 1.6277 0.3493 2.3137 0.9416 0.85 1.6939 0.3579 2.3969 0.9909 0.9 1.7704 0.3721 2.5014 1.0394 0.95 1.8571 0.3913 2.6257 1.0885
4 - Modified B31.G Method - B31.G surface correction, 0.85dl area, AGA Folias factor
1.0 1.9529 0.4116 2.7614 1.1444 0.7 1.5703 0.2634 2.0876 1.0529 0.75 1.6176 0.2525 2.1136 1.1217 0.8 1.6730 0.2479 2.1600 1.1860 0.85 1.7364 0.2519 2.2311 1.2416 0.9 1.8127 0.2635 2.3302 1.2952 0.95 1.9006 0.2791 2.4488 1.3523
5 - Modified B31.G Method (RSTRENG) - B31.G surface correction, effective area, AGA Folias factor 1.0 1.9981 0.2940 2.5757 1.4206
0.7 1.5435 0.2807 2.0949 0.9920 0.75 1.5876 0.2671 2.1123 1.0628 0.8 1.6400 0.2587 2.1480 1.1319 0.85 1.7005 0.2582 2.2076 1.1934 0.9 1.7739 0.2666 2.2976 1.2503 0.95 1.8596 0.2805 2.4105 1.3087
6 - Modified B31.G Method - B31.G surface correction, exact area, AGA Folias factor
1.0 1.9550 0.2951 2.5347 1.3754
189
Table 24 – MAWP Ratio vs. Allowable RSF for ASME B31.4 and ASME B31.8, Class 1, Division 2 (Continued)
Method Allowable RSF
Mean MAWP Ratio
MAWP Ratio
Standard Deviation
MAWP Ratio Upper 95% Prediction
Limit
MAWP Ratio Lower 95% Prediction
Limit 0.7 1.5451 0.4249 2.3797 0.7105 0.75 1.5903 0.4438 2.4619 0.7186 0.8 1.6422 0.4662 2.5581 0.7264 0.85 1.7089 0.4914 2.6742 0.7436 0.9 1.7835 0.5190 2.8030 0.7639 0.95 1.8681 0.5484 2.9452 0.7909
7 - Original B31.G Method - B31.G surface correction, parabolic area, B31-G Folias factor
1.0 1.9638 0.5774 3.0980 0.8297 0.7 2.1327 0.4910 3.0971 1.1682 0.75 2.1327 0.4910 3.0971 1.1682 0.8 2.1327 0.4910 3.0971 1.1682 0.85 2.1327 0.4910 3.0971 1.1682 0.9 2.1327 0.4910 3.0971 1.1682 0.95 2.1327 0.4910 3.0971 1.1682
8 - Thickness Averaging - API 510, 8th Edition
1.0 2.1327 0.4910 3.0971 1.1682 0.7 2.3134 0.5638 3.4208 1.2059 0.75 2.3134 0.5638 3.4208 1.2059 0.8 2.3134 0.5638 3.4208 1.2059 0.85 2.3134 0.5638 3.4208 1.2059 0.9 2.3134 0.5638 3.4208 1.2059 0.95 2.3134 0.5638 3.4208 1.2059
9 - Thickness Averaging - API 653, 2nd Edition
1.0 2.3134 0.5638 3.4208 1.2059 0.7 1.5895 0.3519 2.2808 0.8983 0.75 1.6471 0.3662 2.3665 0.9277 0.8 1.7116 0.3864 2.4705 0.9527 0.85 1.7831 0.4108 2.5901 0.9761 0.9 1.8645 0.4373 2.7234 1.0055 0.95 1.9542 0.4646 2.8669 1.0416
10 - British Gas Single Defect Method - B31.G surface correction, exact area, BG Folias factor
1.0 2.0536 0.4900 3.0162 1.0911 0.7 1.6172 0.2550 2.1181 1.1162 0.75 1.6732 0.2638 2.1914 1.1549 0.8 1.7353 0.2803 2.2859 1.1847 0.85 1.8068 0.3023 2.4006 1.2130 0.9 1.8891 0.3275 2.5324 1.2457 0.95 1.9803 0.3524 2.6725 1.2881
11 - British Gas Complex Defect Method - B31.G surface correction, exact area, BG Folias factor
1.0 2.0812 0.3726 2.8132 1.3492 0.7 1.4877 0.3427 2.1608 0.8146 0.75 1.5365 0.3407 2.2058 0.8673 0.8 1.5946 0.3453 2.2729 0.9163 0.85 1.6641 0.3571 2.3656 0.9627 0.9 1.7463 0.3755 2.4839 1.0086 0.95 1.8347 0.3974 2.6153 1.0541
12 - Chell Method - Chell surface correction, exact area, B31-G Folias factor
1.0 1.9305 0.4185 2.7525 1.1084
190
Table 24 – MAWP Ratio vs. Allowable RSF for ASME B31.4 and ASME B31.8, Class 1, Division 2 (Continued)
Method Allowable RSF
Mean MAWP Ratio
MAWP Ratio
Standard Deviation
MAWP Ratio Upper 95% Prediction
Limit
MAWP Ratio Lower 95% Prediction
Limit 0.7 1.4222 0.3361 2.0823 0.7620 0.75 1.4538 0.3164 2.0753 0.8323 0.8 1.4936 0.3002 2.0833 0.9038 0.85 1.5443 0.2910 2.1160 0.9727 0.9 1.6119 0.2948 2.1911 1.0328 0.95 1.6917 0.3077 2.2962 1.0873
13 – Osage Method – Chell surface correction, effective area, D/t dependent Folias factor
1.0 1.7805 0.3237 2.4164 1.1446 0.7 1.4869 0.3429 2.1603 0.8134 0.75 1.5355 0.3408 2.2049 0.8661 0.8 1.5933 0.3453 2.2716 0.9151 0.85 1.6627 0.3570 2.3638 0.9615 0.9 1.7446 0.3753 2.4819 1.0073 0.95 1.8329 0.3971 2.6130 1.0528
14 – API 579, Level 1, Hybrid 1 Analysis – Chell surface correction, rectangular area, API level 1 Folias factor 1.0 1.9285 0.4183 2.7501 1.1070
0.7 1.4153 0.3434 2.0899 0.7408 0.75 1.4441 0.3245 2.0816 0.8066 0.8 1.4800 0.3087 2.0864 0.8737 0.85 1.5269 0.2988 2.1138 0.9400 0.9 1.5896 0.3016 2.1820 0.9972 0.95 1.6646 0.3138 2.2810 1.0483
15 – API 579, Level 2, Hybrid 1 Analysis – Chell surface correction, effective area, API level 2 Folias factor 1.0 1.7503 0.3300 2.3984 1.1022
0.7 1.4514 0.3539 2.1467 0.7562 0.75 1.4901 0.3475 2.1727 0.8074 0.8 1.5365 0.3474 2.2188 0.8542 0.85 1.5949 0.3540 2.2902 0.8996 0.9 1.6673 0.3688 2.3918 0.9429 0.95 1.7489 0.3882 2.5115 0.9863
16 – API 579, Level 1, Hybrid 2 Analysis – Chell surface correction, rectangular area, BG Folias factor
1.0 1.8381 0.4089 2.6414 1.0348 0.7 1.4116 0.3489 2.0969 0.7263 0.75 1.4385 0.3312 2.0890 0.7879 0.8 1.4716 0.3161 2.0924 0.8507 0.85 1.5145 0.3069 2.1172 0.9117 0.9 1.5726 0.3087 2.1790 0.9661 0.95 1.6440 0.3201 2.2726 1.0153
17 – API 579, Level 2, Hybrid 2 Analysis – Chell surface correction, effective area, BG Folias factor
1.0 1.7265 0.3363 2.3872 1.0658 0.7 1.4188 0.3623 2.1305 0.7071 0.75 1.4493 0.3498 2.1363 0.7622 0.8 1.4872 0.3406 2.1562 0.8182 0.85 1.5339 0.3364 2.1947 0.8732 0.9 1.5889 0.3377 2.2523 0.9255 0.95 1.6507 0.3444 2.3273 0.9741
18 – API 579, Level 1, Hybrid 3 Analysis – Chell surface correction, rectangular area, JO Folias factor
1.0 1.7204 0.3560 2.4197 1.0211
191
Table 24 – MAWP Ratio vs. Allowable RSF for ASME B31.4 and ASME B31.8, Class 1, Division 2 (Continued)
Method Allowable RSF
Mean MAWP Ratio
MAWP Ratio
Standard Deviation
MAWP Ratio Upper 95% Prediction
Limit
MAWP Ratio Lower 95% Prediction
Limit 0.7 1.3905 0.3651 2.1077 0.6734 0.75 1.4089 0.3456 2.0878 0.7300 0.8 1.4340 0.3250 2.0724 0.7956 0.85 1.4673 0.3062 2.0688 0.8658 0.9 1.5108 0.2919 2.0840 0.9375 0.95 1.5649 0.2851 2.1249 1.0049
19 - API 579, Level 2, Hybrid 3 Analysis - Chell surface correction, effective area, JO Folias factor
1.0 1.6290 0.2863 2.1913 1.0667 0.7 1.5808 0.3580 2.2840 0.8776 0.75 1.6364 0.3721 2.3673 0.9055 0.8 1.7005 0.3913 2.4692 0.9318 0.85 1.7737 0.4145 2.5878 0.9596 0.9 1.8572 0.4394 2.7204 0.9941 0.95 1.9514 0.4646 2.8641 1.0388
20 - Battelle Method - B31.G surface correction, rectangular area, Battelle Folias factor
1.0 2.0531 0.4892 3.0140 1.0922 0.7 1.5895 0.3519 2.2808 0.8983 0.75 1.6471 0.3662 2.3665 0.9277 0.8 1.7116 0.3864 2.4705 0.9527 0.85 1.7831 0.4108 2.5901 0.9761 0.9 1.8645 0.4373 2.7234 1.0055 0.95 1.9542 0.4646 2.8669 1.0416
21 - BS 7910, Appendix G (Isolated Defect) - B31.G surface correction, rectangular area, BG Folias factor 1.0 2.0536 0.4900 3.0162 1.0911
0.7 1.5310 0.3169 2.1535 0.9085 0.75 1.5777 0.3169 2.2002 0.9552 0.8 1.6309 0.3235 2.2663 0.9954 0.85 1.6898 0.3365 2.3507 1.0289 0.9 1.7582 0.3540 2.4536 1.0628 0.95 1.8359 0.3750 2.5725 1.0993
22 - BS 7910, Appendix G (Grouped Defects) - B31.G surface correction, rectangular area, BG Folias factor 1.0 1.9257 0.3957 2.7030 1.1484
0.7 1.9615 0.7017 3.3399 0.5832 0.75 2.0587 0.7674 3.5661 0.5514 0.8 2.1616 0.8332 3.7982 0.5249 0.85 2.2729 0.8964 4.0336 0.5121 0.9 2.3909 0.9572 4.2710 0.5108 0.95 2.5163 1.0143 4.5087 0.5238
23 - Kanninen Equivalent Stress - B31.G surface correction, rectangular area, shell theory Folias factor 1.0 2.6475 1.0684 4.7461 0.5488
0.7 1.7185 0.3879 2.4805 0.9566 0.75 1.7827 0.4251 2.6178 0.9476 0.8 1.8524 0.4655 2.7667 0.9380 0.85 1.9308 0.5061 2.9250 0.9366 0.9 2.0185 0.5456 3.0903 0.9468 0.95 2.1155 0.5826 3.2598 0.9711
24 - Shell Theory Method - Chell surface correction, exact area, shell theory Folias factor
1.0 2.2237 0.6146 3.4310 1.0164
192
Table 24 – MAWP Ratio vs. Allowable RSF for ASME B31.4 and ASME B31.8, Class 1, Division 2 (Continued)
Method Allowable RSF
Mean MAWP Ratio
MAWP Ratio
Standard Deviation
MAWP Ratio Upper 95% Prediction
Limit
MAWP Ratio Lower 95% Prediction
Limit 0.7 2.1720 0.7237 3.5936 0.7504 0.75 2.2715 0.8131 3.8686 0.6744 0.8 2.3869 0.9321 4.2178 0.5559 0.85 2.5570 1.0532 4.6258 0.4882 0.9 2.7652 1.2119 5.1456 0.3848 0.95 3.0044 1.3501 5.6564 0.3524
25 - Thickness Averaging - API 579, Level 1
1.0 3.3496 1.5034 6.3027 0.3964 0.7 1.6590 0.4864 2.6145 0.7035 0.75 1.7908 0.5838 2.9376 0.6439 0.8 1.9662 0.7201 3.3806 0.5518 0.85 2.1894 0.8849 3.9276 0.4513 0.9 2.4889 1.0882 4.6265 0.3513 0.95 2.8527 1.2824 5.3716 0.3337
26 - Thickness Averaging - API 579, Level 2
1.0 3.3496 1.5034 6.3027 0.3964 0.7 1.6955 0.3976 2.4765 0.9145 0.75 1.7724 0.4261 2.6093 0.9355 0.8 1.8554 0.4588 2.7566 0.9542 0.85 1.9450 0.4936 2.9145 0.9755 0.9 2.0438 0.5280 3.0809 1.0068 0.95 2.1513 0.5598 3.2510 1.0516
27 - Modified API 579 Section 5, Level 1 Analysis - B31.G surface correction, rectangular area, Modified API Folias factor 1.0 2.2635 0.5898 3.4220 1.1050
0.7 1.5451 0.2521 2.0402 1.0499 0.75 1.5937 0.2428 2.0706 1.1168 0.8 1.6506 0.2405 2.1230 1.1781 0.85 1.7150 0.2465 2.1993 1.2307 0.9 1.7925 0.2596 2.3025 1.2826 0.95 1.8816 0.2753 2.4223 1.3408
28 - Modified API 579 Section 5, Level 2 Analysis - B31.G surface correction, effective area, Modified API Folias factor 1.0 1.9788 0.2900 2.5484 1.4093
0.7 1.5863 0.3405 2.2550 0.9175 0.75 1.6553 0.3503 2.3434 0.9672 0.8 1.7319 0.3668 2.4523 1.0115 0.85 1.8178 0.3879 2.5798 1.0558 0.9 1.9158 0.4103 2.7219 1.1098 0.95 2.0202 0.4334 2.8715 1.1688
29 - Janelle Method, Level 1 - rectangular area
1.0 2.1265 0.4562 3.0226 1.2303 0.7 1.4876 0.2783 2.0343 0.9409 0.75 1.5332 0.2592 2.0424 1.0239 0.8 1.5885 0.2464 2.0726 1.1045 0.85 1.6548 0.2436 2.1332 1.1763 0.9 1.7377 0.2505 2.2297 1.2458 0.95 1.8299 0.2628 2.3461 1.3137
30 - Janelle Method, Level 1 - effective area
1.0 1.9260 0.2766 2.4693 1.3828
193
Table 25 – MAWP Ratio vs. Allowable RSF for ASME B31.8, Class 1, Division 1
Method Allowable RSF
Mean MAWP Ratio
MAWP Ratio
Standard Deviation
MAWP Ratio Upper 95% Prediction
Limit
MAWP Ratio Lower 95% Prediction
Limit 0.7 1.5562 0.3768 2.2963 0.8161 0.75 1.6292 0.4065 2.4276 0.8307 0.8 1.7075 0.4393 2.5704 0.8445 0.85 1.7917 0.4735 2.7217 0.8616 0.9 1.8842 0.5065 2.8792 0.8893 0.95 1.9841 0.5370 3.0389 0.9294
1 - API 579 Section 5, Level 1 Analysis - B31.G surface correction, rectangular area, API level 1 Folias factor 1.0 2.0877 0.5657 3.1988 0.9765
0.7 1.3882 0.2270 1.8342 0.9423 0.75 1.4318 0.2184 1.8609 1.0027 0.8 1.4827 0.2162 1.9074 1.0581 0.85 1.5404 0.2213 1.9751 1.1056 0.9 1.6101 0.2329 2.0675 1.1526 0.95 1.6901 0.2468 2.1749 1.2053
2 - API 579 Section 5, Level 2 Analysis - B31.G surface correction, effective area, API level 2 Folias factor 1.0 1.7775 0.2599 2.2880 1.2669
0.7 1.3625 0.2422 1.8383 0.8868 0.75 1.4029 0.2308 1.8564 0.9495 0.8 1.4509 0.2244 1.8917 1.0101 0.85 1.5059 0.2253 1.9483 1.0634 0.9 1.5726 0.2339 2.0320 1.1132 0.95 1.6505 0.2463 2.1343 1.1667
3 - API-579 Section 5, Level 2 Analysis - B31.G surface correction, exact area, API level 2 Folias factor 1.0 1.7358 0.2592 2.2448 1.2267
0.7 1.3665 0.3169 1.9889 0.7441 0.75 1.4106 0.3128 2.0250 0.7962 0.8 1.4637 0.3141 2.0807 0.8468 0.85 1.5233 0.3218 2.1555 0.8911 0.9 1.5921 0.3347 2.2494 0.9347 0.95 1.6701 0.3519 2.3613 0.9789
