Last Updated: Aug 19 2015, By: LRB

The requirements for FEA reports are outlined in CSA B51-14 annex J “Annex J (normative) Requirements regarding the use of finite element analysis (FEA) to support a pressure equipment design submission”. These requirements are mandatory to B51, but not universally accepted across Canada. At this date (Aug 2015) Alberta reviews are still done to ABSA AB-520, a similar but not identical document. Some extracts from the B51 standard are included in italics below.

J.1 General

This analysis method requires extensive knowledge of, and experience with, pressure equipment design, FEA fundamentals, and the FEA software involved. The FEA software selected by the designer shall be applicable for pressure equipment design.

FEA programs are physics engines. We have found that any of the main commercially available programs are suitable for pressure vessel analysis. In particular we use SolidWorks Simulation and ABACUS, but others also work.

J.2 Submission requirements

FEA may be used to support pressure equipment design where the configuration is not covered by the available rules in the ASME Code. The designer should check with the regulatory authority to confirm that use of FEA is acceptable. When this method is used to justify code compliance of the design, the requirements in Clauses J.3 to J.10 shall be met.

In general we find it acceptable to use FEA for design of non code items or portions of items. It is important to include code calculations for those portions of the vessel that are code calculable. On rare occasions a product is forced to be re-designed so that regular code sections can be used.

J.3 Special design requirement

The FEA analysis and reports shall be completed by individuals knowledgeable in and experienced with FEA methods. The FEA report shall be certified by a professional engineer.

We sometimes get asked to provide a report of our experience. See our Contacts page where we have posted qualification resumes for our review engineers. For example, the resumes of Ben, Cameron and Matt
have been written to present qualifications for performing FEA and reviewing FEA reports.
For the sections J.4 through J.10 we refer to sample reports found in our FEA samples section. These reports are written to meet this or various previous provincial guidelines. Beyond this CSA guideline, our sample reports are also modified to answer common questions from CRN review engineers and customers.

J.4 Report executive summary

The FEA report shall contain an executive summary briefly describing how the FEA is being used to support the design, the FEA model used, the results of the FEA, the accuracy of the FEA results, the validation of the results, and the conclusions relating to the FEA results supporting the design submitted for registration.

J.5 Report introduction

The report introduction shall describe the scope of the FEA analysis relating to the design, the justification for using FEA to support the design calculations, the FEA software used for the analysis, the type of FEA analysis (static, dynamic, elastic, plastic, small deformations, large deformations, etc.), a complete description of the material properties used in the analysis, and the assumptions used for the FEA modelling.

J.6 Model description


The report shall include a section describing the FEA model used for the analysis. The description shall include dimensional information and/or drawings relating the model geometry to the actual pressure equipment geometry. Simplification of geometry shall be explained and justified as appropriate. The mesh and type (h, p, 2D, 3D), shape, degrees of freedom, and order (2nd order or above) of the elements used shall be described. If different types of elements (mixed meshes) are used, a description of how the different elements were connected together shall be included. When shell elements are being used, a description of the top or bottom orientation with plots of the elements shall be included and shall indicate if they are thick or thin elements.


The model description shall include a list of all assumptions.


The turn angle of each element used on inside fillet radii shall be indicated.

The turn angle is simply the number of elements it takes to go around a circle. This Inventor support page explains the use of a turn angle. It is normal that a mesher needs around 8 elements to get around a circular hole which would produce a turn angle of 45 degrees per element. Decreasing the turn angle increases the number of elements and the accuracy of the FEA results, however not all areas of a model need to be highly accurate. The turn angle does not provide any predictive value, and the B51 standard provides no acceptance criteria. The use of an error plot as discussed in J.6.8 below is a much more useful measure of mesh and results quality.


The method used to select the size of mesh elements with reference to global or local mesh refinement shall be indicated.

We use the error plot to determine if the mesh is adequately refined. Beyond the scope of this standard, it is important to realize that pressure vessels have areas of discontinuity where in theory the stress approaches infinity as the mesh size is decreased. In practice the vessel experiences stresses above the yield point. Refer to our sample jobs for linearization analysis that can deal with stresses approaching infinity.


