In order to define a vessel direction vector, you first need to designate the output data points (A-D), as defined by the WRC 107 Bulletin. The line between data points B and A defines the vessel centerline (except for nozzles on heads, where the vessel centerline has to be defined along a direction that is perpendicular to that of the nozzle). Because, in the vessel/nozzle configuration shown, point A is assigned to the bottom of the nozzle, the vessel direction vector can be written as (0.0, -1.0, 0.0), while the nozzle direction vector is (1.0, 0.0, 0.0).

The nozzle direction vector is always defined as the vector pointing from the vessel nozzle connection to the centerline of the vessel.

In the previous figure, there are two nodes occupying the same space at the nozzle/vessel surface junction: nodes 55 and 56. You can use an anchor at node 55 with a connecting node at 56 to model the local vessel flexibility as rigid.

If you are not familiar with this modeling approach, see "Piping Input" in the CAESAR II User's Guide for more details.

You can then replace the anchor with a WRC 297 local vessel flexibility model, and re-run the job to see the range of loads and displacements that exist in the system around the vessel nozzle. In either case, the restraint loads forces and moments can be obtained from the CAESAR II Restraint report. These loads reflect the action of the piping on the vessel. The following figure displays the restraint report of the rigid anchor model.

The total sustained axial load on the nozzle may not be reflected in the restraint report. A pressure thrust load contributes an additional axial load to the nozzle. The pressure thrust force always tends to push the nozzle away from the vessel. For example, with a pressure of 275 psi over the inside area of the 12-inch pipe, the total P load becomes:

P = -26 - P(A)

= -26 - 275p (122)/4

= -31,128

If needed, the P load can be adjusted automatically for the input using the WRC 107/297 analysis module. To begin the analysis, click Analysis > Components > WRC 107(537)/297/PD5500 on the main window ribbon. The software first prompts you to create a new WRC job and then prompts you to enter geometric data that describes the nozzle (Nozzle Data tab) and the vessel (Vessel Data tab), followed by loadings data (Loads Data tab).

To do a WRC 297 calculation, click , and a new tab appears on the left side of the dialog box.

You can enter up to three sets of loadings representing Sustained (SUS), Expansion (EXP), and Occasional (OCC) load cases. CAESAR II automatically performs the stress calculation of each of the load cases consecutively and then performs the WRC 107 stress summation routine to compare the computed stress intensities against the stress allowables as required in Appendix 4 of ASME Section VIII, Division 2. The focus in the current example is only on the sustained and thermal expansion cases. The loads are shown in the figure below. You can elect to leave any boxes blank if they are not applicable. If a static analysis has been performed on the system you are analyzing with WRC-107, CAESAR II can import the loads directly from the output file. To do this, click Import Loads from Job for each load case. CAESAR II reads in the loads for the nozzle node number that was specified on the Nozzle Data tab.

To run the analysis, click Local Stress Analysis on the WRC 107/297 toolbar. The software opens an output dialog box and displays the processing results.

You can also click View Report Using Microsoft Word on the WRC 107/297 toolbar to perform the initial WRC 107 calculation and summation and send the results directly to Microsoft™ Word.

After the input echo, the parameters extracted from the WRC 107 figures are printed to this report. This step is similar to collecting the data by hand. These non-dimensional values are combined with the nozzle loads to calculate the two normal and one shear stress. The stresses are reported on the outer and inner vessel surfaces of the four points A, B, C and D located around the nozzle. CAESAR II provides the normal and shear stresses and translates them into stress intensities, which can be used for comparisons against material allowables. The outputs of the stress computations are shown in the following examples. As the output shows, the largest expansion stress intensity (117485 psi) occurs at the outer surface of point B (Bu).

WRC 107 Stress Calculation for SUStained Loads

WRC 107 Stress Calculation for EXPansions Loads

WRC 107 Stress Summations: Vessel Stress Summation at Nozzle Junction

Failed items display in red.

Because the present nozzle loading causes stress intensities that are not acceptable to the ASME Section VIII, Division 2 criteria, the nozzle loading must be corrected. One option is to adjust the nozzle loading from its source; another option is to reinforce the nozzle connection on the vessel side either by increasing the vessel thickness or by adding a reinforcing pad. You can repeat the same analysis procedure until the final results are acceptable.

After a reinforcing pad is selected, the CAESAR II automatically computes the stress at the edge of the pad as well.