4 - Modified B31.G Method - B31.G surface correction, 0.85dl area, AGA Folias factor
1.0 1.7562 0.3702 2.4833 1.0291 0.7 1.4121 0.2369 1.8774 0.9469 0.75 1.4547 0.2271 1.9007 1.0087 0.8 1.5045 0.2230 1.9424 1.0665 0.85 1.5615 0.2265 2.0064 1.1166 0.9 1.6301 0.2369 2.0955 1.1647 0.95 1.7091 0.2510 2.2021 1.2161
5 - Modified B31.G Method (RSTRENG) - B31.G surface correction, effective area, AGA Folias factor 1.0 1.7969 0.2644 2.3163 1.2775
0.7 1.3880 0.2525 1.8839 0.8921 0.75 1.4277 0.2402 1.8996 0.9558 0.8 1.4748 0.2326 1.9317 1.0179 0.85 1.5292 0.2322 1.9852 1.0732 0.9 1.5953 0.2397 2.0662 1.1244 0.95 1.6723 0.2522 2.1677 1.1769
6 - Modified B31.G Method - B31.G surface correction, exact area, AGA Folias factor
1.0 1.7581 0.2654 2.2794 1.2368
194
Table 25 – MAWP Ratio vs. Allowable RSF for ASME B31.8, Class 1, Division 1 (Continued)
Method Allowable RSF
Mean MAWP Ratio
MAWP Ratio
Standard Deviation
MAWP Ratio Upper 95% Prediction
Limit
MAWP Ratio Lower 95% Prediction
Limit 0.7 1.3895 0.3821 2.1400 0.6389 0.75 1.4301 0.3991 2.2139 0.6462 0.8 1.4768 0.4193 2.3004 0.6532 0.85 1.5368 0.4419 2.4048 0.6687 0.9 1.6039 0.4668 2.5207 0.6870 0.95 1.6799 0.4931 2.6486 0.7113
7 - Original B31.G Method - B31.G surface correction, parabolic area, B31-G Folias factor
1.0 1.7660 0.5192 2.7859 0.7461 0.7 1.9179 0.4415 2.7852 1.0506 0.75 1.9179 0.4415 2.7852 1.0506 0.8 1.9179 0.4415 2.7852 1.0506 0.85 1.9179 0.4415 2.7852 1.0506 0.9 1.9179 0.4415 2.7852 1.0506 0.95 1.9179 0.4415 2.7852 1.0506
8 - Thickness Averaging - API 510, 8th Edition
1.0 1.9179 0.4415 2.7852 1.0506 0.7 2.0804 0.5070 3.0763 1.0844 0.75 2.0804 0.5070 3.0763 1.0844 0.8 2.0804 0.5070 3.0763 1.0844 0.85 2.0804 0.5070 3.0763 1.0844 0.9 2.0804 0.5070 3.0763 1.0844 0.95 2.0804 0.5070 3.0763 1.0844
9 - Thickness Averaging - API 653, 2nd Edition
1.0 2.0804 0.5070 3.0763 1.0844 0.7 1.4294 0.3165 2.0510 0.8078 0.75 1.4812 0.3294 2.1282 0.8343 0.8 1.5392 0.3475 2.2217 0.8567 0.85 1.6035 0.3695 2.3292 0.8778 0.9 1.6767 0.3932 2.4491 0.9042 0.95 1.7574 0.4178 2.5781 0.9367
10 - British Gas Single Defect Method - B31.G surface correction, exact area, BG Folias factor
1.0 1.8468 0.4407 2.7124 0.9812 0.7 1.4543 0.2294 1.9048 1.0038 0.75 1.5047 0.2373 1.9707 1.0386 0.8 1.5605 0.2521 2.0556 1.0654 0.85 1.6248 0.2718 2.1588 1.0908 0.9 1.6988 0.2945 2.2773 1.1203 0.95 1.7808 0.3169 2.4033 1.1583
11 - British Gas Complex Defect Method - B31.G surface correction, exact area, BG Folias factor
1.0 1.8716 0.3351 2.5299 1.2133 0.7 1.3379 0.3082 1.9432 0.7326 0.75 1.3818 0.3064 1.9836 0.7799 0.8 1.4340 0.3105 2.0440 0.8240 0.85 1.4965 0.3211 2.1273 0.8658 0.9 1.5704 0.3377 2.2337 0.9070 0.95 1.6499 0.3574 2.3519 0.9480
12 - Chell Method - Chell surface correction, exact area, B31-G Folias factor
1.0 1.7360 0.3764 2.4753 0.9968
195
Table 25 – MAWP Ratio vs. Allowable RSF for ASME B31.8, Class 1, Division 1 (Continued)
Method Allowable RSF
Mean MAWP Ratio
MAWP Ratio
Standard Deviation
MAWP Ratio Upper 95% Prediction
Limit
MAWP Ratio Lower 95% Prediction
Limit 0.7 1.2789 0.3022 1.8726 0.6853 0.75 1.3074 0.2845 1.8663 0.7485 0.8 1.3431 0.2700 1.8735 0.8128 0.85 1.3888 0.2617 1.9029 0.8747 0.9 1.4496 0.2652 1.9704 0.9288 0.95 1.5214 0.2767 2.0649 0.9778
13 - Osage Method - Chell surface correction, effective area, D/t dependent Folias factor
1.0 1.6011 0.2911 2.1730 1.0293 0.7 1.3371 0.3083 1.9428 0.7315 0.75 1.3808 0.3065 1.9828 0.7789 0.8 1.4329 0.3105 2.0428 0.8229 0.85 1.4952 0.3210 2.1258 0.8647 0.9 1.5689 0.3375 2.2319 0.9059 0.95 1.6483 0.3571 2.3499 0.9468
14 - API 579, Level 1, Hybrid 1 Analysis - Chell surface correction, rectangular area, API level 1 Folias factor 1.0 1.7343 0.3761 2.4731 0.9955
0.7 1.2728 0.3088 1.8794 0.6662 0.75 1.2986 0.2919 1.8719 0.7254 0.8 1.3309 0.2776 1.8762 0.7857 0.85 1.3731 0.2687 1.9009 0.8454 0.9 1.4295 0.2712 1.9622 0.8968 0.95 1.4970 0.2822 2.0512 0.9427
15 - API 579, Level 2, Hybrid 1 Analysis - Chell surface correction, effective area, API level 2 Folias factor 1.0 1.5740 0.2967 2.1569 0.9912
0.7 1.3052 0.3183 1.9305 0.6800 0.75 1.3400 0.3125 1.9539 0.7261 0.8 1.3817 0.3124 1.9953 0.7682 0.85 1.4343 0.3183 2.0595 0.8090 0.9 1.4994 0.3317 2.1509 0.8479 0.95 1.5728 0.3491 2.2586 0.8870
16 - API 579, Level 1, Hybrid 2 Analysis - Chell surface correction, rectangular area, BG Folias factor
1.0 1.6530 0.3678 2.3753 0.9306 0.7 1.2694 0.3137 1.8857 0.6531 0.75 1.2936 0.2978 1.8786 0.7086 0.8 1.3233 0.2842 1.8816 0.7651 0.85 1.3619 0.2760 1.9040 0.8198 0.9 1.4142 0.2776 1.9595 0.8688 0.95 1.4784 0.2878 2.0437 0.9130
17 - API 579, Level 2, Hybrid 2 Analysis - Chell surface correction, effective area, BG Folias factor
1.0 1.5526 0.3025 2.1467 0.9585 0.7 1.2759 0.3258 1.9160 0.6359 0.75 1.3033 0.3145 1.9211 0.6855 0.8 1.3374 0.3063 1.9391 0.7358 0.85 1.3794 0.3025 1.9736 0.7852 0.9 1.4289 0.3037 2.0255 0.8323 0.95 1.4844 0.3098 2.0929 0.8760
18 - API 579, Level 1, Hybrid 3 Analysis - Chell surface correction, rectangular area, JO Folias factor
1.0 1.5471 0.3201 2.1760 0.9183
196
Table 25 – MAWP Ratio vs. Allowable RSF for ASME B31.8, Class 1, Division 1 (Continued)
Method Allowable RSF
Mean MAWP Ratio
MAWP Ratio
Standard Deviation
MAWP Ratio Upper 95% Prediction
Limit
MAWP Ratio Lower 95% Prediction
Limit 0.7 1.2505 0.3283 1.8954 0.6056 0.75 1.2670 0.3108 1.8775 0.6565 0.8 1.2896 0.2923 1.8637 0.7154 0.85 1.3195 0.2754 1.8604 0.7786 0.9 1.3586 0.2625 1.8741 0.8431 0.95 1.4073 0.2564 1.9109 0.9037
19 - API 579, Level 2, Hybrid 3 Analysis - Chell surface correction, effective area, JO Folias factor
1.0 1.4649 0.2574 1.9706 0.9592 0.7 1.4216 0.3219 2.0539 0.7892 0.75 1.4716 0.3346 2.1289 0.8143 0.8 1.5292 0.3519 2.2205 0.8379 0.85 1.5950 0.3727 2.3271 0.8629 0.9 1.6702 0.3952 2.4464 0.8940 0.95 1.7549 0.4178 2.5756 0.9342
20 - Battelle Method - B31.G surface correction, rectangular area, Battelle Folias factor
1.0 1.8463 0.4399 2.7105 0.9822 0.7 1.4294 0.3165 2.0510 0.8078 0.75 1.4812 0.3294 2.1282 0.8343 0.8 1.5392 0.3475 2.2217 0.8567 0.85 1.6035 0.3695 2.3292 0.8778 0.9 1.6767 0.3932 2.4491 0.9042 0.95 1.7574 0.4178 2.5781 0.9367
21 - BS 7910, Appendix G (Isolated Defect) - B31.G surface correction, rectangular area, BG Folias factor 1.0 1.8468 0.4407 2.7124 0.9812
0.7 1.3768 0.2850 1.9366 0.8170 0.75 1.4188 0.2850 1.9786 0.8590 0.8 1.4666 0.2909 2.0380 0.8952 0.85 1.5196 0.3026 2.1139 0.9253 0.9 1.5811 0.3184 2.2065 0.9558 0.95 1.6510 0.3372 2.3134 0.9886
22 - BS 7910, Appendix G (Grouped Defects) - B31.G surface correction, rectangular area, BG Folias factor 1.0 1.7318 0.3559 2.4308 1.0327
0.7 1.7640 0.6310 3.0035 0.5245 0.75 1.8514 0.6901 3.2069 0.4959 0.8 1.9438 0.7493 3.4157 0.4720 0.85 2.0439 0.8061 3.6273 0.4605 0.9 2.1501 0.8607 3.8408 0.4593 0.95 2.2628 0.9122 4.0546 0.4711
23 - Kanninen Equivalent Stress - B31.G surface correction, rectangular area, shell theory Folias factor 1.0 2.3808 0.9608 4.2681 0.4935
0.7 1.5454 0.3488 2.2307 0.8602 0.75 1.6031 0.3823 2.3541 0.8522 0.8 1.6658 0.4186 2.4880 0.8435 0.85 1.7364 0.4552 2.6304 0.8423 0.9 1.8152 0.4907 2.7791 0.8514 0.95 1.9024 0.5239 2.9315 0.8733
24 - Shell Theory Method - Chell surface correction, exact area, shell theory Folias factor
1.0 1.9997 0.5527 3.0854 0.9140
197
Table 25 – MAWP Ratio vs. Allowable RSF for ASME B31.8, Class 1, Division 1 (Continued)
Method Allowable RSF
Mean MAWP Ratio
MAWP Ratio
Standard Deviation
MAWP Ratio Upper 95% Prediction
Limit
MAWP Ratio Lower 95% Prediction
Limit 0.7 1.9532 0.6508 3.2316 0.6748 0.75 2.0427 0.7312 3.4790 0.6065 0.8 2.1465 0.8382 3.7930 0.4999 0.85 2.2995 0.9472 4.1599 0.4390 0.9 2.4867 1.0898 4.6274 0.3461 0.95 2.7018 1.2141 5.0867 0.3169
25 – Thickness Averaging – API 579, Level 1
1.0 3.0122 1.3520 5.6679 0.3565 0.7 1.4919 0.4375 2.3511 0.6326 0.75 1.6104 0.5250 2.6417 0.5791 0.8 1.7682 0.6475 3.0401 0.4963 0.85 1.9689 0.7958 3.5320 0.4058 0.9 2.2382 0.9786 4.1605 0.3159 0.95 2.5653 1.1532 4.8306 0.3001
26 – Thickness Averaging – API 579, Level 2
1.0 3.0122 1.3520 5.6679 0.3565 0.7 1.5247 0.3575 2.2270 0.8224 0.75 1.5939 0.3831 2.3465 0.8413 0.8 1.6685 0.4126 2.4790 0.8581 0.85 1.7491 0.4439 2.6210 0.8772 0.9 1.8380 0.4748 2.7706 0.9054 0.95 1.9346 0.5035 2.9235 0.9457
27 – Modified API 579 Section 5, Level 1 Analysis – B31.G surface correction, rectangular area, Modified API Folias factor 1.0 2.0355 0.5304 3.0773 0.9937
0.7 1.3895 0.2267 1.8347 0.9442 0.75 1.4332 0.2183 1.8621 1.0044 0.8 1.4843 0.2163 1.9092 1.0594 0.85 1.5423 0.2217 1.9777 1.1068 0.9 1.6120 0.2335 2.0706 1.1534 0.95 1.6921 0.2476 2.1784 1.2058
28 – Modified API 579 Section 5, Level 2 Analysis – B31.G surface correction, effective area, Modified API Folias factor 1.0 1.7795 0.2608 2.2917 1.2673
0.7 1.4265 0.3062 2.0279 0.8251 0.75 1.4886 0.3150 2.1074 0.8698 0.8 1.5574 0.3298 2.2053 0.9096 0.85 1.6347 0.3489 2.3199 0.9495 0.9 1.7229 0.3690 2.4477 0.9980 0.95 1.8167 0.3898 2.5823 1.0511
29 – Janelle Method, Level 1 – rectangular area
1.0 1.9123 0.4103 2.7182 1.1064 0.7 1.3378 0.2503 1.8294 0.8461 0.75 1.3787 0.2331 1.8367 0.9208 0.8 1.4285 0.2216 1.8639 0.9932 0.85 1.4881 0.2191 1.9184 1.0578 0.9 1.5627 0.2252 2.0051 1.1203 0.95 1.6456 0.2363 2.1098 1.1814
30 – Janelle Method, Level 1 – effective area
1.0 1.7321 0.2487 2.2206 1.2435
198
Table 26 – MAWP Ratio vs. Allowable RSF for ASME B31.8, Class 2
Method Allowable RSF
Mean MAWP Ratio
MAWP Ratio
Standard Deviation
MAWP Ratio Upper 95% Prediction
Limit
MAWP Ratio Lower 95% Prediction
Limit 0.7 2.0791 0.5034 3.0678 1.0903 0.75 2.1766 0.5431 3.2433 1.1098 0.8 2.2812 0.5869 3.4340 1.1283 0.85 2.3937 0.6326 3.6362 1.1512 0.9 2.5173 0.6767 3.8466 1.1881 0.95 2.6508 0.7174 4.0599 1.2416
1 – API 579 Section 5, Level 1 Analysis – B31.G surface correction, rectangular area, API level 1 Folias factor 1.0 2.7891 0.7558 4.2736 1.3046
0.7 1.8547 0.3033 2.4504 1.2589 0.75 1.9129 0.2918 2.4862 1.3397 0.8 1.9809 0.2888 2.5482 1.4136 0.85 2.0579 0.2957 2.6388 1.4771 0.9 2.1510 0.3111 2.7622 1.5399 0.95 2.2580 0.3297 2.9057 1.6103
2 – API 579 Section 5, Level 2 Analysis – B31.G surface correction, effective area, API level 2 Folias factor 1.0 2.3747 0.3473 3.0568 1.6926
0.7 1.8204 0.3236 2.4560 1.1847 0.75 1.8743 0.3084 2.4801 1.2686 0.8 1.9384 0.2998 2.5274 1.3494 0.85 2.0118 0.3009 2.6030 1.4207 0.9 2.1010 0.3125 2.7148 1.4872 0.95 2.2051 0.3291 2.8514 1.5587
3 – API-579 Section 5, Level 2 Analysis – B31.G surface correction, exact area, API level 2 Folias factor 1.0 2.3190 0.3462 2.9991 1.6389
0.7 1.8257 0.4233 2.6572 0.9942 0.75 1.8846 0.4179 2.7054 1.0637 0.8 1.9555 0.4196 2.7798 1.1313 0.85 2.0351 0.4300 2.8798 1.1905 0.9 2.1270 0.4471 3.0052 1.2488 0.95 2.2312 0.4701 3.1547 1.3077
4 – Modified B31.G Method – B31.G surface correction, 0.85dl area, AGA Folias factor