When items in contact (e.g., flange joints, threaded joints) are modeled, the model shall describe how two separate areas in contact are linked. Adequate mesh size shall be used to ensure that the elements are small enough to model contact stress distribution properly.


Boundary conditions, such as supports, restraints, loads, contact elements, and forces, shall be clearly described and shown in the report (present the figures). The method of restraining the model to prevent rigid body motion shall also be indicated and justified. When partial models are used (typically based on symmetry), the rationale for the partial model shall be described with an explanation of the boundary conditions used to compensate for the missing model sections.


The FEA report shall include validation and verification of FEA results. Validation should demonstrate that FEA results correctly describe the real-life behavior of the pressure equipment, and verification should demonstrate that a mathematical model, as submitted for solution with FEA, has been solved correctly.

Verification is as simple as comparing the reaction forces from the FEA run with the theoretical loads that can be calculated at the boundary conditions. What is acceptable for validation varies by reviewer. Rarely FEA runs must be provided that predict burst test results. Occasionally strain gauge testing or displacement testing must be provided that can be run against a standard non destructive hydrotest. Other methods used are comparing Roark’s predicted radial displacement of a shell with the results of a model run. Most commonly, it is recognized that a FEA run that meets the other requirements of this standard is far more accurate than other available methods of study so no further physical testing proof is required.


The accuracy of the FEA results shall be included in the FEA report, either by the use of convergence studies or by comparison to the accuracy of previous successful in-house models. An error of 5% or less from the convergence study shall be acceptable.

Note: FEA inaccuracy usually consists of discretization errors, which result from matching geometry and displacement distribution due to the inherent limitation of elements, and computational errors, which are round-off errors from the computer floating-point calculation and the formulations of the numerical integration scheme.

A convergence study only proves that a single point of a model has converged, whereas an error plot proves a whole model and does not required multiple FEA runs. As mentioned in J.6.4, we use error plots to prove convergence. Also mentioned above, not all areas of a pressure vessel model converge.  The areas that do not converge require special study that cannot be handled by convergence studies. These areas are usually handled by Linearization as outlined by ASME VIII-2 part 5.

J.7 Acceptance criteria

The criteria for acceptance of the FEA results shall be based on the code of construction and factor of safety established under that code. The FEA methodology may be based on another code. The acceptance criteria and code reference shall be presented in the report.

Note: For example, if the code of construction is Section VIII, Division 1, of the ASME Code, the allowable stress values are from Section VIII, Division 1, of the ASME Code. The FEA methodology could be based on Section VIII, Division 2, of the ASME Code (Figure 5.1).

J.8 Presentation of results


The following information and figures in colored prints shall be presented:
(a) resultant displacements (plot);
(b) deformed shape with undeformed shape superimposed;
(c) stress plot with mesh that
(c)(i) shows fringes using discrete color separation for stress ranges or plots; and
(c)(ii) allows comparison between the size of stress concentrations and the size of the mesh;
(d) plot with element stress and a comparison of nodal (average) stress vs. element (non-averaged) stress;
(e) reaction forces compared to applied loads (free-body diagrams);
(f) stress linearization methodology and the stress values in the area of interest; and
(g) accuracy of the FEA results.
The results shall be plotted to graphically verify convergence. The x axis of this plot shall show some indication of mesh density in the area of interest (number of elements on a curve, elements per unit length, etc.). This is necessary to show true convergence over apparent convergence that is due only to a relatively small change in the mesh.


When plots or figures are presented, an explanation relating to each figure shall be included to describe the purpose of the figure and its importance.

J.9 Analysis of results

Overall model results, including areas of high stress and deformation, shall be presented with acceptance criteria. The analysis shall include a comparison of the results with acceptance criteria.

Results that are to be disregarded shall be identified, and the determination to disregard them shall be justified.

J.10 Conclusion

As a minimum, the conclusion shall include
(a) a summary of the FEA results in support of the design;
(b) a comparison of the results and the acceptance criteria; and
(c) overall recommendations.