May 2022

Process Optimization

Assessment protocol for nozzle loads on pressure vessels

From a historical perspective, the traditional approach to deal with “unknown magnitude of nozzle loads” can be summarized here.

Stikvoort, W., P3 Engineering

From a historical perspective, the traditional approach to deal with “unknown magnitude of nozzle loads” can be summarized here.

In EN 13445-3 (EU)1 clause and, if the ratio Φp = 1, then the other ratios, ΦZ and ΦB, must be zero for the interaction requirements to be met, although there is some provision in equations 16.4-15 and 16.5-15 for the other ratios to be slightly greater than zero. The equivalent clauses, as indicated in PD 5500 (UK),2 are, respectively, G. and G., and the equations G.2.8-13 and G.2.8-39.

This means that for the initial design, some provision must be made for nozzle loads that are not yet known. This has always been the case, and many companies have produced their own data tables of nozzle loads that are used for the initial design. The piping stress analysts then know that they must maintain the calculated nozzle loads to less than the tabulated values and design the piping accordingly.

In the absence of tabulated nozzle loads for a particular job, vessel designers must use their engineering judgement and experience to assess whether the loads are likely to be small (moderate temperatures and well-designed piping with plenty of flexibility), or large (high temperatures, compact layout with little piping flexibility) and then design the nozzles for appropriate, estimated loads. The designer may choose to use tabulated loads from another similar project.

Some degree of overdesign always exists in any pressure vessel, but it is not usually practical to wait until the piping design has been completed before beginning to design the vessels. If the vessels are designed before the nozzle loads are known, it is often cheaper to overdesign the nozzles rather than try and modify the design at a later stage after fabrication has begun.

Where ASME BPVC Section VIII Division 13 is the prevailing design code, the commonly used approach to assess nozzle loading is using WRC Bulletins 1074, 5375 and 2976—with the understanding that the internal pressure load must also be considered, which is not an integral part of the WRC bulletins.

To support the engineer involved in the design of pressure vessels, a protocol has been developed that enables the engineer to gain insight into the individually permissible loads on a flanged nozzle configuration of a pressure vessel. This protocol can be applied to recognized pressure vessel codes and/or standards including: EN 13445 (EU)1, PD 5500 (UK)2 and ASME BPVC Section VIII-Division 1(U.S.)3. The involvement of the piping stress analyst is limited to evaluating the piping reactions from the pipe stress analysis to the allowable nozzle loads determined by the vessel design engineer, considering only internal pressure.

It has been noted that in the methodologies contained in both EN 13445-3 (clauses 16.4.6 and 16.5.6) and PD 5500 (clauses G.2.8.2 and G.2.8.3), no external loads can be allowed by the nozzle exerted piping reactions if ΦP = Pdesign/MAWP = 1.

However, this implies that only external loads are allowed if ΦP < 1, which means that a certain amount of “overdesign” must be created compared to exclusively incorporating internal pressure loading in the nozzle design. ANNEX V of EN 13445-3 (amendment A8: 2019)7 states that a buffer should be considered for unknown nozzle loads that relate to the opening design. Literature8 highlights the doubts that have arisen about this approach.

From this perspective, an alternative approach has been developed that is based on the fact that nozzles designed for internal pressure still have sufficient load-carrying capacity left to accommodate the piping reactions on the nozzle. The advantage of this approach lies in the fact that, in contrast to the traditional approach outlined, the permitted (individual) nozzle loads can already be determined during the initial pressure vessel design by the vessel design engineer and can be made available to the piping stress analyst. Obviously, this requires the necessary coordination between the two engineering disciplines. This innovative approach has proven itself in successful applications for many years in predominantly statically loaded pressure vessels.

Determination of individually permissible loads

The method described by the author9, which is based on Dekker and Bos10, was used to determine the individually permissible nozzle loads.

FIG. 1 shows the acting loads on the nozzles. The shear stress caused by the transverse force and the torsional moment at the nozzle-shell intersection are neglected, since it is assumed by this simple approximation that their contribution will normally not exceed 0.15 f.