1.0 2.3463 0.4945 3.3177 1.3749 0.7 1.8866 0.3164 2.5082 1.2651 0.75 1.9435 0.3034 2.5394 1.3476 0.8 2.0100 0.2979 2.5951 1.4249 0.85 2.0861 0.3026 2.6805 1.4917 0.9 2.1778 0.3165 2.7996 1.5561 0.95 2.2834 0.3353 2.9420 1.6248
5 – Modified B31.G Method (RSTRENG) – B31.G surface correction, effective area, AGA Folias factor 1.0 2.4007 0.3532 3.0945 1.7068
0.7 1.8544 0.3373 2.5169 1.1918 0.75 1.9074 0.3210 2.5378 1.2769 0.8 1.9703 0.3108 2.5807 1.3599 0.85 2.0430 0.3102 2.6523 1.4338 0.9 2.1313 0.3203 2.7604 1.5022 0.95 2.2342 0.3369 2.8960 1.5723
6 – Modified B31.G Method – B31.G surface correction, exact area, AGA Folias factor
1.0 2.3488 0.3545 3.0452 1.6524
199
Table 26 – MAWP Ratio vs. Allowable RSF for ASME B31.8, Class 2 (Continued)
Method Allowable RSF
Mean MAWP Ratio
MAWP Ratio
Standard Deviation
MAWP Ratio Upper 95% Prediction
Limit
MAWP Ratio Lower 95% Prediction
Limit 0.7 1.8564 0.5105 2.8591 0.8536 0.75 1.9106 0.5331 2.9578 0.8634 0.8 1.9730 0.5602 3.0733 0.8727 0.85 2.0531 0.5904 3.2129 0.8934 0.9 2.1428 0.6236 3.3677 0.9178 0.95 2.2444 0.6588 3.5385 0.9503
7 - Original B31.G Method - B31.G surface correction, parabolic area, B31-G Folias factor
1.0 2.3594 0.6937 3.7220 0.9968 0.7 2.5623 0.5899 3.7210 1.4035 0.75 2.5623 0.5899 3.7210 1.4035 0.8 2.5623 0.5899 3.7210 1.4035 0.85 2.5623 0.5899 3.7210 1.4035 0.9 2.5623 0.5899 3.7210 1.4035 0.95 2.5623 0.5899 3.7210 1.4035
8 - Thickness Averaging - API 510, 8th Edition
1.0 2.5623 0.5899 3.7210 1.4035 0.7 2.7794 0.6774 4.1099 1.4488 0.75 2.7794 0.6774 4.1099 1.4488 0.8 2.7794 0.6774 4.1099 1.4488 0.85 2.7794 0.6774 4.1099 1.4488 0.9 2.7794 0.6774 4.1099 1.4488 0.95 2.7794 0.6774 4.1099 1.4488
9 - Thickness Averaging - API 653, 2nd Edition
1.0 2.7794 0.6774 4.1099 1.4488 0.7 1.9097 0.4228 2.7402 1.0792 0.75 1.9789 0.4400 2.8432 1.1146 0.8 2.0564 0.4642 2.9682 1.1446 0.85 2.1423 0.4936 3.1119 1.1727 0.9 2.2400 0.5254 3.2720 1.2080 0.95 2.3479 0.5582 3.4444 1.2514
10 - British Gas Single Defect Method - B31.G surface correction, exact area, BG Folias factor
1.0 2.4673 0.5887 3.6238 1.3109 0.7 1.9429 0.3064 2.5448 1.3411 0.75 2.0102 0.3170 2.6328 1.3876 0.8 2.0848 0.3368 2.7463 1.4234 0.85 2.1707 0.3632 2.8841 1.4573 0.9 2.2696 0.3935 3.0425 1.4967 0.95 2.3792 0.4234 3.2108 1.5475
11 - British Gas Complex Defect Method - B31.G surface correction, exact area, BG Folias factor
1.0 2.5005 0.4477 3.3799 1.6210 0.7 1.7874 0.4117 2.5961 0.9787 0.75 1.8460 0.4093 2.6501 1.0420 0.8 1.9158 0.4149 2.7307 1.1009 0.85 1.9994 0.4290 2.8421 1.1566 0.9 2.0980 0.4512 2.9843 1.2118 0.95 2.2043 0.4774 3.1421 1.2665
12 - Chell Method - Chell surface correction, exact area, B31-G Folias factor
1.0 2.3193 0.5028 3.3070 1.3317
200
Table 26 – MAWP Ratio vs. Allowable RSF for ASME B31.8, Class 2 (Continued)
Method Allowable RSF
Mean MAWP Ratio
MAWP Ratio
Standard Deviation
MAWP Ratio Upper 95% Prediction
Limit
MAWP Ratio Lower 95% Prediction
Limit 0.7 1.7087 0.4038 2.5018 0.9155 0.75 1.7467 0.3801 2.4933 1.0000 0.8 1.7944 0.3607 2.5030 1.0859 0.85 1.8554 0.3497 2.5422 1.1686 0.9 1.9366 0.3542 2.6325 1.2408 0.95 2.0325 0.3697 2.7587 1.3064
13 - Osage Method - Chell surface correction, effective area, D/t dependent Folias factor
1.0 2.1391 0.3890 2.9031 1.3751 0.7 1.7864 0.4119 2.5955 0.9773 0.75 1.8448 0.4094 2.6490 1.0406 0.8 1.9143 0.4148 2.7292 1.0994 0.85 1.9976 0.4289 2.8400 1.1552 0.9 2.0960 0.4509 2.9818 1.2103 0.95 2.2022 0.4771 3.1394 1.2649
14 - API 579, Level 1, Hybrid 1 Analysis - Chell surface correction, rectangular area, API level 1 Folias factor 1.0 2.3170 0.5025 3.3041 1.3300
0.7 1.7005 0.4126 2.5109 0.8900 0.75 1.7350 0.3899 2.5009 0.9691 0.8 1.7781 0.3709 2.5066 1.0497 0.85 1.8345 0.3590 2.5396 1.1294 0.9 1.9098 0.3623 2.6215 1.1981 0.95 2.0000 0.3770 2.7405 1.2594
15 - API 579, Level 2, Hybrid 1 Analysis - Chell surface correction, effective area, API level 2 Folias factor 1.0 2.1029 0.3964 2.8816 1.3242
0.7 1.7438 0.4252 2.5791 0.9085 0.75 1.7902 0.4176 2.6104 0.9700 0.8 1.8460 0.4173 2.6657 1.0263 0.85 1.9162 0.4253 2.7515 1.0808 0.9 2.0032 0.4431 2.8736 1.1328 0.95 2.1012 0.4664 3.0174 1.1850
16 - API 579, Level 1, Hybrid 2 Analysis - Chell surface correction, rectangular area, BG Folias factor
1.0 2.2084 0.4913 3.1734 1.2433 0.7 1.6959 0.4192 2.5192 0.8726 0.75 1.7282 0.3979 2.5098 0.9467 0.8 1.7680 0.3797 2.5139 1.0221 0.85 1.8195 0.3687 2.5437 1.0953 0.9 1.8894 0.3709 2.6179 1.1608 0.95 1.9751 0.3845 2.7304 1.2198
17 - API 579, Level 2, Hybrid 2 Analysis - Chell surface correction, effective area, BG Folias factor
1.0 2.0743 0.4041 2.8680 1.2806 0.7 1.7046 0.4353 2.5597 0.8496 0.75 1.7412 0.4202 2.5666 0.9158 0.8 1.7868 0.4092 2.5906 0.9830 0.85 1.8429 0.4041 2.6367 1.0490 0.9 1.9090 0.4058 2.7060 1.1120 0.95 1.9832 0.4138 2.7961 1.1703
18 - API 579, Level 1, Hybrid 3 Analysis - Chell surface correction, rectangular area, JO Folias factor
1.0 2.0670 0.4277 2.9071 1.2268
201
Table 26 – MAWP Ratio vs. Allowable RSF for ASME B31.8, Class 2 (Continued)
Method Allowable RSF
Mean MAWP Ratio
MAWP Ratio
Standard Deviation
MAWP Ratio Upper 95% Prediction
Limit
MAWP Ratio Lower 95% Prediction
Limit 0.7 1.6707 0.4386 2.5322 0.8091 0.75 1.6927 0.4153 2.5084 0.8771 0.8 1.7229 0.3905 2.4899 0.9558 0.85 1.7629 0.3679 2.4855 1.0402 0.9 1.8151 0.3506 2.5039 1.1263 0.95 1.8801 0.3425 2.5529 1.2073
19 – API 579, Level 2, Hybrid 3 Analysis – Chell surface correction, effective area, JO Folias factor
1.0 1.9572 0.3439 2.6328 1.2816 0.7 1.8992 0.4301 2.7441 1.0543 0.75 1.9660 0.4471 2.8441 1.0879 0.8 2.0430 0.4702 2.9666 1.1195 0.85 2.1310 0.4979 3.1091 1.1529 0.9 2.2313 0.5279 3.2683 1.1943 0.95 2.3445 0.5582 3.4410 1.2481
20 – Battelle Method – B31.G surface correction, rectangular area, Battelle Folias factor
1.0 2.4667 0.5878 3.6212 1.3122 0.7 1.9097 0.4228 2.7402 1.0792 0.75 1.9789 0.4400 2.8432 1.1146 0.8 2.0564 0.4642 2.9682 1.1446 0.85 2.1423 0.4936 3.1119 1.1727 0.9 2.2400 0.5254 3.2720 1.2080 0.95 2.3479 0.5582 3.4444 1.2514
21 – BS 7910, Appendix G (Isolated Defect) – B31.G surface correction, rectangular area, BG Folias factor 1.0 2.4673 0.5887 3.6238 1.3109
0.7 1.8394 0.3807 2.5873 1.0915 0.75 1.8955 0.3807 2.6433 1.1476 0.8 1.9594 0.3887 2.7228 1.1959 0.85 2.0302 0.4042 2.8242 1.2362 0.9 2.1124 0.4254 2.9479 1.2769 0.95 2.2057 0.4505 3.0907 1.3208
22 – BS 7910, Appendix G (Grouped Defects) – B31.G surface correction, rectangular area, BG Folias factor 1.0 2.3136 0.4755 3.2475 1.3797
0.7 2.3567 0.8430 4.0126 0.7007 0.75 2.4734 0.9220 4.2844 0.6625 0.8 2.5970 1.0011 4.5633 0.6306 0.85 2.7307 1.0770 4.8461 0.6153 0.9 2.8725 1.1500 5.1313 0.6137 0.95 3.0231 1.2187 5.4169 0.6293
23 – Kanninen Equivalent Stress – B31.G surface correction, rectangular area, shell theory Folias factor 1.0 3.1808 1.2837 5.7022 0.6593
0.7 2.0647 0.4661 2.9802 1.1493 0.75 2.1418 0.5108 3.1451 1.1385 0.8 2.2255 0.5593 3.3240 1.1270 0.85 2.3198 0.6081 3.5142 1.1253 0.9 2.4252 0.6556 3.7128 1.1375 0.95 2.5416 0.7000 3.9165 1.1667
24 – Shell Theory Method – Chell surface correction, exact area, shell theory Folias factor
1.0 2.6716 0.7384 4.1221 1.2212
202
Table 26 – MAWP Ratio vs. Allowable RSF for ASME B31.8, Class 2 (Continued)
Method Allowable RSF
Mean MAWP Ratio
MAWP Ratio
Standard Deviation
MAWP Ratio Upper 95% Prediction
Limit
MAWP Ratio Lower 95% Prediction
Limit 0.7 2.6095 0.8695 4.3174 0.9016 0.75 2.7291 0.9769 4.6479 0.8103 0.8 2.8677 1.1199 5.0675 0.6679 0.85 3.0721 1.2654 5.5577 0.5865 0.9 3.3223 1.4560 6.1822 0.4624 0.95 3.6096 1.6221 6.7958 0.4234
25 - Thickness Averaging - API 579, Level 1
1.0 4.0243 1.8063 7.5723 0.4762 0.7 1.9931 0.5844 3.1411 0.8452 0.75 2.1515 0.7015 3.5293 0.7737 0.8 2.3623 0.8651 4.0615 0.6630 0.85 2.6304 1.0631 4.7187 0.5422 0.9 2.9902 1.3075 5.5584 0.4220 0.95 3.4273 1.5407 6.4537 0.4009
26 - Thickness Averaging - API 579, Level 2
1.0 4.0243 1.8063 7.5723 0.4762 0.7 2.0370 0.4777 2.9753 1.0987 0.75 2.1295 0.5119 3.1349 1.1240 0.8 2.2292 0.5512 3.3119 1.1464 0.85 2.3368 0.5930 3.5016 1.1720 0.9 2.4556 0.6343 3.7015 1.2096 0.95 2.5846 0.6726 3.9058 1.2634
27 - Modified API 579 Section 5, Level 1 Analysis - B31.G surface correction, rectangular area, Modified API Folias factor 1.0 2.7194 0.7086 4.1113 1.3276
0.7 1.8563 0.3029 2.4512 1.2614 0.75 1.9148 0.2917 2.4877 1.3418 0.8 1.9831 0.2890 2.5507 1.4154 0.85 2.0604 0.2962 2.6423 1.4786 0.9 2.1536 0.3119 2.7663 1.5409 0.95 2.2606 0.3308 2.9103 1.6109
28 - Modified API 579 Section 5, Level 2 Analysis - B31.G surface correction, effective area, Modified API Folias factor 1.0 2.3775 0.3484 3.0617 1.6932
0.7 1.9058 0.4091 2.7093 1.1023 0.75 1.9888 0.4209 2.8154 1.1621 0.8 2.0807 0.4406 2.9463 1.2152 0.85 2.1840 0.4661 3.0994 1.2685 0.9 2.3018 0.4930 3.2702 1.3334 0.95 2.4271 0.5207 3.4499 1.4043
29 - Janelle Method, Level 1 - rectangular area
1.0 2.5548 0.5481 3.6315 1.4782 0.7 1.7873 0.3344 2.4441 1.1304 0.75 1.8420 0.3115 2.4538 1.2302 0.8 1.9085 0.2961 2.4901 1.3269 0.85 1.9881 0.2927 2.5630 1.4132 0.9 2.0878 0.3009 2.6789 1.4967 0.95 2.1985 0.3157 2.8187 1.5784
30 - Janelle Method, Level 1 - effective area
1.0 2.3140 0.3323 2.9667 1.6613
203
Table 27 – MAWP Ratio vs. Allowable RSF for ASME B31.8, Class 3
Method Allowable RSF
Mean MAWP Ratio
MAWP Ratio
Standard Deviation
MAWP Ratio Upper 95% Prediction
Limit
MAWP Ratio Lower 95% Prediction
Limit 0.7 2.4899 0.6028 3.6741 1.3058 0.75 2.6067 0.6504 3.8842 1.3291 0.8 2.7319 0.7029 4.1126 1.3513 0.85 2.8667 0.7576 4.3547 1.3786 0.9 3.0148 0.8105 4.6068 1.4228 0.95 3.1746 0.8592 4.8622 1.4870
1 - API 579 Section 5, Level 1 Analysis - B31.G surface correction, rectangular area, API level 1 Folias factor 1.0 3.3403 0.9051 5.1181 1.5624
0.7 2.2212 0.3632 2.9347 1.5077 0.75 2.2909 0.3495 2.9774 1.6044 0.8 2.3724 0.3459 3.0518 1.6929 0.85 2.4646 0.3541 3.1602 1.7690 0.9 2.5761 0.3726 3.3080 1.8441 0.95 2.7042 0.3949 3.4798 1.9285
2 - API 579 Section 5, Level 2 Analysis - B31.G surface correction, effective area, API level 2 Folias factor 1.0 2.8440 0.4159 3.6609 2.0270
0.7 2.1801 0.3876 2.9413 1.4188 0.75 2.2447 0.3693 2.9702 1.5193 0.8 2.3214 0.3591 3.0268 1.6161 0.85 2.4094 0.3604 3.1173 1.7014 0.9 2.5162 0.3742 3.2513 1.7811 0.95 2.6408 0.3941 3.4149 1.8667
3 - API-579 Section 5, Level 2 Analysis - B31.G surface correction, exact area, API level 2 Folias factor 1.0 2.7772 0.4146 3.5917 1.9628
0.7 2.1865 0.5070 3.1823 1.1906 0.75 2.2570 0.5005 3.2400 1.2739 0.8 2.3420 0.5025 3.3291 1.3549 0.85 2.4373 0.5150 3.4488 1.4258 0.9 2.5473 0.5354 3.5991 1.4956 0.95 2.6721 0.5630 3.7780 1.5662
4 - Modified B31.G Method - B31.G surface correction, 0.85dl area, AGA Folias factor
1.0 2.8099 0.5923 3.9733 1.6466 0.7 2.2594 0.3790 3.0038 1.5150 0.75 2.3275 0.3633 3.0412 1.6139 0.8 2.4072 0.3567 3.1079 1.7064 0.85 2.4983 0.3624 3.2102 1.7865 0.9 2.6082 0.3791 3.3528 1.8636 0.95 2.7346 0.4016 3.5234 1.9458
5 - Modified B31.G Method (RSTRENG) - B31.G surface correction, effective area, AGA Folias factor 1.0 2.8750 0.4230 3.7060 2.0441
