FEA Analysis of Vessel Skirt with Opening (HH-VV-103)
ASME VIII-2 structural analysis of a stainless-steel vessel skirt with nozzle openings under combined pressure, wind, and seismic loading all 4 load cases pass with 65% maximum utilization
Contents
1. Executive Summary
A vertical process vessel (HH-VV-103) with a skirt support containing nozzle openings required structural validation. The skirt opening weakens the load path between vessel and foundation, and the vessel must withstand combined internal pressure, wind shear, seismic forces, and hydrostatic test conditions. The critical engineering question: does the skirt with openings maintain code-compliant stress levels under all loading scenarios?
- Linear static FEA per ASME VIII Div 2, Part 5, Ed. 2021
- All 4 load cases PASS, plastic collapse protection verified
- Max primary local membrane stress: 117.55 MPa vs 179.7 MPa allowable (65% utilization)
- FEA validated against hand calculation, hoop stress within 0.006%
- Mesh convergence confirmed with <1% error across element sizes
Business Impact: This analysis confirmed the vessel skirt design is safe for service, eliminating the need for costly redesign and enabling the client to proceed with fabrication confidence. The documented stress margins provide assurance for future regulatory reviews.
2. Project Overview
Design Parameters
Figure 1: General Arrangement Drawing (GAD)
3. FEA Methodology
Linear static FEA using high-order SOLID186 elements (20-node, 3 DOF/node, quadratic displacement). The shell geometry extends 2.5*sqrt(RT) from the skirt-to-shell junction to ensure stress decay is fully captured and boundary effects do not contaminate the Stress Categorization Line (SCL) results.
Model Statistics
Mesh Quality
Figure 2: FE Mesh – 40K SOLID186 elements
4. Boundary Conditions & Loading
The vessel model includes the full skirt with nozzle openings, shell, heads, and nozzle connections. Boundary and loading conditions are applied as follows:
- Internal pressure: 0.8 MPa applied on all internal wetted surfaces (shell, heads, nozzle bores)
- External pressure: 0.1013 MPa applied on external surfaces for vacuum load case
- Nozzle thrust forces: Applied at nozzle cutouts N02 and N02A to balance pressure end loads
- Hydrostatic pressure: Applied on internal surfaces for water-filled conditions
- Wind loading: Wind shear force and overturning moment applied at top of skirt
- Seismic loading: Seismic shear force and overturning moment per site-specific seismic data
- Gravity: Standard Earth gravity applied to entire assembly
- Fixed boundary: All DOFs fixed at skirt base (foundation bolt circle)
Figure 3: Fixed boundary conditions at skirt base
Figure 4: Internal pressure + thrust + wind loading (LC1A)
5. Load Case Analysis
LC1A: MAWP + Wind
Internal design pressure combined with wind-induced lateral loading:
- Internal pressure: 0.8 MPa + hydrostatic head
- Nozzle thrust forces at N02 and N02A
- Wind shear force + overturning moment
- Self-weight (gravity)
LC1B: MAWP + Seismic
Internal design pressure combined with seismic loading, governing case:
- Internal pressure: 0.8 MPa + hydrostatic head
- Nozzle thrust forces at N02 and N02A
- Seismic shear force + overturning moment
- Self-weight (gravity)
LC2: External Pressure (Vacuum)
Full vacuum condition with gravity and thrust loads:
- External pressure: 0.1013 MPa
- Nozzle thrust + self-weight
LC3: Hydrotest
Elevated test pressure at ambient temperature with water-filled vessel:
- Test pressure: 1.2 MPa (1.5x MAWP)
- Hydrostatic head + self-weight
6. Detailed Results
Figure 5: Von Mises stress at skirt opening region
Figure 6: Displacement results
Stress Acceptance per ASME VIII Div.2
Primary Local Membrane (PL) - Skirt
Primary + Secondary (PL+Pb+Q) - Skirt
General Membrane (Pm) - Shell
Hydrotest (LC3)
7. Stress Linearization (SCL)
Stress Categorization Lines (SCL) were placed at all maximum stress areas per ASME VIII-2 guidelines. The SCL method separates total stress into membrane, bending, and peak components along a line through the wall thickness. This allows direct comparison with ASME allowable stress limits for protection against plastic collapse.
Figure 7: SCL analysis at skirt-to-shell junction
Figure 8: Equivalent stress contour – full model
8. Model Validation
Hoop Stress Validation
ASME VIII-2 Clause 4.3.10.2 hand calculation compared against FEA:
Mesh Convergence Study
Selected: 39,995 elements, converged within 0.6%.