FIG. 1. Nozzle configurations and loadings.
FIG. 1. Nozzle configurations and loadings.

In case of doubt, the maximum total shear stress in the shell at the outer diameter of the nozzle should be calculated according to clauses and, respectively, of EN 13445-3:2014 / A8:20197, or alternatively according to PD 5500 clause G. (f) and G. (f)2. If it appears that the limit of 0.15 f is exceeded, a more rigorous analysis should be considered. The applicable formulas for calculating the permissible individual nozzle loads are included in TABLE 1. Nomenclature is listed in TABLE 2.

Note: In the case of relatively thin-walled nozzle necks—i.e., the ratio of shell thickness and nozzle neck thickness exceeding 1—it is recommended to divide the permissible individual loads at the nozzle-shell intersection by that ratio (TABLE 3). This is due to the possibility that the stress in the nozzle neck may be a determining factor.

Assessment protocol

The following step-by-step approach explains the roles of the vessel design engineer and the piping stress analyst.

Vessel design engineer:

  • Step 1: The vessel design conforms to the applicable code or standard considering only internal design pressure.
  • Step 2: The allowable individual loads for each process nozzle are calculated, including the flange.
  • Step 3: The vendor/vessel manufacturer furnishes the individual allowable forces and moments for each process nozzle-vessel intersection, as well as for the nozzle flange, in a tabular form on the appropriate drawing of the relevant equipment item. Normally this should be done twice: in the preliminary bid phase, and in the final mechanical design phase.
  • Step 4: The information compiled in Step 3 must be transferred to the piping stress analyst.

Piping stress analyst: The starting point for the piping stress analyst is the compliance of the connected piping with the applicable design code:

  • Step 5: Determine exerted nozzle loads (piping reactions) using an accepted software program.
  • Step 6: Prepare a summary of piping reactions for the relevant process nozzles.
  • Step 7: Provide load interaction checks at each process nozzle-vessel intersection and flange connection. In practice, this often means a joint effort of the vessel design engineer and the piping stress analyst. Both disciplines must be convinced that simultaneous action of internal pressure and external loads are acceptable.

Linear load interaction rules that apply are shown in TABLE 4. The result of the load interaction rules must be recorded in the piping stress report.

Note: In cases where the piping reactions are not permissible, re-routing of the piping system or rearrangement of the pipe supports should be considered. Often, discounting the nozzle flexibility in the pipe stress analysis results in a drastic reduction of the piping reactions—this is certainly the case with relatively thin-walled pressure vessels where the nozzles are not equipped with reinforcing pads.

The pressure vessel nozzle is considered acceptable if the load interaction conditions are met. It is the author’s view that the nozzle design according to the recognized codes/standards will provide a reasonable amount of piping-imposed loading ability. The worked example here will demonstrate this approach.

Worked example

A pressure vessel with an outer diameter of 2,000 mm is equipped with torispherical heads (type korbbogen, according to DIN 2801311). The wall thicknesses are net 10 mm. A flush nozzle with a nominal diameter of 12 in. (NB 300) is fitted to the cylindrical shell. The nozzle neck of this nozzle has a nominal thickness of 17.48 mm (corresponds to schedule 80) and is provided with a Class 150 welding neck flange (according to ASME B16.5). The bottom is equipped with a flush 20-in. nozzle (NB 500), of which the nominal neck thickness is 15.09 mm (Schedule 40) and is located in the middle of the curved part of the head. This nozzle is also equipped with a Class 150 welding neck flange.

The shell and head are made of ASTM A515 Grade 60 material, while the nozzle necks are made of ASTM A106 Grade B seamless pipe material. Both nozzle flanges are made of ASTM A105 forged material. The nozzle flange connections are provided with a spiral wound gasket according to ASME B16.2012. The pressure vessel has a design pressure of 10 bar and a design temperature of 200°C. The rated pressure of the Class 150 flange is 13.8 bar at 200°C. No corrosion allowance applies.The design code for this pressure vessel is EN 13445. The design stress is 126 MPa (two thirds the yield strength at 200°C).

