FEM Analysis of a Large Nozzle-to-Cylinder Shell Junction

By Doug Stelling


Due to anticipated piping system changes, it was necessary to evaluate a large diameter nozzle-to-cylindrical shell junction to assess the stresses in the nozzle, insert plate, and shell. The loadings considered were due to weight, pressure, and piping thermal expansion. For the nozzle-to-insert plate junction, the geometric parameters were well within the range of two commercially available computer programs which are based on the WRC 107 and WRC 297 Bulletins. Since the nozzle was reinforced with a thickened insert plate, an assessment was also attempted at the edge of the insert plate by assuming that the insert plate was a rigid plug with the same outside dimensions as the insert plate. However, the geometric parameters at the outside edge of the insert plate are somewhat outside the applicable limits of WRC methods.

At the nozzle-to-shell junction, the two programs yield reasonable, although somewhat different results; however, the programs yielded somewhat dubious results for the stresses at the edge of the insert plate. Therefore, a Finite Element Analysis (FEA) was conducted. The FEA gave comparable results to the other methods at the nozzle-to-shell junction, but are believed to be much more accurate at the insert plate-to-shell junction. The FEA results were then used to demonstrate that the nozzle is not overstressed for the assumed nozzle design loads.


The vessel cylindrical shell is 29 ft I.D. and 0.75 in. thick; the nozzle is 60 in. I.D. and 1 in. thick; and the nozzle opening in the shell is reinforced by a 118 in. wide by 121 in. high by 1.5 in. thick insert plate. The base material of the shell, insert plate and nozzle neck is carbon steel. The vessel was originally designed to the ASME Code Section VIII, Division 1. Since the Division 1 Code does not explicitly treat assessment of stresses at nozzle-to-shell junctions due to external loadings, the integrity of the nozzle was assessed using Division 2 allowable stress criteria.

In the evaluation, it was assumed that a nozzle pressure thrust load of approximately 90 kips due to internal pressure acting on the nozzle internal area should be included, and this is incorporated into the commercially available nozzle stress analysis programs. Although there are numerous papers written on the subject of nozzle load evaluation, the pressure thrust load is often overlooked or tacitly dismissed without a good explanation. It is our opinion that such a load must be considered when doing a detailed nozzle load evaluation, and stresses due to the pressure thrust cannot just be ignored. Since there are various methods for handling the pressure thrust load, a comparison of stresses due to internal pressure and the pressure thrust load was made using commercially available WRC 107 and WRC 297 programs, equations from WRC 368, and a commercially available FEA program.

The WRC 107 program calculates the stresses in the shell at eight points on the inside and outside surface at the nozzle junction due to external loads on the nozzle based on Bijlaard's method. The program also calculates the nominal circumferential and longitudinal stresses in a cylindrical shell due to internal pressure and adds these general membrane stresses to the stresses due to external loads. The program has an option which includes the effect of the pressure thrust load on the nozzle by adding it to the imposed external loads.

The WRC 297 program also calculates the stresses in a nozzle-to-cylindrical shell junction due to external loads. WRC 297 is indicated as being an improvement of the WRC 107 (Bijlaard's) methods in that the curves in WRC 297 cover a wider range of geometric parameters. The WRC 297 method also calculates the stresses in the nozzle neck as well as at eight points on the inside and outside surface around the nozzle. In the program used, the effect of the end pressure thrust load is also accounted for by assuming that the pressure thrust load should be added to the external nozzle loads. However, the stresses due to pressure thrust at then added to stresses calculated based on multiplying the nominal membrane stress in the shell by fatigue stress indices from the ASME Code Section VIII, Division 2. These intensified stresses are then added to those due to external loads.

The WRC 368 equations are indicated as being based on best fitting a polynomial solution to stress analysis results based on a parametric study of the nozzle-to-shell junction problem using the FAST 2 computer program. The WRC 368 equations only predict the local membrane stress intensity and surface stress intensity in the shell and the nozzle of the junction due to internal pressure and the end pressure load. WRC 368 is not used to evaluate imposed piping loads.

The FEA model was built in about two hours and the solution takes only about two minutes for one load case on a 100 MHz Pentium PC. The mesh consists of 720 elements representing a 45 degree wedge of the vessel. A comparison of the maximum membrane and total surface stress intensities (ksi) among the four methods for the case of internal plus pressure thrust load is shown below: 

Method Insert Plate Membrane (Pl) Insert Plate Surface
Nozzle Membrane (Pl) Nozzle Surface (Pl+Pb+Q)
WRC 107 8.7 19.0 N.A. N.A.
WRC 297 13.7 32.5 6.9 44.5
WRC 368 12.7 16.9 13.7 24.9
FEA 11.2 15.4 13.1 24.0

Based on the above, it appears that the WRC 107 program may under-predict the membrane stress in the shell, while the total surface stress seems reasonable. The WRC 297 program appears to over-predict the maximum surface stress in the shell and the nozzle by a wide margin while it under-predicts the nozzle membrane stress. The WRC 368 solution also appears to be in agreement with the FEA solution although it should be noted that the authors of the WRC 368 method indicate the stresses are within about ± 20%.

The stresses in the nozzle neck-to-insert plate and the insert plate-to-shell junctions were then determined and compared for the combination of pressure, weight, and external piping loads. In general, at the nozzle neck-to-insert plate junction, the stresses calculated using WRC 107 program are only about half as high as those calculated using the FEA program. The stresses calculated using the WRC 297 program are about 40 percent higher than those calculated using the FEA program. The implication of these differences for our particular problem was that if the WRC 107 solution is correct, the nozzle junction is not overstressed; however, assuming the WRC 297 solution is correct, the junction is overstressed. In the latter case, either the existing nozzle and insert plate had to be replaced with a stronger design or the piping loads had to be reduced.

The WRC 107 and WRC 297 programs were also used to calculate the stresses at the edge of the insert plate-to-shell junction assuming that the insert plate is a rigid plug with dimensions equal to the insert plate length and width. The stresses calculated in the shell at the periphery of the insert plate using the WRC 107 program are about five times higher than the stresses calculated by the FEA program. Using the same rigid plug assumption, the WRC 297 program predicts stresses which are eight times higher than the FEA program. The high stresses predicted in the shell at the edge of the insert plate by both the WRC-based programs are considered to be due to the over-conservatism of the rigid plug assumption. The loads are actually applied at the nozzle not at the edge of the insert plate. Therefore, the discontinuity forces and moments dampen out by the time they reach the edge of the insert plate. In addition, the size of the insert plate for this case yielded geometric parameter values that somewhat exceeded the limits of both the WRC 107 and 297 methods. Here again, using the results based on the WRC programs would have required a major redesign; whereas, the FEA results confirmed that no changes were necessary.

In summary, for the nozzle in this particular case, it was determined that the nozzle-to-insert plate and insert plate-to-shell junctions would not be overstressed considering the combination of pressure, weight, and piping loads due to thermal expansion. It was determined that the stresses at the nozzle-to-shell junction due to pressure and pressure thrust loads should be considered. However, not all analytical methods are equivalent since the various methods can yield stresses that vary by a factor of at least three. The rigid plug concept is probably too conservative, and in some cases may give erroneous results. In addition, it considered that when a nozzle is too large to be appropriately handled by the WRC methods, an FEA should be made rather than trying to “kluge” together a solution from various sources.