When designing pressure vessels with nozzles supporting agitators, fatigue analysis is crucial to ensure long-term reliability. While Finite Element Analysis (FEA) provides a detailed evaluation, a simpler and quicker method can be used by leveraging Welding Research Council (WRC) analyses, fatigue curves, and appropriate correction factors. This article presents a streamlined approach to fatigue assessment without FEA, helping execute pressure vessel calculations quickly and efficiently.
An agitator nozzle is a nozzle on static equipment, designed to support a mechanical agitator, typically used for mixing or maintaining homogeneity in process fluids. These nozzles experience significant cyclic loading due to the rotational and fluctuating forces from the agitator. The main sources of fatigue loading include:
-
Bending moments from dynamic forces of the agitator shaft
-
Torsion and shear forces due to the fluid reaction and mechanical movement.
-
Constant weight from the agitator motor positioned on top of the nozzle
To improve fatigue resistance, agitator nozzles are often stiffened using reinforcing pads, gussets, or increased thickness at the nozzle-vessel junction. However, despite these reinforcements, welded joints remain the critical fatigue points due to stress concentrations and potential imperfections.
These are the steps engineers should follow in order to perform fatigue assessment of the agitator nozzle, without FEA. Please note that pressure or temperature fluctuations are not considered on the agitator nozzle. A similar assessment however can be applied accordingly during detailed phase of pressure vessel analysis.
1. Using WRC Analysis to Determine Stresses
WRC bulletis, specifically WRC 537 (since typically agitator nozzle is positioned on the center of a spherical part of a torispherical end) provide a method to calculate local stresses at nozzle-vessel junctions caused by external loads. By applying WRC calculations, we obtain membrane and bending stresses at critical points. However, WRC does not inherently account for weld effects, which are essential in fatigue assessment.
2. Considering Welded Joint Effects
Since the nozzle is a welded component, it requires additional considerations beyond WRC results. Welds introduce stress concentrations and defects that lower fatigue strength. To compensate for this:
-
Apply a Fatigue Strength Reduction Factor (FSRF or Kf) to the WRC-calculated stress.
-
Consider Stress Concentration Factors (SCF) due to weld geometry (1.5 – 3.0 for fillet welds).
-
Use weld fatigue classifications (FAT values) from EN 1993-1-9, IIW, or ASME VIII-2 Annex 3.F.
3. Choosing Between S-N Curves or Haigh Diagrams
To assess fatigue life, two main methods apply:
-
S-N Curves (Wöhler Diagrams): Used to estimate the number of cycles until failure based on material-specific fatigue data. The stress range (Δσ) from WRC is adjusted using SCF and compared against the allowable fatigue strength for the expected cycle count.
-
Haigh Diagram (Mean Stress Correction): Suitable for cases where mean stress effects influence fatigue life. The diagram determines if the stress state falls within the infinite-life region based on adjusted stress values and Ensures the combination of mean stress (σm) and alternating stress (σa) remains within safe limits.
Practical Implementation for an Agitator Nozzle and Step-by-Step Fatigue Check:
-
Perform WRC 107/297 Analysis to obtain membrane and bending stresses.
-
Apply Kf and SCF to adjust for weld effects and local stress concentrations.
-
Determine the stress range (Δσ) for fatigue assessment.
-
Compare against S-N curves to estimate fatigue life or use a Haigh diagram for infinite-life checks.
-
If necessary, refine weld quality or design parameters to reduce stress levels.
Conclusion
By combining WRC analysis, weld correction factors, and fatigue curves, a reliable fatigue assessment can be performed without FEA. This approach provides a quick yet effective method to evaluate nozzle integrity under cyclic loading. While conservative, it ensures safe and efficient design for pressure vessels with agitator-mounted nozzles. For complex cases, further validation with FEA or strain gauge testing may be recommended.
