Overview of ASME B&PV Design by Analysis
Introduction
Design by Analysis offers engineers greater design flexibility and can result in significant material and cost savings compared to traditional Design by Rule methods. When pressure vessel geometries become complex or operating conditions are demanding, Design by Analysis in ASME Section VIII Division 2 Part 5 provides the analytical tools needed for safe, optimized designs.
The Design by Rule methods in Section VIII, Division 1, and Section VIII, Division 2, Part 4, of the ASME Boiler & Pressure Vessel Code usually involve calculating the minimum required thickness for a pressure vessel part or finding the maximum allowable pressure for a given thickness.
The Design by Analysis methods in Section VIII, Division 2 are different. Instead of calculating thickness or pressure directly, the exact design of the pressure vessel part is analyzed to make sure it will not fail under the expected loads. Part 5 of Section VIII, Division 2 lists four types of failure that must be checked. The pressure vessel or its parts must be evaluated for each type when it applies. These failure types are: plastic collapse, local failure, buckling, and fatigue.
Protection Against Plastic Collapse
Plastic collapse happens when the material bends or deforms permanently enough that the pressure vessel part can no longer hold the applied load. This causes the part to break or collapse. To prevent plastic collapse, the ASME Code requires one of three analysis methods:
- Elastic Stress Analysis – Stresses are calculated assuming the material behaves elastically (it returns to its original shape). The stresses are categorized (primary, secondary, local) and compared to allowable limits. This method requires stress categorization into primary membrane, primary bending, secondary, and peak stresses. Primary stresses have strict limits (typically 1.5 times the allowable stress) to prevent gross plastic deformation, while combined primary and secondary stresses are limited to prevent ratcheting (progressive deformation under cyclic loading).
- Limit Load Method – Uses higher loads (scaled by factors like 1.3 or 1.5) and assumes the material behaves elastic-perfectly plastic. This means the material behaves elastically up to the yield stress, and then plastically with no further hardening (constant stress beyond yield). The yield point is often set conservatively at 1.5 times the allowable stress.
- Elastic-Plastic Stress Analysis – Uses scaled loads and modeling a more realistic elastic-plastic material model that can include hardening or softening after yield. This reflects real material behavior better, meaning the vessel can sometimes bear more load before failure.
Protection Against Local Failure
Sometimes a local small area can fail even if the rest of the vessel is structurally sound. This is important in hydrostatic loading conditions, where stresses are triaxial (three directions). Local failure is particularly critical in areas of high stress concentration where material is constrained in three directions – such as nozzle-to-shell intersections, closely-spaced openings, or thick-section transitions. Under triaxial tension, normally ductile materials lose their ability to redistribute stress through plastic flow, effectively behaving in a brittle manner. This occurs because the material cannot deform laterally when stressed in all three directions simultaneously.
Under these conditions, ductile materials act more brittle because they have no space to deform. This lowers the strain needed to cause failure. The ASME Code allows two methods to guard against local failure:
- Elastic Stress Analysis – The sum of the three principal stresses (main stress directions) is checked against a limit.
- Elastic Plastic Analysis – The combined strain from triaxial and forming effects is compared to a strain limit.
The Elastic-Plastic Method is Considered more Accurate but both are Allowed by the Code.
Protection Against Buckling
Buckling is a critical concern for thin-walled pressure vessels under external pressure, vacuum service, or compressive loads from supports or attachments. Unlike other failure modes that occur gradually, buckling represents a sudden instability where the structure can catastrophically collapse.
Five-Step Elastic Analysis Method:
This approach uses linear eigenvalue analysis to identify potential buckling modes – the characteristic deformation shapes the vessel would take if it buckled. The analysis determines the theoretical buckling load (eigenvalue) for each mode. Because real vessels always contain small geometric imperfections (out-of-roundness, dents, weld distortions), the Code requires applying conservative knockdown factors – typically reducing the theoretical buckling load by 20-40%. The vessel’s actual stresses under these reduced loads must remain below allowable limits.
Elastic-Plastic Analysis Method:
This more sophisticated approach explicitly models realistic geometric imperfections (typically 0.5% to 1% of radius or thickness-dependent values specified in the Code) directly into the finite element model. The analysis then incrementally increases load while tracking both material yielding and geometric nonlinearity. If the model successfully converges to the required load level without exhibiting instability, the design passes. This method often allows higher design pressures than the elastic method because it more realistically captures vessel behavior.
Protection Against Fatigue
Fatigue happens when repeated loading causes failure over time, even when stress levels are well below the material’s yield strength. Whether fatigue needs to be checked depends on the stress magnitude and number of cycles. The ASME Code provides screening criteria to determine if full fatigue evaluation is necessary – generally, fewer than a few hundred full pressure cycles during the vessel’s design life may be exempted. The Code also allows skipping detailed analysis if there is proven experience with similar equipment operating under comparable conditions.
For fatigue analysis, the ASME Code allows two methods:
Elastic Stress Analysis Method: This approach calculates the alternating stress intensity (essentially the stress range between maximum and minimum loading conditions) and applies adjustment factors for mean stress effects. The alternating stress is then compared against design fatigue curves provided in the Code, which show allowable stress amplitude versus number of cycles. These curves are based on strain-controlled testing with safety factors of 2 on stress and 20 on cycles. For vessels experiencing multiple different loading cycles, cumulative fatigue damage is calculated – the sum of cycle ratios (actual cycles divided by allowable cycles) must remain below 1.0.
