CONTENTS
ANNEX 2D – STRESS ANALYSIS OVERVIEW FOR A FFS ASSESSMENT ... 2D-1 2D.1 GENERAL REQUIREMENTS ... 2D-1 2D.1.1 Scope ... 2D-1 2D.1.2 ASME B&PV Code, Section VIII, Division 2 (VIII-2) ... 2D-2 2D.1.3 Applicability ... 2D-2 2D.1.4 Protection Against Failure Modes ... 2D-2 2D.1.5 Numerical Analysis... 2D-2 2D.1.6 Material Properties ... 2D-3 2D.1.7 Applicable Loads and Load Case Combinations ... 2D-3 2D.1.8 Loading Histogram ... 2D-3 2D.2 PROTECTION AGAINST PLASTIC COLLAPSE ... 2D-4 2D.2.1 Overview ... 2D-4 2D.2.2 Elastic Stress Analysis Method ... 2D-4 2D.2.3 Limit-Load Analysis Method ... 2D-4 2D.2.4 Elastic-Plastic Stress Analysis Method ... 2D-5 2D.2.5 Treatment of the Weld Joint Efficiency ... 2D-5 2D.3 PROTECTION AGAINST LOCAL FAILURE ... 2D-5 2D.3.1 Overview ... 2D-5 2D.3.2 Elastic Analysis Method ... 2D-6 2D.3.3 Elastic-Plastic Analysis Method ... 2D-6 2D.4 PROTECTION AGAINST COLLAPSE FROM BUCKLING ... 2D-6 2D.4.1 Assessment Procedure ... 2D-6 2D.4.2 Supplemental Requirements for Components with Flaws ... 2D-6 2D.5 SUPPLEMENTAL REQUIREMENTS FOR STRESS CLASSIFICATION IN NOZZLE NECKS ... 2D-7 2D.6 NOMENCLATURE ... 2D-7 2D.7 REFERENCES ... 2D-7 2D.8 TABLES ... 2D-8 2D.1 General Requirements
2D.1.1 Scope
The analytical methods contained within this Annex can be used for stress analysis when performing a Fitness-For-Service (FFS) Assessment of a component with a volumetric flaw. These methods are typically employed in either a Level 2 or Level 3 assessment. Detailed assessment procedures utilizing the results from a stress analysis are provided to evaluate components for plastic collapse, local failure, and buckling.
Recommendations are provided on how to perform and utilize results from a stress analysis in an FFS
assessment. Procedures for performing linear and non-linear analysis, determination of stress categories and classification of stress results obtained from a linear analysis, and a methodology to perform an elastic-plastic analysis to determine a collapse load or to perform a fatigue evaluation are among the items covered in this Annex.
2D.1.2 ASME B&PV Code, Section VIII, Division 2 (VIII-2)
The stress analysis methods in this Annex are based on ASME B&PV Code, Section VIII, Division 2 (VIII-2), Part 5. The methods in this Annex reference VIII-2 directly and provide exceptions that are to be used in an
FFS Assessment.
2D.1.3 Applicability
The assessment procedures in this Annex may only be used if the allowable stress from the applicable construction code evaluated at the design temperature is governed by time-independent properties unless otherwise noted in a specific design procedure. If the allowable stress from the applicable construction code evaluated at the design temperature is governed by time-dependent properties and the fatigue screening criteria of Part 14 are satisfied, then the elastic stress analysis procedures in this Annex may be used.
2D.1.4 Protection Against Failure Modes
The analysis requirements for volumetric flaws are organized based on protection against the failure modes listed below. If multiple assessment procedures are provided for a failure mode, only one of these procedures must be satisfied to qualify the component for continued operation. In addition, the component shall be evaluated for each applicable failure mode.
a) Protection Against Plastic Collapse – The requirements of paragraph 2D.2 shall be satisfied.
b) Protection Against Local Failure – The requirements of paragraph 2D.3 shall be satisfied.
c) Protection Against Collapse From Buckling – The requirements of paragraph 2D.4 shall be satisfied.
d) Protection Against Creep or Creep-Fatigue Damage – Assessment procedures for components subject to cyclic operation in the creep regime are covered in Part 10.
e) Protection Against Fatigue Damage – Assessment procedures for components subject to cyclic operation below the creep regime are covered in Part 14.