0.7 2.2208 0.4040 3.0143 1.4273 0.75 2.2843 0.3844 3.0393 1.5292 0.8 2.3597 0.3722 3.0907 1.6287 0.85 2.4468 0.3715 3.1764 1.7171 0.9 2.5524 0.3836 3.3058 1.7990 0.95 2.6757 0.4035 3.4683 1.8830
6 - Modified B31.G Method - B31.G surface correction, exact area, AGA Folias factor
1.0 2.8130 0.4246 3.6470 1.9789
204
Table 27 – MAWP Ratio vs. Allowable RSF for ASME B31.8, Class 3 (Continued)
Method Allowable RSF
Mean MAWP Ratio
MAWP Ratio
Standard Deviation
MAWP Ratio Upper 95% Prediction
Limit
MAWP Ratio Lower 95% Prediction
Limit 0.7 2.2232 0.6114 3.4241 1.0223 0.75 2.2881 0.6385 3.5423 1.0340 0.8 2.3629 0.6709 3.6806 1.0452 0.85 2.4589 0.7071 3.8477 1.0700 0.9 2.5662 0.7468 4.0331 1.0992 0.95 2.6879 0.7890 4.2377 1.1380
7 - Original B31.G Method - B31.G surface correction, parabolic area, B31-G Folias factor
1.0 2.8256 0.8308 4.4575 1.1938 0.7 3.0686 0.7065 4.4563 1.6809 0.75 3.0686 0.7065 4.4563 1.6809 0.8 3.0686 0.7065 4.4563 1.6809 0.85 3.0686 0.7065 4.4563 1.6809 0.9 3.0686 0.7065 4.4563 1.6809 0.95 3.0686 0.7065 4.4563 1.6809
8 - Thickness Averaging - API 510, 8th Edition
1.0 3.0686 0.7065 4.4563 1.6809 0.7 3.3286 0.8112 4.9221 1.7351 0.75 3.3286 0.8112 4.9221 1.7351 0.8 3.3286 0.8112 4.9221 1.7351 0.85 3.3286 0.8112 4.9221 1.7351 0.9 3.3286 0.8112 4.9221 1.7351 0.95 3.3286 0.8112 4.9221 1.7351
9 - Thickness Averaging - API 653, 2nd Edition
1.0 3.3286 0.8112 4.9221 1.7351 0.7 2.2871 0.5063 3.2817 1.2925 0.75 2.3700 0.5270 3.4051 1.3349 0.8 2.4627 0.5559 3.5547 1.3707 0.85 2.5656 0.5911 3.7268 1.4044 0.9 2.6827 0.6292 3.9186 1.4468 0.95 2.8119 0.6685 4.1250 1.4987
10 - British Gas Single Defect Method - B31.G surface correction, exact area, BG Folias factor
1.0 2.9549 0.7051 4.3398 1.5699 0.7 2.3269 0.3670 3.0477 1.6061 0.75 2.4074 0.3796 3.1531 1.6618 0.8 2.4968 0.4033 3.2890 1.7046 0.85 2.5997 0.4350 3.4541 1.7453 0.9 2.7181 0.4713 3.6438 1.7924 0.95 2.8493 0.5070 3.8453 1.8533
11 - British Gas Complex Defect Method - B31.G surface correction, exact area, BG Folias factor
1.0 2.9946 0.5362 4.0478 1.9414 0.7 2.1406 0.4930 3.1090 1.1721 0.75 2.2108 0.4902 3.1737 1.2479 0.8 2.2944 0.4969 3.2703 1.3185 0.85 2.3944 0.5138 3.4037 1.3852 0.9 2.5126 0.5403 3.5740 1.4512 0.95 2.6399 0.5718 3.7630 1.5168
12 - Chell Method - Chell surface correction, exact area, B31-G Folias factor
1.0 2.7776 0.6022 3.9605 1.5948
205
Table 27 – MAWP Ratio vs. Allowable RSF for ASME B31.8, Class 3 (Continued)
Method Allowable RSF
Mean MAWP Ratio
MAWP Ratio
Standard Deviation
MAWP Ratio Upper 95% Prediction
Limit
MAWP Ratio Lower 95% Prediction
Limit 0.7 2.0463 0.4836 2.9962 1.0964 0.75 2.0918 0.4553 2.9860 1.1976 0.8 2.1490 0.4320 2.9976 1.3005 0.85 2.2220 0.4187 3.0446 1.3995 0.9 2.3193 0.4242 3.1527 1.4860 0.95 2.4342 0.4427 3.3038 1.5645
13 – Osage Method – Chell surface correction, effective area, D/t dependent Folias factor
1.0 2.5618 0.4658 3.4768 1.6468 0.7 2.1394 0.4933 3.1084 1.1704 0.75 2.2094 0.4903 3.1725 1.2462 0.8 2.2926 0.4968 3.2685 1.3167 0.85 2.3923 0.5136 3.4012 1.3834 0.9 2.5102 0.5401 3.5710 1.4494 0.95 2.6373 0.5714 3.7598 1.5149
14 – API 579, Level 1, Hybrid 1 Analysis – Chell surface correction, rectangular area, API level 1 Folias factor 1.0 2.7749 0.6018 3.9570 1.5928
0.7 2.0365 0.4941 3.0071 1.0659 0.75 2.0778 0.4670 2.9951 1.1606 0.8 2.1295 0.4442 3.0020 1.2571 0.85 2.1970 0.4299 3.0414 1.3526 0.9 2.2872 0.4339 3.1396 1.4349 0.95 2.3952 0.4515 3.2820 1.5083
15 – API 579, Level 2, Hybrid 1 Analysis – Chell surface correction, effective area, API level 2 Folias factor 1.0 2.5184 0.4748 3.4510 1.5859
0.7 2.0884 0.5093 3.0887 1.0881 0.75 2.1440 0.5001 3.1262 1.1617 0.8 2.2108 0.4998 3.1925 1.2291 0.85 2.2948 0.5093 3.2952 1.2944 0.9 2.3991 0.5307 3.4414 1.3567 0.95 2.5164 0.5586 3.6137 1.4192
16 – API 579, Level 1, Hybrid 2 Analysis – Chell surface correction, rectangular area, BG Folias factor
1.0 2.6447 0.5884 3.8005 1.4890 0.7 2.0310 0.5020 3.0171 1.0450 0.75 2.0697 0.4765 3.0057 1.1337 0.8 2.1173 0.4548 3.0106 1.2241 0.85 2.1791 0.4415 3.0464 1.3118 0.9 2.2627 0.4442 3.1353 1.3901 0.95 2.3654 0.4605 3.2700 1.4609
17 – API 579, Level 2, Hybrid 2 Analysis – Chell surface correction, effective area, BG Folias factor
1.0 2.4842 0.4839 3.4348 1.5336 0.7 2.0415 0.5213 3.0655 1.0174 0.75 2.0853 0.5033 3.0738 1.0967 0.8 2.1398 0.4901 3.1025 1.1772 0.85 2.2071 0.4840 3.1578 1.2563 0.9 2.2862 0.4860 3.2408 1.3317 0.95 2.3751 0.4956 3.3486 1.4016
18 – API 579, Level 1, Hybrid 3 Analysis – Chell surface correction, rectangular area, JO Folias factor
1.0 2.4754 0.5122 3.4816 1.4693
206
Table 27 – MAWP Ratio vs. Allowable RSF for ASME B31.8, Class 3 (Continued)
Method Allowable RSF
Mean MAWP Ratio
MAWP Ratio
Standard Deviation
MAWP Ratio Upper 95% Prediction
Limit
MAWP Ratio Lower 95% Prediction
Limit 0.7 2.0008 0.5253 3.0326 0.9690 0.75 2.0272 0.4973 3.0041 1.0504 0.8 2.0633 0.4677 2.9819 1.1447 0.85 2.1112 0.4406 2.9767 1.2458 0.9 2.1738 0.4199 2.9986 1.3489 0.95 2.2517 0.4102 3.0574 1.4459
19 - API 579, Level 2, Hybrid 3 Analysis - Chell surface correction, effective area, JO Folias factor
1.0 2.3439 0.4119 3.1530 1.5348 0.7 2.2745 0.5151 3.2863 1.2627 0.75 2.3545 0.5354 3.4062 1.3029 0.8 2.4467 0.5631 3.5528 1.3407 0.85 2.5521 0.5963 3.7234 1.3807 0.9 2.6723 0.6323 3.9142 1.4304 0.95 2.8078 0.6685 4.1210 1.4947
20 - Battelle Method - B31.G surface correction, rectangular area, Battelle Folias factor
1.0 2.9541 0.7039 4.3367 1.5715 0.7 2.2871 0.5063 3.2817 1.2925 0.75 2.3700 0.5270 3.4051 1.3349 0.8 2.4627 0.5559 3.5547 1.3707 0.85 2.5656 0.5911 3.7268 1.4044 0.9 2.6827 0.6292 3.9186 1.4468 0.95 2.8119 0.6685 4.1250 1.4987
21 - BS 7910, Appendix G (Isolated Defect) - B31.G surface correction, rectangular area, BG Folias factor 1.0 2.9549 0.7051 4.3398 1.5699
0.7 2.2029 0.4560 3.0985 1.3072 0.75 2.2700 0.4560 3.1657 1.3743 0.8 2.3466 0.4655 3.2609 1.4323 0.85 2.4314 0.4841 3.3823 1.4804 0.9 2.5298 0.5094 3.5304 1.5292 0.95 2.6416 0.5396 3.7015 1.5818
22 - BS 7910, Appendix G (Grouped Defects) - B31.G surface correction, rectangular area, BG Folias factor 1.0 2.7708 0.5694 3.8893 1.6523
0.7 2.8223 1.0096 4.8055 0.8392 0.75 2.9622 1.1041 5.1310 0.7934 0.8 3.1101 1.1989 5.4651 0.7552 0.85 3.2703 1.2898 5.8037 0.7368 0.9 3.4401 1.3772 6.1453 0.7349 0.95 3.6205 1.4595 6.4873 0.7537
23 - Kanninen Equivalent Stress - B31.G surface correction, rectangular area, shell theory Folias factor 1.0 3.8093 1.5373 6.8290 0.7896
0.7 2.4727 0.5581 3.5691 1.3764 0.75 2.5650 0.6117 3.7666 1.3635 0.8 2.6653 0.6698 3.9809 1.3497 0.85 2.7782 0.7282 4.2086 1.3477 0.9 2.9044 0.7851 4.4465 1.3622 0.95 3.0438 0.8383 4.6904 1.3973
24 - Shell Theory Method - Chell surface correction, exact area, shell theory Folias factor
1.0 3.1996 0.8844 4.9367 1.4625
207
Table 27 – MAWP Ratio vs. Allowable RSF for ASME B31.8, Class 3 (Continued)
Method Allowable RSF
Mean MAWP Ratio
MAWP Ratio
Standard Deviation
MAWP Ratio Upper 95% Prediction
Limit
MAWP Ratio Lower 95% Prediction
Limit 0.7 3.1251 1.0413 5.1706 1.0797 0.75 3.2684 1.1699 5.5663 0.9704 0.8 3.4344 1.3412 6.0688 0.7999 0.85 3.6791 1.5155 6.6559 0.7024 0.9 3.9788 1.7437 7.4038 0.5537 0.95 4.3228 1.9426 8.1386 0.5070
25 – Thickness Averaging – API 579, Level 1
1.0 4.8195 2.1632 9.0687 0.5704 0.7 2.3870 0.6999 3.7618 1.0122 0.75 2.5766 0.8401 4.2268 0.9265 0.8 2.8291 1.0360 4.8641 0.7940 0.85 3.1502 1.2732 5.6512 0.6493 0.9 3.5811 1.5658 6.6568 0.5054 0.95 4.1045 1.8452 7.7290 0.4801
26 – Thickness Averaging – API 579, Level 2
1.0 4.8195 2.1632 9.0687 0.5704 0.7 2.4396 0.5721 3.5633 1.3159 0.75 2.5503 0.6130 3.7544 1.3461 0.8 2.6697 0.6601 3.9664 1.3730 0.85 2.7986 0.7102 4.1936 1.4036 0.9 2.9408 0.7596 4.4329 1.4486 0.95 3.0954 0.8055 4.6777 1.5131
27 – Modified API 579 Section 5, Level 1 Analysis – B31.G surface correction, rectangular area, Modified API Folias factor 1.0 3.2568 0.8486 4.9237 1.5899
0.7 2.2231 0.3627 2.9356 1.5107 0.75 2.2931 0.3493 2.9793 1.6070 0.8 2.3749 0.3461 3.0547 1.6951 0.85 2.4676 0.3547 3.1644 1.7708 0.9 2.5792 0.3736 3.3130 1.8454 0.95 2.7073 0.3961 3.4854 1.9293
28 – Modified API 579 Section 5, Level 2 Analysis – B31.G surface correction, effective area, Modified API Folias factor 1.0 2.8472 0.4172 3.6668 2.0277
0.7 2.2824 0.4899 3.2446 1.3201 0.75 2.3818 0.5040 3.3718 1.3917 0.8 2.4919 0.5277 3.5285 1.4553 0.85 2.6155 0.5582 3.7119 1.5191 0.9 2.7566 0.5904 3.9164 1.5968 0.95 2.9067 0.6236 4.1316 1.6818
29 – Janelle Method, Level 1 – rectangular area
1.0 3.0597 0.6564 4.3491 1.7702 0.7 2.1404 0.4005 2.9271 1.3538 0.75 2.2060 0.3730 2.9387 1.4733 0.8 2.2857 0.3546 2.9822 1.5891 0.85 2.3809 0.3505 3.0694 1.6925 0.9 2.5003 0.3604 3.2082 1.7925 0.95 2.6330 0.3781 3.3757 1.8903
30 – Janelle Method, Level 1 – effective area
1.0 2.7713 0.3980 3.5530 1.9896
208
Table 28 – MAWP Ratio vs. Allowable RSF for ASME B31.8, Class 4
Method Allowable RSF
Mean MAWP Ratio
MAWP Ratio
Standard Deviation
MAWP Ratio Upper 95% Prediction
Limit
MAWP Ratio Lower 95% Prediction
Limit 0.7 3.1124 0.7536 4.5926 1.6322 0.75 3.2584 0.8130 4.8553 1.6614 0.8 3.4149 0.8786 5.1407 1.6891 0.85 3.5833 0.9469 5.4434 1.7233 0.9 3.7685 1.0131 5.7584 1.7785 0.95 3.9682 1.0739 6.0777 1.8587
1 – API 579 Section 5, Level 1 Analysis – B31.G surface correction, rectangular area, API level 1 Folias factor 1.0 4.1753 1.1314 6.3976 1.9530
0.7 2.7765 0.4541 3.6683 1.8846 0.75 2.8637 0.4369 3.7218 2.0055 0.8 2.9655 0.4324 3.8147 2.1162 0.85 3.0807 0.4427 3.9502 2.2112 0.9 3.2201 0.4658 4.1350 2.3052 0.95 3.3802 0.4936 4.3498 2.4106
2 – API 579 Section 5, Level 2 Analysis – B31.G surface correction, effective area, API level 2 Folias factor 1.0 3.5549 0.5199 4.5761 2.5338
0.7 2.7251 0.4845 3.6767 1.7735 0.75 2.8059 0.4617 3.7127 1.8991 0.8 2.9018 0.4489 3.7835 2.0201 0.85 3.0117 0.4505 3.8967 2.1268 0.9 3.1452 0.4678 4.0641 2.2264 0.95 3.3010 0.4926 4.2686 2.3334
3 – API-579 Section 5, Level 2 Analysis – B31.G surface correction, exact area, API level 2 Folias factor 1.0 3.4716 0.5183 4.4896 2.4535
0.7 2.7331 0.6337 3.9779 1.4883 0.75 2.8212 0.6256 4.0501 1.5924 0.8 2.9275 0.6282 4.1613 1.6936 0.85 3.0466 0.6437 4.3110 1.7823 0.9 3.1842 0.6693 4.4988 1.8695 0.95 3.3401 0.7038 4.7226 1.9577
4 – Modified B31.G Method – B31.G surface correction, 0.85dl area, AGA Folias factor
1.0 3.5124 0.7403 4.9666 2.0582 0.7 2.8243 0.4737 3.7547 1.8938 0.75 2.9094 0.4541 3.8015 2.0174 0.8 3.0090 0.4459 3.8849 2.1331 0.85 3.1229 0.4530 4.0127 2.2331 0.9 3.2602 0.4738 4.1910 2.3295 0.95 3.4183 0.5020 4.4043 2.4323
5 – Modified B31.G Method (RSTRENG) – B31.G surface correction, effective area, AGA Folias factor 1.0 3.5938 0.5288 4.6325 2.5551
0.7 2.7760 0.5049 3.7678 1.7842 0.75 2.8553 0.4805 3.7991 1.9115 0.8 2.9496 0.4652 3.8634 2.0358 0.85 3.0584 0.4643 3.9705 2.1464 0.9 3.1905 0.4795 4.1323 2.2488 0.95 3.3446 0.5044 4.3354 2.3538