  • Step 1: The design calculation is performed by the vessel design engineer according EN 13445-3 considering only internal pressure (TABLE 5).
  • Step 2: The maximum allowable individual loads of Nozzle N1 located on the spherical part of the head and Nozzle N2 located on the cylindrical shell are determined. The calculation schedule is shown in TABLE 6.
  • Step 3: A summary of individual allowable flanged nozzle loads is shown in TABLE 7.
  • Step 4: Successively, the vessel design engineer must provide the piping stress analyst with the calculated allowable individual allowable loads. This implies that the vessel design engineer must make the summary of Step 3 available to the piping stress analyst.
  • Step 5: The pipe stress engineer performs the pipe stress analysis using software approved by the inspecting body and client. Determining the piping reactions is part of the pipe stress analysis.
  • Step 6: The pipe stress engineer successively makes a summary of the loads acting on the process nozzle (piping reactions). For the relevant nozzles N1 and N2, the loads in TABLE 8 have been derived from the formal pipe stress analysis.
  • Step 7: Perform load interaction checks for nozzles N1 and N2.

° Nozzle N1: At nozzle-head intersection: utilization factor = 0.9392 < 1 → OK!

   At flange facing: utilization factor = 0.3218 < 1  OK !

° Nozzle N2: At nozzle- shell intersection: utilization factor = 0.9739 < 1  OK!

   At flange facing: utilization factor = 0.2623. < 1  OK!

Conclusion: All piping reactions remain within acceptable limits.


The protocol developed is ideal for processing in a spreadsheet. The worked example proves its applicability and is a guideline for the user. In addition, it lends itself well to implementation in an engineering specification. The advantage lies in the simplicity of the protocol and it provides a safe approach to the assessment of nozzle loads. Time is also saved when using the protocol and additional costs for strengthening the nozzles can be avoided. The protocol has an excellent track record over many years in the hydrocarbon processing industry (HPI). HP


The author would like to express sincere thanks to Keith Kachelhofer from MacAljon Fabrication/MacAljon Engineering (USA) and Daniel Hofer from BASF (Germany) for reviewing the manuscript.


  1. EN 13445 Standard, “Unfired pressure vessels: Part 3—Design,” EU, Iss. 5, 2018.
  2. PD 5500 “Specification for unfired fusion welded pressure vessels,” British Standard, 2018 (UK).
  3. American Society of Mechanical Engineers (ASME) BPVC, “Rules for construction of pressure vessels,” Section VIII, Div. 1, 2017.
  4. Welding Research Council (WRC) Bulletin 107, “Local stresses in spherical and cylindrical shells due to external loadings,” January 1965.
  5. Welding Research Council (WRC) Bulletin 537, “Precision equations and enhanced diagrams for local stresses in spherical and cylindrical shells due to external loadings for implementation of WRC Bulletin 107.”
  6. Welding Research Council (WRC) Bulletin 297, “Local stresses in cylindrical shells due to external loadings on nozzles,” supplement to WRC Bulletin 107.
  7. EN 13445 Standard, “Unfired pressure vessels: Part 3—Design,” Addendum A8, 2019.
  8. Stikvoort, W., “Review of buffer approach to compensate unknown nozzle loads,” American Journal of Engineering Research (AJER), Vol. 9, Iss. 3., 2020.
  9. Stikvoort, W., “Load capacity limits of flanged pressure vessel nozzles,” Chemical and Petroluem Engineering, January 2018.
  10. Dekker, C. J. and H. J. Bos, “Nozzles—on external loads and internal pressure,” International Journal of Pressure Vessels and Piping, June 1997.
  11. DIN 28013 “Ellipsoidal dished ends,” König + Co., 1993.
  12. American Society of Mechanical Engineers (ASME) B16.20, “Metallic gaskets for pipe flanges,” 2017.

The Author

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