2D.1.5 Numerical Analysis
a) The assessment methods in this Annex are based on the use of results obtained from a detailed stress analysis of a component. Depending on the loading condition, a thermal analysis to determine the temperature distribution and resulting thermal stresses may also be required.
b) Procedures are provided for performing stress analyses to determine protection against plastic collapse, local failure, buckling, and cyclic loading. These procedures provide the necessary details to obtain a consistent result with regards to development of loading conditions, selection of material properties, post- processing of results, and comparison to acceptance criteria to determine the suitability of a component.
c) Recommendations on a stress analysis method, modeling of a component, and validation of analysis results are not provided. While these aspects of the assessment process are important and shall be considered in the analysis, a detailed treatment of the subject is not provided because of the variability in approaches and design processes. However, an accurate stress analysis including validation of results shall be provided as part of the assessment.
2D.1.6 Material Properties
The following material properties for use in the stress analysis may be determined using the data and material models in Annex 2E. Material properties may also be obtained from test data from the actual material being evaluated.
a) Physical properties – Young’s Modulus, thermal expansion coefficient, thermal conductivity, thermal diffusivity, density, Poisson’s ratio.
b) Strength Parameters – Allowable stress, minimum specified yield strength, minimum specified tensile strength.
c) Monotonic Stress-Strain Curve – elastic perfectly plastic and elastic-plastic true stress-strain curve with strain hardening.
d) Cyclic Stress-Strain Curve – Stabilized true stress-strain amplitude curve.
2D.1.7 Applicable Loads and Load Case Combinations
a) All applicable applied loads on the component shall be considered when performing an FFS
assessment. Supplemental loads shall be considered in addition to the applied pressure in the form of applicable load cases. An overview of the supplemental loads and loading conditions that shall be considered in a design are shown in Annex 2C, Table 2C.3.
b) Load case combinations shall be considered in the FFS assessment. Typical load definitions are defined in Table 2D.1. Load case combinations for elastic analysis, limit load analysis, and elastic plastic analysis are shown in Tables 2D.2, 2D.3, and 2D.4, respectively. In evaluating load cases involving the pressure term, P, the effects of the pressure being equal to zero shall be considered. The applicable load case combinations shall be considered in addition to any other combinations defined by the Owner- User.
2D.1.8 Loading Histogram
If any of the loads vary with time, a loading histogram shall be developed to show the time variation of each specific load. The loads in the histogram shall satisfy the requirements of this Annex. In addition, these loads shall be evaluated for fatigue in accordance with Part 14, as applicable.
a) The loading histogram shall include all significant operating temperatures, pressures, supplemental loads, and the corresponding cycles or time periods for all significant events that are applied to the component.
The following shall be considered in developing the loading histogram.
1) The number of cycles associated with each event during the operation life, these events shall include start-ups, normal operation, upset conditions, and shutdowns.
2) When creating the histogram, the history to be used in the assessment shall be based on the anticipated sequence of operation.
3) Applicable loadings such as pressure, temperature, supplemental loads such as weight, support displacements, and nozzle reaction loadings.
4) The relationship between the applied loadings during the time history.
b) If an accurate histogram cannot be generated, then an approximate histogram shall be developed based on information obtained from plant personnel. This information shall include a description of all
sensitivity analysis (see Part 2) shall be included in the FFS assessment to determine and evaluate the effects of the assumptions made to develop the operating history.
2D.2 Protection Against Plastic Collapse 2D.2.1 Overview
Three alternative analysis methods are provided in VIII-2, Part 5 for evaluating protection against plastic collapse. A brief description of the analysis methods is provided below.
a) Elastic Stress Analysis Method – Stresses are computed using an elastic analysis, classified into categories, and limited to allowable values that have been conservatively established such that a plastic collapse will not occur.
b) Limit-Load Method – A calculation is performed to determine a lower bound to the limit load of a component. The allowable load on the component is established by applying design factors to the limit load such that the onset of gross plastic deformations (plastic collapse) will not occur.
c) Elastic-Plastic Stress Analysis Method – A collapse load is derived from an elastic-plastic analysis considering both the applied loading and deformation characteristics of the component. The allowable load on the component is established by applying design factors to the plastic collapse load.
2D.2.2 Elastic Stress Analysis Method
a) Assessment procedure – The assessment procedures for the Elastic Stress Analysis Method including the basis for determining stresses based on elastic analysis, stress categorization, and linearization shall be in accordance with VIII-2, Part 5, paragraph 5.2.2 except that the allowable stresses that incorporate the Allowable Remaining Strength Factor (RSFa) as shown in Table 2D.2 may be used in the assessment. The load case combinations from VIII-2 are shown in Table 2D.2.
b) Allowable Equivalent Stress – The allowable equivalent stress, S, to be used in conjunction with the Elastic Stress Analysis Method in a FFS assessment is established based on the type of equipment.