Figure 9: Mesh convergence study – stress vs element count
9. Lessons Learned
Skirt Openings Demand Local Refinement
The stress concentration at skirt openings is highly geometry-dependent. The 2.5*sqrt(RT) modelling rule ensures sufficient shell length is captured to correctly represent the stress decay away from the discontinuity. Without adequate model extent, boundary effects contaminate the SCL results and produce unreliable stress categorization.
Seismic Governs Over Wind
LC1B (seismic) produced higher stresses than LC1A (wind) at every location: 117.55 MPa vs 94.66 MPa for PL. For vessels in seismic zones, wind loading alone is not sufficient; seismic must always be evaluated as the governing lateral load case. Engineers who only check wind loads may miss the governing condition.
SCL Placement Is Critical
SCL placement at skirt-to-shell junctions and around openings must follow ASME VIII-2 guidelines precisely. Misplaced SCLs can misclassify peak stresses as membrane stresses, leading to unconservative or overly conservative assessments. The SCL must pass through the thickness at appropriate locations away from geometric singularities.
10. What Could Have Gone Wrong
Omitting the Skirt Opening from the Model
Modelling the skirt as a continuous cylinder without the openings would miss the stress concentration entirely, predicting uniform low stresses and giving a false sense of safety. The opening creates the highest local membrane stresses in the entire analysis.
Shell Elements Instead of Solid Elements
Using shell elements at the skirt-to-shell junction would underestimate bending effects through the wall thickness. SOLID186 captures the 3D stress state essential for accurate SCL evaluation. Shell elements cannot provide the through-thickness stress gradient needed for stress linearization.
Ignoring Nozzle Thrust Forces
Without nozzle thrust (balancing forces from pressure on capped ends), the model would be unrealistically unstable. These forces are required per ASME VIII-2 to maintain structural equilibrium and their omission would produce incorrect stress distributions throughout the vessel.
11. Recommendations
For Fabrication
- Ensure proper weld preparation at skirt-to-shell junction, this is the highest-stress region
- Verify dimensional accuracy of skirt opening geometry to match the FEA model assumptions
- Apply post-weld heat treatment (PWHT) at nozzle-to-skirt weld connections if required by code
For Installation
- Ensure foundation bolt pattern matches the FEA fixed boundary condition assumptions
- Verify plumbness of vessel installation, eccentricity could increase bending at skirt base
- Confirm orientation of openings relative to prevailing wind direction matches design assumptions
For Inspection
- Prioritize NDE inspections at skirt opening edges, highest stress concentration area
- Monitor skirt-to-shell weld for fatigue indications if the vessel experiences cyclic wind or operational loading
- Schedule baseline thickness measurements at skirt opening for corrosion monitoring
12. Limitations & Assumptions
- Linear elastic material model – SA-240 GR316 at 90 deg C. No plastic redistribution modelled. Stress results are conservative relative to elastic-plastic analysis.
- Wind and seismic loads applied as static equivalent forces per design basis. Dynamic amplification effects are not explicitly modelled.
- Nozzle piping loads are applied as thrust forces only. If actual piping loads (moments) are available, the analysis should be revisited with those specific values.
- Weld residual stresses are not modelled. SCL results at weld locations should be interpreted with this limitation in mind.
- The model does not include corrosion-induced wall thinning. Future-state assessment would require updated geometry.
13. Conclusion
- All 4 load cases PASS – max utilization 65% at skirt (seismic, LC1B)
- PL+Pb+Q max utilization 41% – well within ASME limits
- Hydrotest: Pm = 64.2 MPa vs 196.65 MPa – ample margin
- FEA validated against hand calculation within 0.006%
- Mesh convergence confirmed within 0.6% error
- Global equilibrium verified – reactions match within 0.6%
Status: The vessel skirt with opening design is structurally adequate for all loading conditions, confirming safe operation under design, wind, seismic, and hydrotest scenarios. The design may proceed to fabrication with confidence.
Download the Full Technical Case Study
The full technical report includes:
- Stress linearization (SCL) results at critical locations
- Complete load case definitions (pressure, wind, seismic, hydrotest)
- Stress contour plots and displacement results for governing cases
- FEA modeling approach, element selection, and boundary conditions
- Mesh convergence and hand calculation validation
- ASME Section VIII Division 2 code compliance references