6 – Modified B31.G Method – B31.G surface correction, exact area, AGA Folias factor
1.0 3.5162 0.5307 4.5587 2.4737
209
Table 28 – MAWP Ratio vs. Allowable RSF for ASME B31.8, Class 4 (Continued)
Method Allowable RSF
Mean MAWP Ratio
MAWP Ratio
Standard Deviation
MAWP Ratio Upper 95% Prediction
Limit
MAWP Ratio Lower 95% Prediction
Limit 0.7 2.7790 0.7642 4.2801 1.2779 0.75 2.8602 0.7981 4.4279 1.2925 0.8 2.9536 0.8386 4.6008 1.3064 0.85 3.0736 0.8839 4.8097 1.3374 0.9 3.2077 0.9335 5.0414 1.3740 0.95 3.3598 0.9863 5.2971 1.4225
7 - Original B31.G Method - B31.G surface correction, parabolic area, B31-G Folias factor
1.0 3.5321 1.0385 5.5719 1.4923 0.7 3.8357 0.8831 5.5703 2.1011 0.75 3.8357 0.8831 5.5703 2.1011 0.8 3.8357 0.8831 5.5703 2.1011 0.85 3.8357 0.8831 5.5703 2.1011 0.9 3.8357 0.8831 5.5703 2.1011 0.95 3.8357 0.8831 5.5703 2.1011
8 - Thickness Averaging - API 510, 8th Edition
1.0 3.8357 0.8831 5.5703 2.1011 0.7 4.1607 1.0141 6.1526 2.1689 0.75 4.1607 1.0141 6.1526 2.1689 0.8 4.1607 1.0141 6.1526 2.1689 0.85 4.1607 1.0141 6.1526 2.1689 0.9 4.1607 1.0141 6.1526 2.1689 0.95 4.1607 1.0141 6.1526 2.1689
9 - Thickness Averaging - API 653, 2nd Edition
1.0 4.1607 1.0141 6.1526 2.1689 0.7 2.8589 0.6329 4.1021 1.6156 0.75 2.9625 0.6587 4.2563 1.6686 0.8 3.0784 0.6949 4.4434 1.7134 0.85 3.2070 0.7389 4.6585 1.7555 0.9 3.3533 0.7865 4.8982 1.8085 0.95 3.5148 0.8356 5.1563 1.8734
10 - British Gas Single Defect Method - B31.G surface correction, exact area, BG Folias factor
1.0 3.6936 0.8813 5.4248 1.9624 0.7 2.9086 0.4587 3.8096 2.0076 0.75 3.0093 0.4745 3.9414 2.0772 0.8 3.1210 0.5041 4.1113 2.1308 0.85 3.2496 0.5437 4.3176 2.1816 0.9 3.3976 0.5891 4.5547 2.2405 0.95 3.5616 0.6338 4.8066 2.3167
11 - British Gas Complex Defect Method - B31.G surface correction, exact area, BG Folias factor
1.0 3.7432 0.6702 5.0597 2.4267 0.7 2.6757 0.6163 3.8863 1.4651 0.75 2.7635 0.6128 3.9672 1.5599 0.8 2.8680 0.6211 4.0879 1.6481 0.85 2.9931 0.6422 4.2546 1.7315 0.9 3.1407 0.6754 4.4675 1.8140 0.95 3.2999 0.7147 4.7038 1.8959
12 - Chell Method - Chell surface correction, exact area, B31-G Folias factor
1.0 3.4721 0.7527 4.9506 1.9935
210
Table 28 – MAWP Ratio vs. Allowable RSF for ASME B31.8, Class 4 (Continued)
Method Allowable RSF
Mean MAWP Ratio
MAWP Ratio
Standard Deviation
MAWP Ratio Upper 95% Prediction
Limit
MAWP Ratio Lower 95% Prediction
Limit 0.7 2.5579 0.6045 3.7452 1.3705 0.75 2.6148 0.5691 3.7325 1.4970 0.8 2.6863 0.5400 3.7470 1.6256 0.85 2.7775 0.5234 3.8057 1.7494 0.9 2.8992 0.5303 3.9408 1.8575 0.95 3.0427 0.5534 4.1298 1.9556
13 – Osage Method – Chell surface correction, effective area, D/t dependent Folias factor
1.0 3.2023 0.5823 4.3460 2.0586 0.7 2.6743 0.6166 3.8855 1.4630 0.75 2.7617 0.6129 3.9656 1.5578 0.8 2.8657 0.6210 4.0856 1.6459 0.85 2.9904 0.6420 4.2515 1.7293 0.9 3.1378 0.6751 4.4638 1.8118 0.95 3.2967 0.7143 4.6997 1.8936
14 – API 579, Level 1, Hybrid 1 Analysis – Chell surface correction, rectangular area, API level 1 Folias factor 1.0 3.4686 0.7523 4.9463 1.9910
0.7 2.5456 0.6176 3.7588 1.3324 0.75 2.5973 0.5837 3.7438 1.4507 0.8 2.6619 0.5552 3.7525 1.5713 0.85 2.7463 0.5374 3.8018 1.6907 0.9 2.8590 0.5424 3.9245 1.7936 0.95 2.9939 0.5644 4.1025 1.8854
15 – API 579, Level 2, Hybrid 1 Analysis – Chell surface correction, effective area, API level 2 Folias factor 1.0 3.1480 0.5934 4.3137 1.9824
0.7 2.6105 0.6366 3.8609 1.3601 0.75 2.6800 0.6251 3.9078 1.4521 0.8 2.7635 0.6247 3.9906 1.5363 0.85 2.8685 0.6366 4.1190 1.6180 0.9 2.9988 0.6633 4.3018 1.6959 0.95 3.1456 0.6983 4.5171 1.7740
16 – API 579, Level 1, Hybrid 2 Analysis – Chell surface correction, rectangular area, BG Folias factor
1.0 3.3059 0.7355 4.7507 1.8612 0.7 2.5388 0.6275 3.7713 1.3063 0.75 2.5872 0.5956 3.7572 1.4172 0.8 2.6467 0.5684 3.7633 1.5301 0.85 2.7238 0.5519 3.8080 1.6397 0.9 2.8284 0.5553 3.9191 1.7377 0.95 2.9568 0.5756 4.0875 1.8261
17 – API 579, Level 2, Hybrid 2 Analysis – Chell surface correction, effective area, BG Folias factor
1.0 3.1052 0.6049 4.2934 1.9170 0.7 2.5519 0.6517 3.8319 1.2718 0.75 2.6066 0.6291 3.8422 1.3709 0.8 2.6748 0.6126 3.8781 1.4715 0.85 2.7588 0.6050 3.9472 1.5704 0.9 2.8578 0.6074 4.0510 1.6646 0.95 2.9688 0.6195 4.1857 1.7519
18 – API 579, Level 1, Hybrid 3 Analysis – Chell surface correction, rectangular area, JO Folias factor
1.0 3.0943 0.6403 4.3520 1.8366
211
Table 28 – MAWP Ratio vs. Allowable RSF for ASME B31.8, Class 4 (Continued)
Method Allowable RSF
Mean MAWP Ratio
MAWP Ratio
Standard Deviation
MAWP Ratio Upper 95% Prediction
Limit
MAWP Ratio Lower 95% Prediction
Limit 0.7 2.5010 0.6566 3.7907 1.2112 0.75 2.5340 0.6216 3.7551 1.3130 0.8 2.5791 0.5846 3.7274 1.4308 0.85 2.6390 0.5507 3.7208 1.5572 0.9 2.7172 0.5249 3.7483 1.6861 0.95 2.8146 0.5128 3.8218 1.8074
19 - API 579, Level 2, Hybrid 3 Analysis - Chell surface correction, effective area, JO Folias factor
1.0 2.9299 0.5149 3.9412 1.9185 0.7 2.8431 0.6439 4.1079 1.5783 0.75 2.9431 0.6692 4.2577 1.6286 0.8 3.0584 0.7039 4.4410 1.6759 0.85 3.1901 0.7454 4.6543 1.7259 0.9 3.3403 0.7903 4.8927 1.7879 0.95 3.5098 0.8356 5.1512 1.8684
20 - Battelle Method - B31.G surface correction, rectangular area, Battelle Folias factor
1.0 3.6926 0.8799 5.4209 1.9643 0.7 2.8589 0.6329 4.1021 1.6156 0.75 2.9625 0.6587 4.2563 1.6686 0.8 3.0784 0.6949 4.4434 1.7134 0.85 3.2070 0.7389 4.6585 1.7555 0.9 3.3533 0.7865 4.8982 1.8085 0.95 3.5148 0.8356 5.1563 1.8734
21 - BS 7910, Appendix G (Isolated Defect) - B31.G surface correction, rectangular area, BG Folias factor 1.0 3.6936 0.8813 5.4248 1.9624
0.7 2.7536 0.5700 3.8732 1.6341 0.75 2.8375 0.5700 3.9571 1.7179 0.8 2.9332 0.5818 4.0761 1.7903 0.85 3.0392 0.6051 4.2278 1.8506 0.9 3.1623 0.6368 4.4130 1.9115 0.95 3.3020 0.6745 4.6268 1.9772
22 - BS 7910, Appendix G (Grouped Defects) - B31.G surface correction, rectangular area, BG Folias factor 1.0 3.4635 0.7118 4.8616 2.0654
0.7 3.5279 1.2621 6.0069 1.0489 0.75 3.7028 1.3802 6.4138 0.9918 0.8 3.8877 1.4986 6.8313 0.9440 0.85 4.0879 1.6122 7.2547 0.9211 0.9 4.3001 1.7215 7.6816 0.9187 0.95 4.5257 1.8244 8.1092 0.9421
23 - Kanninen Equivalent Stress - B31.G surface correction, rectangular area, shell theory Folias factor 1.0 4.7616 1.9217 8.5362 0.9870
0.7 3.0909 0.6977 4.4613 1.7205 0.75 3.2063 0.7646 4.7082 1.7044 0.8 3.3316 0.8372 4.9761 1.6871 0.85 3.4727 0.9103 5.2608 1.6846 0.9 3.6305 0.9814 5.5581 1.7028 0.95 3.8048 1.0478 5.8630 1.7466
24 - Shell Theory Method - Chell surface correction, exact area, shell theory Folias factor
1.0 3.9995 1.1055 6.1709 1.8281
212
Table 28 – MAWP Ratio vs. Allowable RSF for ASME B31.8, Class 4 (Continued)
Method Allowable RSF
Mean MAWP Ratio
MAWP Ratio
Standard Deviation
MAWP Ratio Upper 95% Prediction
Limit
MAWP Ratio Lower 95% Prediction
Limit 0.7 3.9064 1.3017 6.4632 1.3496 0.75 4.0855 1.4624 6.9579 1.2130 0.8 4.2929 1.6765 7.5860 0.9999 0.85 4.5989 1.8943 8.3199 0.8780 0.9 4.9734 2.1796 9.2547 0.6922 0.95 5.4035 2.4283 10.1733 0.6338
25 – Thickness Averaging – API 579, Level 1
1.0 6.0244 2.7040 11.3358 0.7130 0.7 2.9837 0.8749 4.7023 1.2652 0.75 3.2208 1.0501 5.2835 1.1582 0.8 3.5363 1.2951 6.0802 0.9925 0.85 3.9378 1.5915 7.0640 0.8116 0.9 4.4764 1.9573 8.3210 0.6318 0.95 5.1307 2.3065 9.6612 0.6001
26 – Thickness Averaging – API 579, Level 2
1.0 6.0244 2.7040 11.3358 0.7130 0.7 3.0495 0.7151 4.4541 1.6448 0.75 3.1878 0.7663 4.6930 1.6826 0.8 3.3371 0.8252 4.9579 1.7162 0.85 3.4982 0.8877 5.2420 1.7545 0.9 3.6760 0.9496 5.5412 1.8108 0.95 3.8692 1.0069 5.8471 1.8914
27 – Modified API 579 Section 5, Level 1 Analysis – B31.G surface correction, rectangular area, Modified API Folias factor 1.0 4.0710 1.0608 6.1547 1.9874
0.7 2.7789 0.4534 3.6695 1.8884 0.75 2.8664 0.4367 3.7242 2.0087 0.8 2.9687 0.4326 3.8184 2.1189 0.85 3.0845 0.4434 3.9555 2.2135 0.9 3.2240 0.4670 4.1412 2.3068 0.95 3.3842 0.4951 4.3567 2.4116
28 – Modified API 579 Section 5, Level 2 Analysis – B31.G surface correction, effective area, Modified API Folias factor 1.0 3.5591 0.5215 4.5835 2.5347
0.7 2.8530 0.6124 4.0558 1.6502 0.75 2.9772 0.6300 4.2147 1.7396 0.8 3.1149 0.6596 4.4106 1.8192 0.85 3.2694 0.6977 4.6399 1.8989 0.9 3.4458 0.7380 4.8955 1.9961 0.95 3.6334 0.7795 5.1645 2.1022
29 – Janelle Method, Level 1 – rectangular area
1.0 3.8246 0.8205 5.4363 2.2128 0.7 2.6755 0.5006 3.6589 1.6922 0.75 2.7575 0.4663 3.6734 1.8416 0.8 2.8571 0.4433 3.7277 1.9864 0.85 2.9762 0.4381 3.8368 2.1156 0.9 3.1254 0.4505 4.0103 2.2406 0.95 3.2912 0.4726 4.2196 2.3628
30 – Janelle Method, Level 1 – effective area
1.0 3.4641 0.4974 4.4412 2.4870
213
Table 29 – MAWP Ratio vs. Allowable RSF for API 620
Method Allowable RSF
Mean MAWP Ratio
MAWP Ratio
Standard Deviation
MAWP Ratio Upper 95% Prediction
Limit
MAWP Ratio Lower 95% Prediction
Limit 0.7 3.2048 0.7316 4.6419 1.7678 0.75 3.3550 0.7891 4.9050 1.8051 0.8 3.5161 0.8536 5.1928 1.8395 0.85 3.6895 0.9215 5.4996 1.8795 0.9 3.8802 0.9872 5.8193 1.9412 0.95 4.0858 1.0469 6.1422 2.0295
1 – API 579 Section 5, Level 1 Analysis – B31.G surface correction, rectangular area, API level 1 Folias factor 1.0 4.2991 1.1030 6.4657 2.1325
0.7 2.8654 0.4758 3.8000 1.9307 0.75 2.9561 0.4629 3.8653 2.0469 0.8 3.0619 0.4632 3.9718 2.1520 0.85 3.1816 0.4787 4.1220 2.2412 0.9 3.3260 0.5057 4.3194 2.3326 0.95 3.4915 0.5358 4.5438 2.4391
2 – API 579 Section 5, Level 2 Analysis – B31.G surface correction, effective area, API level 2 Folias factor 1.0 3.6719 0.5643 4.7804 2.5635
0.7 2.8113 0.5020 3.7974 1.8252 0.75 2.8954 0.4822 3.8425 1.9483 0.8 2.9952 0.4735 3.9252 2.0651 0.85 3.1093 0.4800 4.0522 2.1665 0.9 3.2477 0.5009 4.2316 2.2637 0.95 3.4086 0.5277 4.4452 2.3720
3 – API-579 Section 5, Level 2 Analysis – B31.G surface correction, exact area, API level 2 Folias factor 1.0 3.5847 0.5553 4.6756 2.4939
0.7 2.8157 0.6332 4.0594 1.5720 0.75 2.9065 0.6201 4.1245 1.6884 0.8 3.0159 0.6182 4.2301 1.8016 0.85 3.1387 0.6305 4.3771 1.9002 0.9 3.2805 0.6544 4.5660 1.9950 0.95 3.4412 0.6880 4.7925 2.0899
4 – Modified B31.G Method – B31.G surface correction, 0.85dl area, AGA Folias factor
1.0 3.6187 0.7237 5.0402 2.1972 0.7 2.9149 0.4975 3.8922 1.9376 0.75 3.0036 0.4821 3.9506 2.0566 0.8 3.1071 0.4787 4.0473 2.1669 0.85 3.2254 0.4908 4.1895 2.2614 0.9 3.3677 0.5157 4.3807 2.3548 0.95 3.5312 0.5464 4.6045 2.4578
5 – Modified B31.G Method (RSTRENG) – B31.G surface correction, effective area, AGA Folias factor 1.0 3.7125 0.5757 4.8432 2.5818
0.7 2.8641 0.5250 3.8953 1.8329 0.75 2.9467 0.5035 3.9358 1.9576 0.8 3.0448 0.4922 4.0116 2.0780 0.85 3.1579 0.4960 4.1321 2.1837 0.9 3.2948 0.5148 4.3060 2.2836 0.95 3.4540 0.5423 4.5192 2.3889
6 – Modified B31.G Method – B31.G surface correction, exact area, AGA Folias factor
1.0 3.6313 0.5706 4.7521 2.5105
214
Table 29 – MAWP Ratio vs. Allowable RSF for API 620 (Continued)
Method Allowable RSF