1) Pressure Vessels– The stress from the applicable pressure vessel construction code shall be used for S. Alternatively, for vessels constructed to the ASME B&PV Code, Section VIII, Division 1, S
may be taken from VIII-2 for use in a FFS assessment if the component has similar design details and NDE prerequisites as originally required for a Division 2 vessel design (see Annex 2C, paragraph 2C.2.4).
2) Piping – The allowable stress from the applicable piping construction code (e.g. ASME B31.3) shall be used for S.
3) Tankage – The allowable stress from the applicable tank construction code (e.g. API 650) shall be used for S.
2D.2.3 Limit-Load Analysis Method
• The assessment procedures for the Limit-Load Analysis Method shall be in accordance with VIII-2, Part 5, paragraph 5.2.3 except that the load case combinations that incorporate the Allowable Remaining Strength Factor ( RSFa) as shown in Table 2D.3 may be used in the assessment.
2D.2.4 Elastic-Plastic Stress Analysis Method
The assessment procedures for the Elastic-Plastic Analysis Method shall be in accordance with VIII-2, Part 5, paragraph 5.2.4 except that the load case combinations that incorporate the construction code design margin for the ultimate tensile stress and the RSFa as shown in Table 2D.5 may be used in the assessment.
Note for the ASME B31.4, ASME B31.8 and B31.12 Piping Codes, the value of β is based on VIII-2 because the design margin in these codes is based on the specified minimum yield strength of the pipe material. The ultimate tensile strength is not used in establishing the design allowable stress. When performing an elastic- plastic analysis in accordance with these codes, the following shall be considered in the analysis.
• ASME B31.4 – the design factor, F.
• ASME B31.8 – the design factor, f, and the temperature correction factor, T.
• ASME B31.12 – the design factor, f, the temperature correction factor, T, and the material performance factor Hf.
2D.2.5 Treatment of the Weld Joint Efficiency
The weld joint efficiency is included in the analysis through either Method A or B as detailed below. Method A takes a global approach and Method B takes a local approach. The material response guidelines in Method B can be applied to an entire component or specifically to a weld band region as defined in paragraph 2C.2.5.
a) Method A
• Elastic Stress Analysis – The material allowable stress is reduced by multiplying by the governing weld joint efficiency.
• Limit Load Analysis – The limit load is computed and subsequently reduced by the governing weld joint efficiency.
• Elastic-Plastic Analysis – The load multipliers on sustained loads as defined in paragraph 2D.2.4 are increased by multiplying by the inverse of the governing weld joint efficiency prior to determination of the plastic collapse load. The material true stress-strain curve is unaffected.
b) Method B
• Elastic Stress Analysis – The allowable stress for a component or weld band region shall be multiplied by the weld joint efficiency for the weld.
• Limit Load Analysis – The elastic perfectly-plastic yield strength limit for a component or weld band region shall be multiplied by the weld joint efficiency for the weld. The load multipliers used in the analysis are as defined in paragraph 2D.2.3.
• Elastic-Plastic Analysis – When defining the material true stress-strain curve for a component or weld band region, both the engineering yield strength and the engineering ultimate tensile strength shall be multiplied by the weld joint efficiency for the weld. The load multipliers used in the analysis are as defined in paragraph 2D.2.4.
2D.3 Protection Against Local Failure 2D.3.1 Overview
In addition to demonstrating protection against plastic collapse as defined in paragraph 2D.2, the applicable local failure criteria below shall be satisfied for a component. The strain limit criterion typically does not need
presence of a flaw does not result in a significant strain concentration. If the significance of a strain concentration cannot be established, then the strain limit criterion should be evaluated as part of the assessment.
Two analysis methodologies are provided for evaluating protection against local failure to limit the potential for fracture under applied design loads.
a) Elastic Analysis Method – An approximation of the protection against local failure based on the results of an elastic analysis.
b) Elastic-Plastic Analysis Method – A more accurate estimate of the protection against local failure of a component is obtained based on the results of an elastic-plastic stress analysis.
If a limit load analysis is used to evaluate protection against plastic collapse, the elastic-plastic analysis method for local failure shall be used to evaluate protection against local failure (see Table 2D.3).
