Pressure Vessel FEA to ASME Section VIII Division 2: A Practical Guide to Design by Analysis

• Nozzles with large external loads from piping, or openings outside the code's rules.
• Supports: saddles, skirts, legs and lugs, plus lifting and tailing lugs.
• Non-standard geometry such as unusual heads, cone transitions and non-circular sections.
• Cyclic service: pressure or temperature cycles that need a fatigue assessment.
• Thermal loads: temperature gradients, hot spots and start-up or shutdown transients.
• Fitness for service: assessing corrosion, dents or cracks found in inspection, using API 579-1/ASME FFS-1.
• Division 1 vessels: where Division 1 gives no rules for a detail, paragraph U-2(g) allows the design to be shown by other means, and Division 2 Part 5 methods are widely used for this, subject to the Authorized Inspector's acceptance.

• Plastic collapse: gross yielding of the vessel under its loads.
• Local failure: rupture at a point of high triaxial stress, even when the vessel as a whole is fine.
• Buckling: collapse under compressive loads such as vacuum, external pressure, wind or seismic loads.
• Cyclic loading: fatigue cracking, and ratcheting, where strain grows a little with every cycle.

The traditional route uses a linear elastic FEA model. Stresses are taken along stress classification lines through the wall and linearised into membrane, bending and peak components, which are then sorted into categories: general primary membrane (Pm), local primary membrane (PL), primary bending (Pb), secondary (Q) and peak (F). Typical limits, with S as the allowable stress, are:

• Pm no more than S.
• PL and PL + Pb no more than 1.5 S.
• The range of primary plus secondary stress no more than SPS, generally three times S or twice the yield strength, whichever is larger.
• For local failure, the sum of the three principal stresses no more than 4 S.

Sharp peaks at corners are not compared with these limits; they feed the fatigue check. In our FEA of a hairpin heat exchanger bolted flange, the peak stress of about 235 MPa sat in a small zone at a geometric transition while the average stayed near 30 MPa, which is why the assessment used the linearised membrane and bending stresses rather than the raw peak. Choosing the lines and the categories takes engineering judgement, which is one reason Part 5 also offers elastic-plastic methods.

• Limit-load analysis uses an elastic-perfectly plastic material and checks that the vessel can carry 1.5 times its design loads.
• Elastic-plastic analysis uses the real stress-strain curve and large deformations, and checks that the vessel stays stable under factored loads, for example 2.4 times the design pressure and dead loads.

These methods need no stress categorisation, model the real behaviour more closely and are often less conservative, which can mean thinner walls or smaller reinforcement. The elastic-plastic route also checks local failure using strain limits.

Vessels under vacuum or external pressure, tall columns under wind and seismic loads, and shells near saddle supports can all fail by buckling. Part 5 covers it both with linear buckling analysis and design factors, and with non-linear analysis that includes the geometric imperfections every real shell has.

• Screening: Part 5 first checks whether the number and size of the cycles call for a full fatigue analysis.
• Unwelded areas are assessed with smooth-bar fatigue curves.
• Welds are assessed with the structural stress method and its master fatigue curve, which is far less sensitive to the mesh than reading peak stresses at the weld toe.
• Ratcheting is checked with shakedown limits or by running several load cycles in an elastic-plastic model.

Our guide to weld fatigue analysis explains structural stress methods in more detail.

• Nozzle loads: WRC 537 (formerly WRC 107) and WRC 297 give quick local stresses within their parameter limits. FEA takes over outside those limits, for closely spaced or hillside nozzles and for large piping loads.
• Saddles: horizontal vessels are traditionally checked with Zick's method, and FEA handles wear plates, stiffening rings and unusual saddle designs.
• Skirts, legs and lugs: local shell stresses, lug strength and weld stresses, including during lifting and erection.

Load-carrying brackets and lugs are everyday FEA work, as in our FEA of a beam bracket for structural integrity.

• Flanges: standard flanges follow their rated pressure classes, but custom and large flanges need design calculations, and FEA shows flange rotation, bolt stress and the gasket contact pressure that keeps the joint tight. Our guide to heat exchanger CFD and FEA covers flanged joints in heat exchangers.
• Thermal stresses: temperature gradients through the wall and between parts, and transients during start-up, shutdown or upsets. A thermal analysis provides the temperature field, which is then applied to the structural model.

Our transient thermal analysis of a plate under a laser heat source shows how temperatures develop over time, and our coupled thermal-mechanical analysis of a 1U CubeSat shows temperatures driving stresses in one model.

• The design basis: code and edition, design conditions, materials and allowable stresses, with the analysis done in the corroded condition.
• The geometry, mesh and a mesh sensitivity check.
• Loads, boundary conditions and the load combinations used.
• Results for each failure mode, with a clear pass or fail against each limit.
• Recommendations wherever a change is needed.

Vessels built to European or British standards follow the same ideas, in EN 13445-3 (Annexes B and C) and PD 5500. For an overview of simulation across the energy sector, see our guide to CFD and FEA in the energy industry.

• Drawings or 3D CAD of the vessel, or drawings for our 3D CAD team to model.
• The design data: design pressure and temperature, corrosion allowance, code and edition.
• Material specifications and grades.
• Nozzle load tables, and wind and seismic data where relevant.
• Cyclic service details and the lifting arrangement, if they apply.

Cover photo: Red Shuheart on Unsplash