In piping, “allowable stress” has two meanings:

1. Material-Based Allowable Stress:
   A property of the material at a given temperature, found in code tables (e.g., Appendix A in ASME B31.1). These values vary by material, temperature, and code of construction.

2. Stress Acceptance Criteria:
   Based on the material’s allowable stress, but adjusted depending on the type of loading and load case—such as sustained or thermal expansion stresses.

Key Examples from ASME B31.3:

1. Sustained Stress (SL):
   Must not exceed the allowable at operating temperature:
   SL < Sh
   where Sh = allowable stress at elevated temperature.

2. Expansion Stress (SE):
   Must meet fatigue-based limits:
   SE < f × [1.25(Sc + Sh) – SL] or SE < f × (1.25Sc + 0.25Sh)

   Sc = allowable at ambient temperature

   f = fatigue reduction factor, where: f = 20(N)^–0.333

   N = number of thermal cycles

These criteria ensure the system can safely handle both sustained loads (like pressure and weight) and cyclic loads (like thermal expansion).

FEA is a computational method used to calculate stresses, forces, and displacements across complex geometries, regardless of size or thickness. It provides detailed stress distribution from loads like pressure and temperature, helping engineers identify critical stress points.

In pressure vessel design, FEA is used to evaluate nozzle loads, stiffness, and local stresses.
In piping systems, it helps define stress intensification factors, stiffness values, and sustained stress indices for use in pipe stress analysis programs.

Standard stress intensification factors (SIFs) and sustained stress indices (SSIs) in ASME B31.1 and B31.3 are only valid for D/t ratios up to 100. For larger D/t ratios, these values must be calculated using more advanced methods.

Finite Element Analysis (FEA) is commonly used:

1. Linear elastic FEA is applied to calculate SIFs.

2. Nonlinear FEA is used to determine SSIs.

The results from FEA can then be used in the pipe stress program to ensure code compliance.

The significant difference between WRC-537 and WRC-107 is that 537 provides curve fits for each of the curves and adds “extrapolated” curves with curve fits as well for several of the cylindrical host curves; in these cases, both the original curves and the extrapolated curves are provided and clearly identified. 

FEA should be chosen over DBR in the following cases: 

1. The pressure vessel’s geometry, loading, service conditions exceed the scope of simplified rules.
   
   
2. The optimization and safety evaluation of the pressure vessel requires precision.
   
   
3. The fatigue and local effects of the pressure vessel need to be addressed explicitly. 
   

FEA can offer detailed, localized characterization of stresses under realistic conditions far beyond the generalized rules of DBR. It is an essential analysis method for complex designs and critical applications to ensure the nozzle withstands complex loading conditions. 

FEA analysis for nozzles can be challenging due to the need for precise modeling, good understanding of the computational rigor, and expert judgment to align with code requirements. 

When nonlinear analysis is started, the stress-strain curve for the given materials must be established. There is guidance in ASME Section III-2 Part 3, Annex 3-D for the development of the stress-strain curve based on the material type, operating temperature and thickness. With the proper stress-strain curves, the nonlinear behavior of the component can be properly determined past the yield strength point. 
 

FEA should be considered when traditional methods like WRC 107/297/537 are too conservative or not applicable due to complex geometries. It offers a deeper and more flexible analysis in the following cases:

1. When WRC methods fall short:
   Use FEA for geometries outside WRC limits or when WRC gives overly conservative results.

2. For cross-checking:
   FEA can validate or refine WRC-based stress estimates.

3. To assess global effects:
   WRC focuses on local junction stresses, while FEA can capture global structural behavior often missed by design-by-rule approaches.