Elastic-Plastic Analysis Method: This advanced approach directly calculates strain ranges per cycle, which more accurately reflect fatigue damage potential. The Twice Yield Method is a simplified elastic-plastic approach where the analysis assumes the material yields at twice the yield strength – providing a reasonable strain approximation without full nonlinear elastic-plastic modeling.
Weld Fatigue Considerations: Welds represent the most fatigue-critical locations in pressure vessels due to geometric stress concentrations, residual stresses, and potential defects. For welds with smooth, ground-flush profiles, standard fatigue curves may be used with appropriate stress concentration factors. For as-welded profiles with rougher surface conditions, the Code provides special procedures using equivalent structural stress methods that account for weld geometry and surface condition. These methods separate stress into membrane and bending components and apply them to specific weld fatigue curves.
Frequently Asked Questions: ASME Design by AnalysiS
When is Design by Analysis required for pressure vessels?
Design by Analysis is required when vessel components fall outside the geometric or loading conditions covered by Design by Rule formulas in ASME Section VIII. Common situations requiring Design by Analysis include: complex nozzle reinforcement configurations that don’t meet standard rules, non-standard head shapes or transitions, vessels with multiple closely-spaced openings where ligament efficiency is difficult to determine, components subjected to significant external loads (wind, seismic, piping reactions), local structural attachments such as lugs or saddle supports, thermal gradients causing significant secondary stresses, and vessels operating in high-cycle fatigue service.
Design by Analysis is also chosen when engineers want to optimize designs for weight or material savings, even when Design by Rule could technically be used. Additionally, Division 2 itself is a Design by Analysis code—while Part 4 provides Design by Rule methods, Part 5 Design by Analysis is often necessary to justify designs that would be overly conservative or impossible using simplified rules. Many fabricators and engineering firms choose Design by Analysis to demonstrate compliance with modern safety standards while achieving economical designs.
What are the four failure modes checked in ASME Section VIII Division 2 Part 5?
ASME Section VIII Division 2 Part 5 requires evaluation of four distinct failure modes to ensure comprehensive vessel safety. First is plastic collapse, which occurs when the vessel or component experiences gross plastic deformation and loses its load-carrying capacity—essentially when the material yields excessively and can no longer support the applied loads. Second is local failure, which addresses situations where triaxial tensile stress states can cause localized material failure even when overall vessel stresses appear acceptable—this is particularly critical in constrained regions like nozzle corners where ductile materials behave in a brittle manner.
Third is buckling, an instability failure mode where thin-walled components under compressive loading (external pressure, vacuum, or structural compression) suddenly collapse – this is a catastrophic failure that occurs without warning when critical buckling loads are exceeded. Fourth is cyclic loading or fatigue, which addresses progressive crack growth and eventual failure under repeated load cycles – even if individual stress levels are well below yield strength, the cumulative effect of thousands or millions of cycles can cause failure through crack initiation and propagation. Each failure mode has specific evaluation procedures and acceptance criteria in the Code, and all applicable failure modes must be checked to achieve ASME compliance. Not all failure modes apply to every vessel—for instance, vessels under steady internal pressure with few cycles may not require fatigue analysis, while thick-walled vessels may not need buckling checks.
Can Design by Analysis reduce vessel weight and cost?
Yes, Design by Analysis frequently achieves significant weight and cost reductions compared to Design by Rule approaches. Design by Rule formulas contain built-in conservatism because they must cover a wide range of geometries and conditions using simplified equations. Design by Analysis eliminates much of this excess conservatism by analyzing the actual stress distribution in the specific geometry under actual loading conditions. For example, nozzle reinforcement calculations using Design by Rule often require substantial reinforcement pads, while Design by Analysis may demonstrate that intrinsic reinforcement in the vessel shell is sufficient—eliminating the pad entirely and saving both material and welding costs.
Similarly, Design by Analysis captures the actual stress distribution and may permit reduced thickness where Design by Rule uses overly conservative assumptions. Real-world examples show weight reductions of 10-25% are achievable in many applications, with even greater savings possible on complex geometries. These material savings translate directly to reduced fabrication costs, lower shipping costs, reduced support structure requirements, and easier field installation. For large vessels or expensive alloys like stainless steel or high-nickel materials, weight reductions of thousands of pounds represent substantial cost savings that far exceed the additional engineering expense.
Summary
The Design by Analysis methods in Part 5 of Section VIII, Division 2 provide engineers with powerful tools to design safe, efficient pressure vessels under complex loading conditions. By systematically evaluating plastic collapse, local failure, buckling, and fatigue, these procedures ensure comprehensive safety while often enabling significant cost and weight reductions compared to simplified Design by Rule methods.
O’Donnell Consulting Engineers has extensive experience applying Design by Analysis to challenging pressure vessel applications. Our team’s deep understanding of ASME Code requirements, combined with advanced finite element analysis capabilities, enables us to optimize designs while ensuring full Code compliance.
Always consult the current ASME Boiler & Pressure Vessel Code edition for complete design requirements and the latest updates to analysis procedures.
This article is based on the 2023 Edition of the ASME Boiler & Pressure Vessel Code.