2D.3.2 Elastic Analysis Method
The assessment procedures for the Elastic Analysis Method shall be in accordance with VIII-2, Part 5, paragraph 5.3.2 except the acceptance criterion may be 4 S RSFa rather than 4S.
2D.3.3 Elastic-Plastic Analysis Method
The assessment procedures for the Elastic-Plastic Analysis Method shall be in accordance with VIII-2, Part 5, paragraph 5.3.3 except that the RSFa may be applied for load case combinations as shown in Table 2D.4.
2D.4 Protection Against Collapse From Buckling 2D.4.1 Assessment Procedure
The assessment procedures for Protection Against Collapse from Buckling shall be in accordance with VIII-2, Part 5, paragraph 5.4 except that the RSFa may be applied for load case combinations as shown in Table 2D.2 in a Type 1 or Type 2 assessment, and that the load case combinations as shown in Table 2D.4 that incorporate RSFa may be used in a Type 3 assessment.
2D.4.2 Supplemental Requirements for Components with Flaws
a) Assessment of the structural stability of a component with flaws should consider growth aspects and remaining life. The location, size and reduced thickness associated with a flaw will affect the structural stability of a component. Therefore, the assessment should be performed for the flaw size at the end of its useful life. For volumetric-type flaws, account should be taken of the possibility of increased metal loss and expansion of the corroded area with time. For crack-like flaws, account should be taken of the possibility of crack growth by fatigue, corrosion-fatigue, stress corrosion cracking and creep.
b) The significance of planar flaws parallel to a plate or shell surface in the direction of compressive stress (laminations, laminar tears, etc.) should be assessed by checking the buckling strength of each part of the material between the flaw and the component surface. This may be done by calculation as if the individual parts of the material are separate plates of the same area as the flaw using the distance between the flaw and the surface as an effective thickness.
c) If a flaw occurs parallel to the surface under the weld attaching a stiffener to a shell or plate loaded in compression, it will reduce the effective length over which the stiffener is attached to the plate. If a flaw of
this type is located, it should be assessed assuming that the stiffener is intermittently welded to the plate and that the flaw forms a "space" between two welds. Rules for determining the allowable weld spacing for stiffener attachment from the original design code may be used in this evaluation.
d) The allowable compressive stress for a shell component with a flaw can be established using the compressive stress equations in VIII-2, Part 4, paragraph 4.4. The thickness to be used in the compressive stress calculation should be the minimum thickness less any future corrosion allowance unless another thickness can be justified.
2D.5 Supplemental Requirements for Stress Classification in Nozzle Necks
Classification of stresses for nozzle necks shall be in accordance with VIII-2, Part 5, paragraph 5.6.
2D.6 Nomenclature
f design factor used in the ASME B31.8 or ASME B31.12 Piping Code, as applicable.
F design factor used in the ASME B31.4 Piping Code.
Hf materials performance factor used in the ASME B31.12 Piping Code.
RSFa allowable remaining strength factor (see Part 2).
S allowable stress based on the material of construction and design temperature.
T design load parameter to represent the self-restraining load case or temperature correction factor used in the ASME B31.8 Piping Code.
2D.7 References
1. Bushnell D., Computerized Buckling Analysis and Shells, Kluwer Academic Publishers, Norwell, MA, 1985.
2. Gerdeen, J.C., Rodabaugh, E.C., and O’Donnell, W.J., A Critical Evaluation of Plastic Behavior Data and a Unified Definition of Plastic Loads for Pressure Components, WRC Bulletin 254, Welding Research Council, New York, 1979.
3. Abaqus Unified FEA, User’s Manual, latest edition, Dassault Systèmes.
4. Miline, I., Ainsworth, R.A., Dowling, A.R., Stewart, A.T., “Assessment of the Integrity of Structures Containing Defects,” Int. J. Pres. Ves. & Piping 32, 1988, pp. 66-72.
5. Osage, D.A., Krishnaswamy, P., Stephens, D.R., Scott, P., Janelle, J., Mohan, R., and Wilkowski, G.M., Technologies for the Evaluation of Non-Crack-Like Flaws in Pressurized Components – Erosion/Corrosion, Pitting, Blisters, Shell Out-Of-Roundness, Weld Misalignment, Bulges and Dents, WRC Bulletin 465, Welding Research Council, New York, N.Y., September, 2001.