Mean MAWP Ratio
MAWP Ratio
Standard Deviation
MAWP Ratio Upper 95% Prediction
Limit
MAWP Ratio Lower 95% Prediction
Limit 0.7 2.8641 0.7653 4.3673 1.3609 0.75 2.9477 0.7968 4.5129 1.3825 0.8 3.0441 0.8357 4.6857 1.4025 0.85 3.1678 0.8802 4.8967 1.4390 0.9 3.3063 0.9297 5.1325 1.4801 0.95 3.4632 0.9824 5.3930 1.5334
7 - Original B31.G Method - B31.G surface correction, parabolic area, B31-G Folias factor
1.0 3.6407 1.0345 5.6728 1.6087 0.7 3.9665 0.9469 5.8264 2.1065 0.75 3.9665 0.9469 5.8264 2.1065 0.8 3.9665 0.9469 5.8264 2.1065 0.85 3.9665 0.9469 5.8264 2.1065 0.9 3.9665 0.9469 5.8264 2.1065 0.95 3.9665 0.9469 5.8264 2.1065
8 - Thickness Averaging - API 510, 8th Edition
1.0 3.9665 0.9469 5.8264 2.1065 0.7 4.2986 1.0714 6.4032 2.1941 0.75 4.2986 1.0714 6.4032 2.1941 0.8 4.2986 1.0714 6.4032 2.1941 0.85 4.2986 1.0714 6.4032 2.1941 0.9 4.2986 1.0714 6.4032 2.1941 0.95 4.2986 1.0714 6.4032 2.1941
9 - Thickness Averaging - API 653, 2nd Edition
1.0 4.2986 1.0714 6.4032 2.1941 0.7 2.9445 0.6128 4.1481 1.7409 0.75 3.0513 0.6343 4.2972 1.8054 0.8 3.1707 0.6669 4.4807 1.8606 0.85 3.3032 0.7087 4.6953 1.9110 0.9 3.4541 0.7551 4.9372 1.9709 0.95 3.6204 0.8030 5.1978 2.0430
10 - British Gas Single Defect Method - B31.G surface correction, exact area, BG Folias factor
1.0 3.8046 0.8472 5.4688 2.1404 0.7 3.0032 0.4884 3.9626 2.0438 0.75 3.1081 0.5102 4.1103 2.1059 0.8 3.2243 0.5452 4.2952 2.1535 0.85 3.3579 0.5899 4.5166 2.1993 0.9 3.5115 0.6394 4.7675 2.2555 0.95 3.6813 0.6873 5.0314 2.3312
11 - British Gas Complex Defect Method - B31.G surface correction, exact area, BG Folias factor
1.0 3.8691 0.7266 5.2964 2.4417 0.7 2.7572 0.6156 3.9663 1.5480 0.75 2.8478 0.6080 4.0422 1.6534 0.8 2.9557 0.6135 4.1608 1.7506 0.85 3.0850 0.6340 4.3303 1.8397 0.9 3.2376 0.6672 4.5481 1.9271 0.95 3.4019 0.7073 4.7911 2.0126
12 - Chell Method - Chell surface correction, exact area, B31-G Folias factor
1.0 3.5794 0.7450 5.0428 2.1160
215
Table 29 – MAWP Ratio vs. Allowable RSF for API 620 (Continued)
Method Allowable RSF
Mean MAWP Ratio
MAWP Ratio
Standard Deviation
MAWP Ratio Upper 95% Prediction
Limit
MAWP Ratio Lower 95% Prediction
Limit 0.7 2.6377 0.6210 3.8574 1.4179 0.75 2.6971 0.5868 3.8497 1.5445 0.8 2.7716 0.5596 3.8708 1.6724 0.85 2.8664 0.5453 3.9375 1.7954 0.9 2.9925 0.5548 4.0822 1.9028 0.95 3.1409 0.5803 4.2808 2.0010
13 – Osage Method – Chell surface correction, effective area, D/t dependent Folias factor
1.0 3.3056 0.6106 4.5050 2.1062 0.7 2.7557 0.6160 3.9658 1.5456 0.75 2.8459 0.6083 4.0408 1.6510 0.8 2.9534 0.6136 4.1587 1.7480 0.85 3.0823 0.6339 4.3274 1.8372 0.9 3.2346 0.6670 4.5446 1.9245 0.95 3.3986 0.7070 4.7872 2.0099
14 – API 579, Level 1, Hybrid 1 Analysis – Chell surface correction, rectangular area, API level 1 Folias factor 1.0 3.5759 0.7447 5.0387 2.1130
0.7 2.6249 0.6345 3.8711 1.3787 0.75 2.6790 0.6016 3.8607 1.4972 0.8 2.7464 0.5753 3.8765 1.6164 0.85 2.8342 0.5599 3.9340 1.7344 0.9 2.9511 0.5677 4.0663 1.8360 0.95 3.0909 0.5928 4.2554 1.9264
15 – API 579, Level 2, Hybrid 1 Analysis – Chell surface correction, effective area, API level 2 Folias factor 1.0 3.2501 0.6238 4.4753 2.0248
0.7 2.6903 0.6426 3.9525 1.4282 0.75 2.7620 0.6275 3.9946 1.5295 0.8 2.8483 0.6241 4.0741 1.6224 0.85 2.9569 0.6349 4.2039 1.7098 0.9 3.0916 0.6617 4.3913 1.7920 0.95 3.2433 0.6975 4.6133 1.8732
16 – API 579, Level 1, Hybrid 2 Analysis – Chell surface correction, rectangular area, BG Folias factor
1.0 3.4087 0.7353 4.8530 1.9645 0.7 2.6178 0.6445 3.8837 1.3519 0.75 2.6684 0.6136 3.8737 1.4632 0.8 2.7307 0.5885 3.8867 1.5746 0.85 2.8110 0.5744 3.9393 1.6827 0.9 2.9195 0.5803 4.0593 1.7796 0.95 3.0526 0.6037 4.2384 1.8667
17 – API 579, Level 2, Hybrid 2 Analysis – Chell surface correction, effective area, BG Folias factor
1.0 3.2060 0.6354 4.4540 1.9580 0.7 2.6293 0.6602 3.9261 1.3326 0.75 2.6856 0.6336 3.9302 1.4411 0.8 2.7559 0.6129 3.9599 1.5520 0.85 2.8423 0.6009 4.0226 1.6620 0.9 2.9442 0.5996 4.1219 1.7664 0.95 3.0585 0.6091 4.2550 1.8620
18 – API 579, Level 1, Hybrid 3 Analysis – Chell surface correction, rectangular area, JO Folias factor
1.0 3.1877 0.6283 4.4218 1.9536
216
Table 29 – MAWP Ratio vs. Allowable RSF for API 620 (Continued)
Method Allowable RSF
Mean MAWP Ratio
MAWP Ratio
Standard Deviation
MAWP Ratio Upper 95% Prediction
Limit
MAWP Ratio Lower 95% Prediction
Limit 0.7 2.5780 0.6729 3.8997 1.2562 0.75 2.6125 0.6377 3.8651 1.3600 0.8 2.6596 0.6010 3.8402 1.4791 0.85 2.7219 0.5675 3.8366 1.6072 0.9 2.8028 0.5417 3.8669 1.7387 0.95 2.9033 0.5297 3.9439 1.8628
19 - API 579, Level 2, Hybrid 3 Analysis - Chell surface correction, effective area, JO Folias factor
1.0 3.0223 0.5321 4.0674 1.9772 0.7 2.9288 0.6283 4.1630 1.6947 0.75 3.0320 0.6498 4.3082 1.7557 0.8 3.1506 0.6809 4.4882 1.8131 0.85 3.2863 0.7205 4.7016 1.8710 0.9 3.4411 0.7641 4.9420 1.9403 0.95 3.6156 0.8078 5.2024 2.0289
20 - Battelle Method - B31.G surface correction, rectangular area, Battelle Folias factor
1.0 3.8040 0.8506 5.4748 2.1332 0.7 2.9445 0.6128 4.1481 1.7409 0.75 3.0513 0.6343 4.2972 1.8054 0.8 3.1707 0.6669 4.4807 1.8606 0.85 3.3032 0.7087 4.6953 1.9110 0.9 3.4541 0.7551 4.9372 1.9709 0.95 3.6204 0.8030 5.1978 2.0430
21 - BS 7910, Appendix G (Isolated Defect) - B31.G surface correction, rectangular area, BG Folias factor 1.0 3.8046 0.8472 5.4688 2.1404
0.7 2.8352 0.5543 3.9240 1.7464 0.75 2.9214 0.5473 3.9965 1.8464 0.8 3.0197 0.5525 4.1050 1.9345 0.85 3.1286 0.5703 4.2489 2.0083 0.9 3.2552 0.5981 4.4299 2.0804 0.95 3.3989 0.6328 4.6419 2.1558
22 - BS 7910, Appendix G (Grouped Defects) - B31.G surface correction, rectangular area, BG Folias factor 1.0 3.5650 0.6678 4.8767 2.2533
0.7 3.6225 1.2252 6.0292 1.2158 0.75 3.8012 1.3414 6.4360 1.1663 0.8 3.9902 1.4581 6.8543 1.1262 0.85 4.1952 1.5701 7.2793 1.1112 0.9 4.4127 1.6775 7.7077 1.1176 0.95 4.6439 1.7782 8.1368 1.1510
23 - Kanninen Equivalent Stress - B31.G surface correction, rectangular area, shell theory Folias factor 1.0 4.8860 1.8732 8.5654 1.2066
0.7 3.1867 0.7110 4.5832 1.7902 0.75 3.3054 0.7781 4.8338 1.7770 0.8 3.4344 0.8516 5.1072 1.7617 0.85 3.5799 0.9259 5.3985 1.7613 0.9 3.7423 0.9975 5.7017 1.7829 0.95 3.9218 1.0646 6.0129 1.8306
24 - Shell Theory Method - Chell surface correction, exact area, shell theory Folias factor
1.0 4.1223 1.1231 6.3284 1.9163
217
Table 29 – MAWP Ratio vs. Allowable RSF for API 620 (Continued)
Method Allowable RSF
Mean MAWP Ratio
MAWP Ratio
Standard Deviation
MAWP Ratio Upper 95% Prediction
Limit
MAWP Ratio Lower 95% Prediction
Limit 0.7 4.0210 1.3186 6.6111 1.4309 0.75 4.2047 1.4881 7.1277 1.2817 0.8 4.4179 1.7164 7.7894 1.0464 0.85 4.7320 1.9457 8.5538 0.9102 0.9 5.1151 2.2351 9.5053 0.7249 0.95 5.5568 2.4859 10.4396 0.6739
25 – Thickness Averaging – API 579, Level 1
1.0 6.1888 2.7354 11.5619 0.8157 0.7 3.0732 0.8900 4.8214 1.3251 0.75 3.3161 1.0699 5.4178 1.2145 0.8 3.6400 1.3263 6.2453 1.0348 0.85 4.0521 1.6349 7.2635 0.8407 0.9 4.6040 2.0071 8.5464 0.6615 0.95 5.2761 2.3611 9.9140 0.6382
26 – Thickness Averaging – API 579, Level 2
1.0 6.1888 2.7354 11.5619 0.8157 0.7 3.1404 0.6949 4.5053 1.7755 0.75 3.2828 0.7436 4.7434 1.8222 0.8 3.4364 0.8010 5.0097 1.8630 0.85 3.6023 0.8630 5.2974 1.9072 0.9 3.7854 0.9244 5.6011 1.9698 0.95 3.9844 0.9806 5.9104 2.0583
27 – Modified API 579 Section 5, Level 1 Analysis – B31.G surface correction, rectangular area, Modified API Folias factor 1.0 4.1922 1.0332 6.2216 2.1628
0.7 2.8680 0.4754 3.8019 1.9341 0.75 2.9590 0.4630 3.8686 2.0495 0.8 3.0653 0.4639 3.9765 2.1540 0.85 3.1856 0.4800 4.1284 2.2428 0.9 3.3301 0.5075 4.3269 2.3333 0.95 3.4956 0.5379 4.5522 2.4390
28 – Modified API 579 Section 5, Level 2 Analysis – B31.G surface correction, effective area, Modified API Folias factor 1.0 3.6763 0.5666 4.7893 2.5633
0.7 2.9394 0.5998 4.1176 1.7612 0.75 3.0673 0.6132 4.2718 1.8627 0.8 3.2091 0.6401 4.4664 1.9517 0.85 3.3684 0.6771 4.6983 2.0384 0.9 3.5499 0.7156 4.9556 2.1443 0.95 3.7432 0.7558 5.2277 2.2586
29 – Janelle Method, Level 1 – rectangular area
1.0 3.9402 0.7956 5.5029 2.3774 0.7 2.7605 0.5194 3.7807 1.7403 0.75 2.8458 0.4878 3.8040 1.8876 0.8 2.9493 0.4687 3.8699 2.0286 0.85 3.0727 0.4676 3.9912 2.1542 0.9 3.2269 0.4820 4.1736 2.2801 0.95 3.3979 0.5053 4.3905 2.4054
30 – Janelle Method, Level 1 – effective area
1.0 3.5765 0.5319 4.6212 2.5317
218
Table 30 – MAWP Ratio vs. Allowable RSF for API 650
Method Allowable RSF
Mean MAWP Ratio
MAWP Ratio
Standard Deviation
MAWP Ratio Upper 95% Prediction
Limit
MAWP Ratio Lower 95% Prediction
Limit 0.7 2.4111 0.5474 3.4864 1.3358 0.75 2.5240 0.5903 3.6835 1.3646 0.8 2.6451 0.6384 3.8992 1.3911 0.85 2.7755 0.6892 4.1293 1.4218 0.9 2.9190 0.7384 4.3693 1.4686 0.95 3.0736 0.7830 4.6117 1.5355
1 – API 579 Section 5, Level 1 Analysis – B31.G surface correction, rectangular area, API level 1 Folias factor 1.0 3.2341 0.8250 4.8546 1.6135
0.7 2.1560 0.3564 2.8561 1.4558 0.75 2.2242 0.3464 2.9046 1.5439 0.8 2.3038 0.3462 2.9837 1.6238 0.85 2.3938 0.3574 3.0958 1.6918 0.9 2.5024 0.3775 3.2439 1.7610 0.95 2.6269 0.3999 3.4123 1.8415
2 – API 579 Section 5, Level 2 Analysis – B31.G surface correction, effective area, API level 2 Folias factor 1.0 2.7627 0.4211 3.5899 1.9355
0.7 2.1153 0.3764 2.8546 1.3760 0.75 2.1786 0.3612 2.8880 1.4692 0.8 2.2536 0.3542 2.9494 1.5578 0.85 2.3395 0.3587 3.0440 1.6350 0.9 2.4435 0.3742 3.1785 1.7085 0.95 2.5646 0.3942 3.3388 1.7904
3 – API-579 Section 5, Level 2 Analysis – B31.G surface correction, exact area, API level 2 Folias factor 1.0 2.6971 0.4147 3.5118 1.8825
0.7 2.1184 0.4747 3.0507 1.1860 0.75 2.1866 0.4644 3.0989 1.2744 0.8 2.2689 0.4624 3.1773 1.3605 0.85 2.3612 0.4712 3.2867 1.4357 0.9 2.4678 0.4887 3.4277 1.5079 0.95 2.5887 0.5136 3.5976 1.5799
4 – Modified B31.G Method – B31.G surface correction, 0.85dl area, AGA Folias factor
1.0 2.7222 0.5402 3.7833 1.6611 0.7 2.1932 0.3726 2.9252 1.4612 0.75 2.2599 0.3607 2.9685 1.5514 0.8 2.3378 0.3577 3.0404 1.6352 0.85 2.4268 0.3664 3.1464 1.7071 0.9 2.5338 0.3848 3.2897 1.7779 0.95 2.6568 0.4078 3.4578 1.8558
5 – Modified B31.G Method (RSTRENG) – B31.G surface correction, effective area, AGA Folias factor 1.0 2.7932 0.4296 3.6369 1.9494
0.7 2.1550 0.3936 2.9281 1.3820 0.75 2.2172 0.3771 2.9580 1.4764 0.8 2.2909 0.3682 3.0142 1.5677 0.85 2.3760 0.3706 3.1039 1.6480 0.9 2.4790 0.3845 3.2342 1.7237 0.95 2.5988 0.4050 3.3942 1.8033
6 – Modified B31.G Method – B31.G surface correction, exact area, AGA Folias factor
1.0 2.7321 0.4261 3.5691 1.8952
219
Table 30 – MAWP Ratio vs. Allowable RSF for API 650 (Continued)
Method Allowable RSF
Mean MAWP Ratio
MAWP Ratio
Standard Deviation
MAWP Ratio Upper 95% Prediction
Limit
MAWP Ratio Lower 95% Prediction
Limit 0.7 2.1548 0.5742 3.2826 1.0269 0.75 2.2177 0.5977 3.3918 1.0436 0.8 2.2901 0.6267 3.5212 1.0591 0.85 2.3832 0.6599 3.6795 1.0870 0.9 2.4873 0.6969 3.8562 1.1184 0.95 2.6053 0.7364 4.0518 1.1589
