Evaluation of Pressure Vessels with External Nozzle Loads
There are two commonly used methods of evaluating pressure vessels subjected to external nozzle loads. The first is using hand calculations and the method described in Welding Research Council (WRC) Bulletin 107, “Local Stresses in Spherical and Cylindrical Shells due to External Loadings”. The second is using finite element analysis. This article briefly discusses these two methods and some things to consider if you are unfamiliar with their use.
External nozzle loads must be considered in the design of pressure vessels as required by Paragraph UG-22 in Section VIII, Division 1 of the ASME Boiler & Pressure Vessel Code. While the external nozzle loads may be negligible for smaller nozzles such as those associated with instrumentation, larger nozzles such as inlets and outlets may have substantial loads.
Evaluation Using WRC 107/297/537
The first commonly used method for evaluating external nozzle loads is using WRC 107, or one of the related Welding Research Council bulletins such as WRC 297 “Local Stresses in Cylindrical Shells due to External Loadings on Nozzles – Supplement to WRC Bulletin No. 107”, or WRC 537 “Precision Equations and Enhanced Diagrams for Local Stresses in Spherical and Cylindrical Shells due to External Loadings for Implementation of WRC Bulletin 107”. While this method is fairly straight-forward it is not for the faint-hearted. The method is based on empirical testing and involves using a variety of graphs (or equations) to determine variables in calculating the stresses in the pressure vessel at a nozzle. Luckily, most of the software available for designing ASME Section VIII, Division 1 pressure vessels have the ability to evaluate vessels for external nozzle loads using these methods. However, even if you are using software that has this capability you should be familiar with the assumptions and limitations of WRC 107 (or one of the other related bulletins, if applicable) to ensure the accuracy of your results.
Evaluation Using Finite Element Analysis
The second method commonly used in evaluating pressure vessels subjected to external nozzle loads is finite element analysis (FEA). This method may be chosen for a variety of reasons. It may be due to vessel geometry, limitations using WRC 107, or that FEA is being used to evaluate other load cases. Mandatory Appendix 46 of Section VIII, Division 1 permits using the Design by Analysis methods in Section VIII, Division 2 when rules are not provided in Division 1 (such as evaluating vessels for external nozzle loads). As such, if FEA is used to evaluate a pressure vessel for external nozzle loads the engineer should be experienced with the methods, requirements, and acceptance criteria of Section VIII, Division 2. For example, the engineer performing the finite element analysis should know how to properly classify the stresses (e.g. primary, secondary, membrane, bending, etc.) from the FEA results.
Combining Results
Whether you use WRC 107 or FEA to evaluate external nozzle loads, the resulting stresses should be combined with those from other load cases. If you are using pressure vessel design software, this is usually done for you. If not, or if you are using FEA to evaluate the pressure vessel for external nozzle loads, you will have to combine the resulting stresses with those from other loads cases, as appropriate.
Source of External Nozzle Loads
In evaluating a pressure vessel for external nozzle loads, you should consider the source of the loads. The reason for this is sometimes the magnitude of the external nozzle loads provided are overly conservative. When this occurs, you can end up unnecessarily adding reinforcement to the pressure vessel or making other design modifications to accommodate these loads.
Generally, external nozzle loads are provided from one of two sources. The first is from “standard nozzle load tables”. These are usually easily identified in that the loads are based on the size of the nozzle rather than the function (e.g. inlet, vent, etc.). These loads also tend to be nice round numbers and are often the same magnitude regardless of direction. The second source of external nozzle loads is from a piping system stress analysis. These loads will usually not be round numbers and will vary depending on the nozzle and load case.
Standard Nozzle Load Tables
With standard nozzle load tables there is conservatism built into the values since they are to be used for all nozzles of the same size regardless of the function. For example, the same magnitude of loads will be applied to a 3-inch vent as a 3-inch inlet nozzle. Because of this, standard nozzle load tables will use the largest anticipated loads for any nozzle of a particular size for all of the nozzles of that size. Normally this would not be a problem because the thickness of the pressure vessel is usually the same at the location of the 3-inch vent and the 3-inch inlet nozzle. However, the problem is these standard nozzle load tables are often used for a variety of pressure vessels. It’s sort of a one-size-fits-all scenario where the standard nozzle load table is used for all vessels regardless of the type of pressure vessel, purpose of the nozzle, location of the vessel, and even project. And that’s where the conservatism comes in. In order to encompass all of the possible permutations, the magnitudes of the nozzle loads will be conservative.
Nozzle Loads from Piping System Stress Analysis
External nozzle loads from a piping system stress analysis are almost always more accurate than those from standard nozzle load tables. This is because these loads are project and nozzle specific. The magnitude of the nozzle loads from the piping system stress analysis, however, may be overly conservative depending on the boundary conditions used in the analysis of the piping system. Sometimes the analyst will completely constrain the ends of the model of the piping system where it connects to the pressure vessel. This is sometimes referred to as treating the pressure vessel as an anchor. While a pressure vessel can be considered relatively stiff, it is not infinitely rigid at the nozzles. Completely constraining the model of the piping system where it connects to the pressure vessel will result in external nozzle loads that may be an order of magnitude higher than reality.
Removing Unnecessary Conservatism in Nozzle Loads
While the magnitude of the nozzle loads may be overly conservative, it is unlikely you will be able to get your customer to remove some conservatism without first showing the design of the pressure vessel would have to be modified. Companies are not apt to change standard nozzle load tables, often because the company’s engineer you are dealing with does not know the details involved in defining the magnitude of the nozzle loads in the tables. Without knowing these details, there is a reluctance to reduce the loads.
If the external nozzle loads provided are from a piping system stress analysis and the ends of the model of the piping system were completely constrained, the loads can be reduced by more accurately modeling the boundary conditions of the piping system. This entails the analyst performing the piping system stress analysis defining stiffness values at the ends of the model of the piping system where it connects to the pressure vessel. Sometimes the analyst will estimate the stiffness based on experience using a rough order of magnitude value. Other times the pressure vessel engineer can provide values for the stiffness of the pressure vessel at the nozzles’ locations for the piping analyst to use. Both of these methods will produce more accurate loads at the nozzles.
Conclusion
In conclusion, evaluating pressure vessels for external nozzles loads is not overly complicated but does require either experience with WRC 107 or finite element analysis. This includes experience with any pertinent software, an understanding of the assumptions and limitations of WRC 107, and a thorough understanding of the applicable sections of the ASME Boiler & Pressure Vessel Code.