6. Osage, D., ASME Section VIII – Division 2 Criteria and Commentary, PTB-1-2013, ASME, New York, New York, 2014.
7. Sowinski, J.C., Osage, D.A., and Brown, R.G., ASME Section VIII - Division 2 Example Problem Manual, PTB-3-2013, ASME, New York, New York, 2013.
2D.8 Tables
Table 2D.1 – Load Descriptions
Design Load Parameter Description
P Internal and external maximum allowable working pressure
Ps Static head from liquid or bulk materials (e.g. catalyst)
D
Dead weight of the vessel, contents, and appurtenances at the location of interest, including the following:
• Weight of vessel including internals, supports (e.g. skirts, lugs, saddles, and legs), and appurtenances (e.g. platforms, ladders, etc.)
• Weight of vessel contents under operating and test conditions
• Refractory linings, insulation
• Static reactions from the weight of attached equipment, such as motors, machinery, other vessels, and piping
• Transportation loads
L
• Appurtenance live loading
• Effects of fluid momentum, steady state and transient
• Wave loading
E Earthquake loads (for example, see ASCE/SEI 7 for the specific definition of the earthquake load, as applicable)
W Wind Loads
Wpt Is the pressure test wind load case. The design wind speed for this case shall be specified by the Owner-User.
Ss Snow Loads
T
Is the self-restraining load case (i.e. thermal loads, applied displacements).
This load case does not typically affect the collapse load, but should be considered in cases where elastic follow-up causes stresses that do not relax sufficiently to redistribute the load without excessive deformation.
Table 2D.2 – Load Case Combinations and Allowable Stresses for an Elastic Analysis
Load Case Design Load Combination (1) Allowable Stress
1 P P D + +s
Determined based on the Stress Category shown in VIII-2, Figure 5.1. The values of S RSFa and
PS a
S RSF may be used.
2 P P D L + + +s
3 P P D L T + + + +s
4 P P D S + + +s s
5 0.6 D + ( 0.6 W or 0.7 E ) (2)
6 0.9 P P D + + +s ( 0.6 W or 0.7 E )
7 0.9 P P D + + +s 0.75 ( L T + ) + 0.75 Ss
8 0.9 P P D + + +s 0.75 0.6 ( W or 0.7 E ) + 0.75 L + 0.75 Ss
Notes:
1. The parameters used in the Design Load Combination column are defined in Table 2D.1.
2. This load combination addresses an overturning condition for foundation design. It does not apply to design of anchorage (if any) to the foundation. Refer to ASCE/SEI 7-10, 2.4.1 Exception 2 for an additional reduction to W that may be applicable.
3. Loads listed herein shall be considered to act in the combinations described above; whichever produces the most unfavorable effect in the component being considered. Effects of one or more loads not acting shall be considered.
Table 2D.3 – Load Case Combinations and Load Factors for a Limit Load Analysis Design Conditions
Criteria Required Factored Load Combinations
Global Criteria
Load
Case Load Combination
1 1.5 ( P P D + +s ) ⋅ RSFa
2 1.3 ( P P D T + + +s ) + 1.7 L + 0.54 Ss ⋅ RSFa
3 1.3 ( P P D + +s ) + 1.7 Ss+ ( 1.1 L or 0.54 W ) ⋅ RSFa
4 1.3 ( P P D + +s ) + 1.1 W + 1.1 L + 0.54 Ss ⋅ RSFa
5 1.3 ( P P D + +s ) + 1.1 E + 1.1 L + 0.21 Ss ⋅ RSFa
Local Criteria Per Table 2D.4 using an Elastic-Plastic Analysis.
Serviceability Criteria Per User’s Design Specification, if applicable (see VIII-2, Part 5, paragraph 5.2.4.3.b).
Hydrostatic Test Conditions
Global Criteria max 1.43, 1.25 ST ( P P D Ws ) pt
S
⋅ + + +
Serviceability Criteria Per User’s Design Specification, if applicable.
Pneumatic Test Conditions
Global Criteria 1.15 ST ( P P D Ws ) pt
S
⋅ + + +
Serviceability Criteria Per User’s Design Specification, if applicable.
Notes:
1. The parameters used in the Design Load Combination column are defined in Table 2D.1. See VIII-2, Part 5, paragraph 5.2.3.4 for descriptions of global and serviceability criteria.
2. S is the allowable membrane stress at the design temperature.
3. ST is the allowable membrane stress at the pressure test temperature.
4. Loads listed herein shall be considered to act in the combinations described above; whichever produces the most unfavorable effect in the component being considered. Effects of one or more loads not acting shall be considered.