7 - Original B31.G Method - B31.G surface correction, parabolic area, B31-G Folias factor
1.0 2.7389 0.7754 4.2619 1.2158 0.7 2.9841 0.7088 4.3763 1.5919 0.75 2.9841 0.7088 4.3763 1.5919 0.8 2.9841 0.7088 4.3763 1.5919 0.85 2.9841 0.7088 4.3763 1.5919 0.9 2.9841 0.7088 4.3763 1.5919 0.95 2.9841 0.7088 4.3763 1.5919
8 - Thickness Averaging - API 510, 8th Edition
1.0 2.9841 0.7088 4.3763 1.5919 0.7 3.2343 0.8041 4.8137 1.6549 0.75 3.2343 0.8041 4.8137 1.6549 0.8 3.2343 0.8041 4.8137 1.6549 0.85 3.2343 0.8041 4.8137 1.6549 0.9 3.2343 0.8041 4.8137 1.6549 0.95 3.2343 0.8041 4.8137 1.6549
9 - Thickness Averaging - API 653, 2nd Edition
1.0 3.2343 0.8041 4.8137 1.6549 0.7 2.2153 0.4586 3.1162 1.3144 0.75 2.2956 0.4744 3.2275 1.3637 0.8 2.3854 0.4986 3.3648 1.4060 0.85 2.4850 0.5296 3.5253 1.4446 0.9 2.5984 0.5641 3.7066 1.4903 0.95 2.7236 0.6000 3.9021 1.5450
10 - British Gas Single Defect Method - B31.G surface correction, exact area, BG Folias factor
1.0 2.8621 0.6330 4.1055 1.6187 0.7 2.2597 0.3658 2.9783 1.5411 0.75 2.3386 0.3820 3.0890 1.5883 0.8 2.4260 0.4080 3.2275 1.6245 0.85 2.5265 0.4415 3.3937 1.6594 0.9 2.6421 0.4787 3.5823 1.7018 0.95 2.7699 0.5146 3.7807 1.7590
11 - British Gas Complex Defect Method - B31.G surface correction, exact area, BG Folias factor
1.0 2.9111 0.5440 3.9797 1.8424 0.7 2.0743 0.4615 2.9807 1.1679 0.75 2.1424 0.4553 3.0368 1.2480 0.8 2.2235 0.4589 3.1250 1.3221 0.85 2.3208 0.4738 3.2515 1.3900 0.9 2.4355 0.4985 3.4147 1.4563 0.95 2.5591 0.5284 3.5969 1.5212
12 - Chell Method - Chell surface correction, exact area, B31-G Folias factor
1.0 2.6926 0.5566 3.7859 1.5994
220
Table 30 – MAWP Ratio vs. Allowable RSF for API 650 (Continued)
Method Allowable RSF
Mean MAWP Ratio
MAWP Ratio
Standard Deviation
MAWP Ratio Upper 95% Prediction
Limit
MAWP Ratio Lower 95% Prediction
Limit 0.7 1.9845 0.4661 2.9001 1.0688 0.75 2.0292 0.4401 2.8937 1.1646 0.8 2.0852 0.4193 2.9088 1.2616 0.85 2.1565 0.4081 2.9581 1.3549 0.9 2.2513 0.4150 3.0665 1.4361 0.95 2.3630 0.4340 3.2154 1.5105
13 - Osage Method - Chell surface correction, effective area, D/t dependent Folias factor
1.0 2.4869 0.4566 3.3838 1.5899 0.7 2.0732 0.4618 2.9803 1.1660 0.75 2.1410 0.4556 3.0358 1.2462 0.8 2.2218 0.4590 3.1234 1.3201 0.85 2.3187 0.4738 3.2493 1.3881 0.9 2.4332 0.4983 3.4121 1.4544 0.95 2.5566 0.5282 3.5940 1.5191
14 - API 579, Level 1, Hybrid 1 Analysis - Chell surface correction, rectangular area, API level 1 Folias factor 1.0 2.6900 0.5564 3.7828 1.5971
0.7 1.9749 0.4763 2.9105 1.0392 0.75 2.0155 0.4514 2.9022 1.1288 0.8 2.0663 0.4313 2.9134 1.2191 0.85 2.1322 0.4193 2.9558 1.3087 0.9 2.2202 0.4249 3.0549 1.3855 0.95 2.3254 0.4436 3.1968 1.4539
15 - API 579, Level 2, Hybrid 1 Analysis - Chell surface correction, effective area, API level 2 Folias factor 1.0 2.4451 0.4668 3.3619 1.5282
0.7 2.0240 0.4821 2.9710 1.0771 0.75 2.0779 0.4704 3.0019 1.1539 0.8 2.1427 0.4674 3.0608 1.2246 0.85 2.2244 0.4750 3.1575 1.2913 0.9 2.3258 0.4949 3.2979 1.3536 0.95 2.4398 0.5216 3.4644 1.4152
16 - API 579, Level 1, Hybrid 2 Analysis - Chell surface correction, rectangular area, BG Folias factor
1.0 2.5643 0.5498 3.6443 1.4842 0.7 1.9695 0.4839 2.9200 1.0190 0.75 2.0076 0.4605 2.9121 1.1031 0.8 2.0544 0.4413 2.9212 1.1875 0.85 2.1148 0.4303 2.9600 1.2695 0.9 2.1964 0.4346 3.0500 1.3428 0.95 2.2965 0.4520 3.1844 1.4086
17 - API 579, Level 2, Hybrid 2 Analysis - Chell surface correction, effective area, BG Folias factor
1.0 2.4119 0.4756 3.3462 1.4776 0.7 1.9782 0.4956 2.9517 1.0046 0.75 2.0205 0.4754 2.9543 1.0868 0.8 2.0734 0.4595 2.9760 1.1708 0.85 2.1383 0.4501 3.0223 1.2543 0.9 2.2149 0.4486 3.0960 1.3338 0.95 2.3008 0.4552 3.1950 1.4066
18 - API 579, Level 1, Hybrid 3 Analysis - Chell surface correction, rectangular area, JO Folias factor
1.0 2.3980 0.4692 3.3196 1.4764
221
Table 30 – MAWP Ratio vs. Allowable RSF for API 650 (Continued)
Method Allowable RSF
Mean MAWP Ratio
MAWP Ratio
Standard Deviation
MAWP Ratio Upper 95% Prediction
Limit
MAWP Ratio Lower 95% Prediction
Limit 0.7 1.9396 0.5055 2.9324 0.9467 0.75 1.9656 0.4788 2.9061 1.0250 0.8 2.0010 0.4511 2.8870 1.1150 0.85 2.0478 0.4256 2.8837 1.2119 0.9 2.1087 0.4058 2.9057 1.3116 0.95 2.1843 0.3962 2.9626 1.4060
19 - API 579, Level 2, Hybrid 3 Analysis - Chell surface correction, effective area, JO Folias factor
1.0 2.2737 0.3975 3.0544 1.4930 0.7 2.2035 0.4704 3.1275 1.2796 0.75 2.2810 0.4861 3.2360 1.3261 0.8 2.3703 0.5092 3.3705 1.3701 0.85 2.4723 0.5385 3.5301 1.4145 0.9 2.5887 0.5710 3.7102 1.4672 0.95 2.7200 0.6036 3.9056 1.5344
20 - Battelle Method - B31.G surface correction, rectangular area, Battelle Folias factor
1.0 2.8617 0.6355 4.1100 1.6133 0.7 2.2153 0.4586 3.1162 1.3144 0.75 2.2956 0.4744 3.2275 1.3637 0.8 2.3854 0.4986 3.3648 1.4060 0.85 2.485 0.5296 3.5253 1.4446 0.9 2.5984 0.5641 3.7066 1.4903 0.95 2.7236 0.6000 3.9021 1.5450
21 - BS 7910, Appendix G (Isolated Defect) - B31.G surface correction, rectangular area, BG Folias factor 1.0 2.8621 0.6330 4.1055 1.6187
0.7 2.1332 0.4155 2.9495 1.3170 0.75 2.1981 0.4100 3.0035 1.3927 0.8 2.2721 0.4136 3.0845 1.4596 0.85 2.3539 0.4267 3.1921 1.5158 0.9 2.4491 0.4473 3.3278 1.5704 0.95 2.5572 0.4734 3.4871 1.6274
22 - BS 7910, Appendix G (Grouped Defects) - B31.G surface correction, rectangular area, BG Folias factor 1.0 2.6823 0.4995 3.6635 1.7010
0.7 2.7253 0.9187 4.5298 0.9207 0.75 2.8596 1.0058 4.8353 0.8839 0.8 3.0018 1.0934 5.1494 0.8541 0.85 3.1559 1.1774 5.4686 0.8432 0.9 3.3194 1.2580 5.7904 0.8484 0.95 3.4933 1.3335 6.1128 0.8739
23 - Kanninen Equivalent Stress - B31.G surface correction, rectangular area, shell theory Folias factor 1.0 3.6755 1.4047 6.4347 0.9162
0.7 2.3979 0.5345 3.4478 1.3481 0.75 2.4872 0.5850 3.6363 1.3382 0.8 2.5843 0.6402 3.8419 1.3268 0.85 2.6937 0.6960 4.0609 1.3266 0.9 2.8159 0.7499 4.2889 1.3430 0.95 2.9509 0.8003 4.5229 1.3790
24 - Shell Theory Method - Chell surface correction, exact area, shell theory Folias factor
1.0 3.1019 0.8443 4.7602 1.4435
222
Table 30 – MAWP Ratio vs. Allowable RSF for API 650 (Continued)
Method Allowable RSF
Mean MAWP Ratio
MAWP Ratio
Standard Deviation
MAWP Ratio Upper 95% Prediction
Limit
MAWP Ratio Lower 95% Prediction
Limit 0.7 3.0244 0.9876 4.9644 1.0844 0.75 3.1626 1.1150 5.3528 0.9724 0.8 3.3229 1.2867 5.8503 0.7955 0.85 3.5594 1.4593 6.4258 0.6929 0.9 3.8477 1.6776 7.1430 0.5525 0.95 4.1801 1.8667 7.8467 0.5135
25 - Thickness Averaging - API 579, Level 1
1.0 4.6557 2.0546 8.6915 0.6200 0.7 2.3118 0.6670 3.6220 1.0017 0.75 2.4945 0.8019 4.0696 0.9194 0.8 2.7381 0.9943 4.6911 0.7850 0.85 3.0480 1.2262 5.4566 0.6393 0.9 3.4632 1.5065 6.4224 0.5041 0.95 3.9690 1.7730 7.4517 0.4863
26 - Thickness Averaging - API 579, Level 2
1.0 4.6557 2.0546 8.6915 0.6200 0.7 2.3626 0.5199 3.3838 1.3414 0.75 2.4697 0.5561 3.5621 1.3773 0.8 2.5852 0.5989 3.7616 1.4087 0.85 2.7099 0.6452 3.9772 1.4426 0.9 2.8477 0.6911 4.2052 1.4901 0.95 2.9973 0.7331 4.4374 1.5572
27 - Modified API 579 Section 5, Level 1 Analysis - B31.G surface correction, rectangular area, Modified API Folias factor 1.0 3.1536 0.7725 4.6709 1.6363
0.7 2.1579 0.3561 2.8574 1.4584 0.75 2.2264 0.3464 2.9069 1.5459 0.8 2.3063 0.3466 2.9872 1.6254 0.85 2.3968 0.3583 3.1005 1.6930 0.9 2.5055 0.3787 3.2494 1.7616 0.95 2.6300 0.4014 3.4186 1.8415
28 - Modified API 579 Section 5, Level 2 Analysis - B31.G surface correction, effective area, Modified API Folias factor 1.0 2.7659 0.4228 3.5965 1.9354
0.7 2.2113 0.4487 3.0928 1.3299 0.75 2.3075 0.4582 3.2076 1.4074 0.8 2.4141 0.4779 3.3528 1.4754 0.85 2.5338 0.5052 3.5261 1.5415 0.9 2.6704 0.5338 3.7190 1.6218 0.95 2.8158 0.5638 3.9232 1.7084
29 - Janelle Method, Level 1 - rectangular area
1.0 2.9640 0.5934 4.1296 1.7983 0.7 2.0769 0.3892 2.8414 1.3124 0.75 2.1411 0.3650 2.8580 1.4241 0.8 2.2189 0.3500 2.9063 1.5314 0.85 2.3117 0.3485 2.9963 1.6271 0.9 2.4277 0.3590 3.1329 1.7225 0.95 2.5564 0.3763 3.2955 1.8172
30 - Janelle Method, Level 1 - effective area
1.0 2.6907 0.3961 3.4686 1.9127
223
Table 31 – Geometry Parameters for the Circumferential Extent Validation Cases
Case Pipe OD (in) Pipe
thickness (in)
Axial extent of the flaw
(in)
Circumferential extent of the
flaw (in)
Flaw depth (% of wall
thickness)
1 48 0.48 18 12 25%
2 48 0.48 6 30 50%
3 48 0.48 18 12 50%
4 48 0.48 30 6 50%
5 48 0.48 6 30 50%
Table 32 – Circumferential Extent Validation Results
Case Pressure at Failure
(psi)
Moment at Failure (in-lb)
Failure Side
Material Ultimate Strength
(psi)
Tension Side
Equivalent Stress (psi)
Compression Side
Equivalent Stress (psi)
Error in calculated
stress
1 1480 34440000 Compression 100000 88790 92570 7.4%
2 950 28956000 Tension 100000 103080 74810 3.1%
3 980 36600000 Compression 100000 88030 97340 2.7%
4 840 39144000 Compression 100000 75620 92600 7.4%
5 950 31032000 Tension 100000 107440 78440 7.4%
224
CHAPTER XIV
FIGURES
Determine tmin(see Appendix A)
Locate Regions of MetalLoss on the Equipment
Assessment UsingThickness Profiles?
Take Point ThicknessReadings and Use
Additional NDE to ConfirmGeneral Corrosion
Determine tmm, tam and COVfrom the Thickness Data
Determine InspectionPlane(s) and Take
Thickness Profile Data
Determine CTP's in theLongitudinal and
Circumferential Directions
Determine tmm and L
Determine s, c, and tamfor the CTP's
Determine AverageThickness, tam, withinthe Zone for Thickness
Averaging, seeParagraph 4.4.3.3
Type B or CComponent?
Evaluate theMAWP Using a
Section 4 Level 2or 3 Assessment
Assessment UsingThickness Profiles?
Is s<=L?
COV > 10%?
Longitudinal orMeridonal Extent of
Metal Loss isAcceptable
Levell 3Assessment?
Cylinder, Coneor Elbow?
ObtainThicknessProfiles?
AssessmentComplete
EvaluateCircumferentialExtent of Metal
Loss UsingSection 5, Level 1
EvaluationOption:
ConservativeApproach
LocalizedMetal Loss
StressAnalysis
ThicknessAveraging
Evaluate UsingSection 5
Evaluate Usinga Level 3
Assessment
Determine tam UsingThickness DataWithin Length L
Use tam=tmm forCalculations
Evaluate UsingSection 4, Level
1 or Level 2Assessment
Use tam forCalculations
Yes
No
Yes
Yes
Yes
Yes
No
No
No
No
Yes
Yes
Yes
No
NoNo
Figure 4.2 - Assessment Procedure To Evaluate A ComponentWith Metal Loss Using Part 4 and Part 5
Figure 1 – Logic Diagram for the Assessment of General or Local Metal Loss in API 579
225
Obtain
Equipment Data
Perform Level 1Assessment?
Equipment IsAcceptable per
Level 1 Criteria?
Remaining LifeAcceptable per
Level 1 Criteria?
Perform a Level 2Assessment?
RerateEquipment?
Perform Rerate per Level1 Criteria to Reduce
Pressure and/orTemperature
Equipment isAcceptable per
Level 2 Criteria?
Remaining LifeAcceptable per
Level 2 Criteria?
Yes
Yes
Yes
Yes
No
No
No
No
No
No
No
Yes
Rerate Equipment?
Perform a Level 3Assessment?
Equipment Acceptableper Level 3 Assessment?
Remaining LifeAcceptable per Level 3
Criteria?
Yes
Repair,Replace, or
RetireEquipment
Return theEqupiment to
Service
Yes
Yes
Yes
No
No
No
Perform Rerate per Level3 Criteria to Reduce
Pressure and/orTemperature
Perform Rerate per Level2 Criteria to Reduce
Pressure and/orTemperature
Rerate Equipment?No
Yes
No
Yes
Yes
Figure 2 – Logic Diagram for the Assessment of Local Thin Areas in API 579
226
Uniform Metal Loss
ttavg
Thicknesstavg
tsd tsd
COV = tsd/tavg
(a) Small Variability in Thickness Profiles and the COV
Uniform Metal Loss
ttavg
Thicknesstavg
tsd tsd
COV = tsd/tavg
(b) Large Variability in Thickness Profiles and the COV
Figure 3 – Coefficient of Variation for Thickness Reading Data
227
C1
C2
C3
M3
C3
C2
C1
Cylindrical Shell Conical Shell
CL CL
Elbow or Pipe Bend
CL
M1 M2 M3
MetalLoss Metal
Loss
M1
M1 M2 M3
Intrados
Extrados
Metal Loss
C3
C2
C1
M1
M3M2
Figure 4 – Examples of an Inspection Grid to Define the Extent of Metal Loss Damage
228
M1
M5C1
CL
Cylindrical ShellLine C - path of minimumthicknessreadings in thecircumferential direction
Line M - path ofminimum thickness
readings in thelongitudinal direction
(a) Inspection Planes and the Critical Thickness Profile
(b) Critical Thickness Profile (CTP) - Longitudinal Plane (Projection of Line M)
(c) Critical Thickness Profile (CTP) - Circumferential Plane (Projection of Line C)
c
t tmin
t
C6 C7
S
C2 C3 C4 C5
M2
M3
M4
C
tmm
tmm
tc
Figure 5 – Establishing Longitudinal and Circumferential Critical Thickness Profiles from an Inspection Grid
229
(a) Isolated Flaw
(b) Network Of Flaws
t
t
Flaw
Path of MaximumMetal Loss
Flaw 1
Flaw 2
tmin
Thickness Profile
Thickness Profile
S
tmm
tmin
S
Figure 6 – Critical Thickness Profiles for Isolated and Multiple LTAs
230
LvLv
Lni
Lno
tn
CL
Nozzle with a Reinforcement Element
di
te
ReinforcementZone
Nozzle
Reinforcing Pad
Shell
tv
Notes: 1. ( )max , 2v i i n vL d d t t = + + (zone for thickness averaging in the horizontal direction).
2. ( )min 2.5 , 2.5no v n eL t t t = + (zone for thickness averaging in the vertical direction on the outside of the shell). 3. [ ]min 2.5 , 2.5ni v nL t t= (zone for thickness averaging in the vertical direction on the inside of the shell). 4. , ,v n et t t are the furnished vessel, nozzle and reinforcing pad thicknesses, respectively. 5.
RSFa
0.70 0.75 0.80 0.85 0.90 0.95 1.00
Low
er 9
5% R
atio
- C
alcu
late
d M
AW
P to
Act
ual F
ailu
re
2.3
2.4
2.5
2.6
2.7
2.8
2.9
3.0
3.1
is the current inside diameter.
Figure 7 – Zone for Thickness Averaging in A Nozzle
231
L1msd
L4msd
L2msd
L3msd
Stiffening Ring
Nozzle
ConicalTransition
Pipe Support
Flaw
Notes: 1. For the example shown above, the minimum distance to a major structural discontinuity is:
1 2 3 4min , , ,msd msd msd msd msdL L L L L
2. Typical major structural discontinues associated with vertical vessels are shown in this figure. 3. For horizontal drums, the saddle supports would constitute a major structural discontinuity and
for a spherical storage vessel, the support locations (shell-to-leg junction) would constitute a major structural discontinuity. The location of the flaw from these support locations would need to be considered in determining msdL as well as the distances from the nearest nozzle, piping/platform support, conical transition, and stiffening ring.
4. The measure of the minimum distances defined in this figure is from the nearest edge of the region of local metal loss to the nearest weld of the structural discontinuity.
Figure 8 – LTA to Major Structural Discontinuity Spacing Requirements in API 579
232
Lv
Lv
RS
RL
tL
tC
tS
Lv
Lv
CL
Small EndCylinder
ConeZones forThicknessAveraging - SmallEnd
Large EndCylinder
Zones for ThicknessAveraging - Large End
Notes: 1. 0.78v S SL R t= (thickness averaging zone for the small end cylinder).
2. 0.78v S CL R t= (thickness averaging zone for the small end cone).
3. 1.0v L CL R t= (thickness averaging zone for the large end cone).
4. 1.0v L LL R t= (thickness averaging zone for the large end cylinder).
5. , ,S C Lt t t are the furnished small end vessel, cone, and large end vessel thicknesses, respectively.
6. ,S LR R are the small end and large end vessel inside radii, respectively.
Figure 9 – Example of a Zone for Thickness Averaging at a Major Structural Discontinuity
233
λ
0 1 2 3 4 5 6 7 8 9 10
Rt
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
UNACCEPTABLE
ACCEPTABLE
Figure 10 – Level 1 Assessment Procedure for Local Metal Loss in Cylindrical Shells (Circumferential Stress)
234
Aio - Area Within BoxCross Hatched Area - Ai
tmint
s1
s2
si
si+1
si+2
si+3
(a) Subsection for the Effective Area Procedure
Minimum RSF
Si
RSFi
(b) Minimum RSF Determination
Figure 11 – Determination of the RSF for the Effective Area Procedure
235
t
li
lsi
lei
d(x)
dx
Figure 12 – Exact Area Integration Bounds
236
t
RiF
p
F
t
Di
Region Of Local Metal Loss
θ
c
Circumferential Plane
A
A
Section A-A
θ
F Mx2
Di2
P
MT
MTMT
My
My
Mx
V
V
My
Mx
Figure 13 – Supplemental Loads for a Longitudinal Stress Assessment
237
(a) Region Of Local Metal Loss Located on the Inside Surface
(b) Region Of Local Metal Loss Located on the Outside Surface
xx
x
yx
x
Metal Loss
Metal Loss
tmm
tmm
t
t
Do
2
Di
2
Df
2
θ θ
x
x
A
Df
2
θ θ
Do
2
AB
yLx
xy
y,y
B
Df
2
Di
2
y,y
yLx
Figure 14 – Assessment Locations and Parameters for a Longitudinal Stress Assessment
238
Circumferential LTA Screening Curve
RSFa=0.9
c/Dm
0.0 0.5 1.0 1.5 2.0 2.5
t mm
/t nom
0.0
0.2
0.4
0.6
0.8
1.0
Figure 15 – Longitudinal Stress, Level 1 Screening Curve
Current Depth Increment, dj
ltotal dpatch
dide,i
dj
te
li si
Figure 16 – BG Depth Increment Approach
239
Figure 17 – Table Curve 3D Fit of the Shell Theory Folias Factor
Lambda, λ
0 5 10 15 20 25 30
RS
F
0.5
0.6
0.7
0.8
0.9
1.0
3D Solid FEAAxisymmetric FEACurrent API 579 Level 1Current API 579 Level 2Modified API 579 Level 1&2
Figure 18 – Comparison Between Analysis Methods and FEA Trends for a Cylinder with a LTA
240
Figure 19 – 3D Solid FEA Model Geometry of a Cylinder for λ = 5
Figure 20 – Axisymmetric FEA Model Geometry of a Cylinder for λ = 5
241
foliasRank 17 Eqn 6007 y=a+bx+cx^2+dx^3+ex^4+fx^5+gx^6+hx^7+ix^8+jx^9+kx^(10)
r^2=1 DF Adj r^2=1 FitStdErr=4.7721507e-08 Fstat=2.152902e+19a=1.00101 b=-0.014196003 c=0.29089777 d=-0.096419915 e=0.020889797 f=-0.0030539593
g=0.00029570201 h=-1.8462059e-05 i=7.1552833e-07 j=-1.5631239e-08 k=1.4655864e-10
0 10 20 30lam
0
50
100
150
200
250
300
350
400
450
500
0
50
100
150
200
250
300
350
400
450
500
Figure 21 – Table Curve 2D Fit of the Modified API 579 Folias Factor
Lambda, λ
0 5 10 15 20
Folia
s Fa
ctor
, Mt
0
5
10
15
20
Current API 579 Level 2RSTRENGOriginal Folias DataProposed API 579 Level 1&2
Figure 22 – Comparison of the Old API 579 Folias Factor to the Modified Folias Factor and the Original Folias Data
242
λl
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
Rt
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
Screening Curve Equations
0.2 0.354tR for λ= ≤ 1
1.0 0.354 20.0a at a
t t
RSF RSFR RSF forM M
λ−
= − − < <
0.90 20.0tR for λ= ≥
Figure 23 – Screening Curve for the Circumferential Extent of an LTA
243
λl
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
Rt
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
Proposed Level 1&2 Remaining Strength FactorCurrent Level 2 Remaining Strength Factor
Figure 24 – Comparison of the Old API 579 Level 1 Screening Curve to the Modified Folias Factor Level 1 Screening Curve
244
Figure 25 – Axisymmetric FEA Model Geometry of a Sphere for λ = 5
Lambda, λ
0 5 10 15 20 25 30 35 40 45
RSF
0.5
0.6
0.7
0.8
0.9
1.0
Axisymmetric FEACurrent API 579
Figure 26 – Comparison Between Analysis Methods and FEA Trends for a Sphere with a LTA
245
Figure 27 – Table Curve 3D Plot of the Janelle Method
246
RSFa
0.70 0.75 0.80 0.85 0.90 0.95 1.00
MA
WP
Mar
gin
on F
ailu
re
2.0
2.5
3.0
3.5
4.0
4.5
5.0
5.5
6.0
Mean Mawp MarginUpper 95% Prediction IntervalLower 95% Prediction Interval
Figure 28 – RSFA vs. MAWP Ratio for ASME Section VIII, Division 1 (pre 1999) and ASME B31.1 (pre 1999) for the Modified API 579 Level 2 Assessment (Method 28)
RSFa
0.70 0.75 0.80 0.85 0.90 0.95 1.00
MAW
P M
argi
n on
Fai
lure
1.5
2.0
2.5
3.0
3.5
4.0
4.5
5.0
5.5
Mean Mawp MarginUpper 95% Prediction IntervalLower 95% Prediction Interval
Figure 29 – RSFA vs. MAWP Ratio for ASME Section VIII, Division 1 (post 1999) and ASME B31.1 (post 1999) for the Modified API 579 Level 2 Assessment (Method 28)
247
RSFa
0.70 0.75 0.80 0.85 0.90 0.95 1.00
MA
WP
Mar
gin
on F
ailu
re
1.5
2.0
2.5
3.0
3.5
4.0
4.5
Mean Mawp MarginUpper 95% Prediction IntervalLower 95% Prediction Interval
Figure 30 – RSFA vs. MAWP Ratio for ASME Section VIII, Division 2 and B31.3 for the Modified API 579 Level 2 Assessment (Method 28)
RSFa
0.70 0.75 0.80 0.85 0.90 0.95 1.00
MA
WP
Mar
gin
on F
ailu
re
1.0
1.5
2.0
2.5
3.0
3.5
4.0
Mean Mawp MarginUpper 95% Prediction IntervalLower 95% Prediction Interval
Figure 31 – RSFA vs. MAWP Ratio for the New Proposed ASME Section VIII, Division 2 for the Modified API 579 Level 2 Assessment (Method 28)
248
RSFa
0.70 0.75 0.80 0.85 0.90 0.95 1.00
MA
WP
Mar
gin
on F
ailu
re
1.5
2.0
2.5
3.0
3.5
4.0
4.5
Mean Mawp MarginUpper 95% Prediction IntervalLower 95% Prediction Interval
Figure 32 – RSFA vs. MAWP Ratio for CODAP for the Modified API 579 Level 2 Assessment (Method 28)
RSFa
0.70 0.75 0.80 0.85 0.90 0.95 1.00
MA
WP
Mar
gin
on F
ailu
re
1.0
1.5
2.0
2.5
3.0
3.5
Mean Mawp MarginUpper 95% Prediction IntervalLower 95% Prediction Interval
Figure 33 – RSFA vs. MAWP Ratio for AS 1210 and BS 5500 for the Modified API 579 Level 2 Assessment (Method 28)
249
RSFa
0.70 0.75 0.80 0.85 0.90 0.95 1.00
MA
WP
Mar
gin
on F
ailu
re
0.8
1.0
1.2
1.4
1.6
1.8
2.0
2.2
2.4
2.6
2.8
Mean Mawp MarginUpper 95% Prediction IntervalLower 95% Prediction Interval
Figure 34 – RSFA vs. MAWP Ratio for ASME B31.4 and B31.8, Class 1, Division 2 for the Modified API 579 Level 2 Assessment (Method 28)
RSFa
0.70 0.75 0.80 0.85 0.90 0.95 1.00
MA
WP
Mar
gin
on F
ailu
re
0.8
1.0
1.2
1.4
1.6
1.8
2.0
2.2
2.4
Mean Mawp MarginUpper 95% Prediction IntervalLower 95% Prediction Interval
Figure 35 – RSFA vs. MAWP Ratio for B31.8, Class 1, Division 1 for the Modified API 579 Level 2 Assessment (Method 28)
250
RSFa
0.70 0.75 0.80 0.85 0.90 0.95 1.00
MA
WP
Mar
gin
on F
ailu
re
1.0
1.2
1.4
1.6
1.8
2.0
2.2
2.4
2.6
2.8
3.0
3.2
Mean Mawp MarginUpper 95% Prediction IntervalLower 95% Prediction Interval
Figure 36 – RSFA vs. MAWP Ratio for B31.8, Class 2 for the Modified API 579 Level 2 Assessment (Method 28)
RSFa
0.70 0.75 0.80 0.85 0.90 0.95 1.00
MA
WP
Mar
gin
on F
ailu
re
1.0
1.5
2.0
2.5
3.0
3.5
4.0
Mean Mawp MarginUpper 95% Prediction IntervalLower 95% Prediction Interval
Figure 37 – RSFA vs. MAWP Ratio for B31.8, Class 3 for the Modified API 579 Level 2 Assessment (Method 28)
251
RSFa
0.70 0.75 0.80 0.85 0.90 0.95 1.00
MA
WP
Mar
gin
on F
ailu
re
1.5
2.0
2.5
3.0
3.5
4.0
4.5
5.0
Mean Mawp MarginUpper 95% Prediction IntervalLower 95% Prediction Interval
Figure 38 – RSFA vs. MAWP Ratio for B31.8, Class 4 for the Modified API 579 Level 2 Assessment (Method 28)
RSFa
0.70 0.75 0.80 0.85 0.90 0.95 1.00
MA
WP
Mar
gin
on F
ailu
re
1.5
2.0
2.5
3.0
3.5
4.0
4.5
5.0
Mean Mawp MarginUpper 95% Prediction IntervalLower 95% Prediction Interval
Figure 39 – RSFA vs. MAWP Ratio for API 620 for the Modified API 579 Level 2 Assessment (Method 28)
252
RSFa
0.70 0.75 0.80 0.85 0.90 0.95 1.00
MA
WP
Mar
gin
on F
ailu
re
1.5
2.0
2.5
3.0
3.5
4.0
4.5
5.0
Mean Mawp MarginUpper 95% Prediction IntervalLower 95% Prediction Interval
Figure 40 – RSFA vs. MAWP Ratio for API 650 for the Modified API 579 Level 2 Assessment (Method 28)
ROT
0 100 200 300 400 500 600 700 800 900 1000
Acc
epta
ble
Bend
ing
Fact
or
0.40
0.41
0.42
0.43
0.44
0.45
0.46
0.47
0.48
0.49
0.50
Figure 41 – Maximum Bending Factor as a Function of the Radius to Thickness Ratio
253
Lambda
0 2 4 6 8 10 12 14 16 18
Rt
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
Maximum Bending MomentNo Bending Moment
Screening Curve Equation (Maximum Bending Moment)
1.285 cDt
λ =
2
2
0.2 0.818
0.6999 1.1178 0.3014 0.8181.0 1.1139 0.3453
t
t
R
R
λ
λ λ λλ λ
= ≤
− + += >
+ +
Screening Curve Equation (No Bending Moment)
2
2
0.2 2.514
0.2498 0.2092 0.001312 2.5141.0 0.1492 0.008318
t
t
R
R
λ
λ λ λλ λ
= ≤
− + += >
+ +
Figure 42 – Screening Curve for the Circumferential Extent of an LTA
254
Folias Factor for Longitudinal Stress
Lambda
0 1 2 3 4 5 6 7 8
Folia
s Fa
ctor
0.00
0.25
0.50
0.75
1.00
1.25
1.50
1.75
2.00
Figure 43 – Longitudinal Stress Folias Factor
255
a.) Subsurface HIC Damage – Actual Area
b.) Subsurface HIC Damage – Area Modeled as an Equivalent Rectangle
Figure 44 – Subsurface HIC Damage
256
t
sLH LH
wH
t
sLH LH
wH
A) Surface Breaking HIC Damage - Actual Area
B) Surface Breaking HIC Damage - Area Modeled as an Equivalent Rectangle
AH - Area Of HIC Damage with ReducedStrength Characterized by DH
AH - Area Of HIC Damage with Reduced StrengthCharacterized by DH
tmm
tmm
Figure 45 – Surface Breaking HIC Damage
257
L1 L2 L3 L4
LT
t1 t2 t3 t4
Actual Cylindrical Shell
Idealized Cylindrical Shell
Stiffening Rings
Figure 46 – Idealized Geometry for a LTA Subject to External Pressure
258
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