126.96.36.199 Calculation of Vessel Stresses Due to Nozzle Loads
The Welding Research Council Bulletin No. 107 (WRC 107) has been used extensively since the mid 60's by design engineers to estimate local stresses in vessel/attachment junctions.
Welding Research Council Bulletin 107 is a parameterization of the results of a set finite element analyses examining stresses in vessels due to loaded attachments. WRC 107 contains equations and non-dimensional curves (based upon parameters such as ratios of the nozzle to vessel diameter and the vessel diameter to vessel thickness) which are used to extract coefficients for the calculation of stresses in the vessel wall at the point of attachment. Note that WRC 107 computes stresses in the vessel shell at the nozzle/vessel interface — stresses in the nozzle wall (which in some cases can be higher than the stresses in the vessel wall) are not computed. Stresses in the nozzle wall may become greater than the stresses in the vessel wall as the t/T (nozzle to vessel thickness) ratio becomes less than one.
WRC 107 may be used to analyze cylindrical or spherical vessel at attachments. The attachments may be round, square, or rectangular; the round and square attachments may be solid or hollow (i.e., a round hollow attachment represents a pipe or nozzle connection), while only solid rectangular attachments (Lugs) are considered—the nozzle thickness does not effect the calculation. Appendix B to WRC 107 provides information on weldment stress intensification factors. Applications include vessel nozzles, pipe junctions, welded lugs and trunnions.
The techniques introduced in this bulletin were updated and extended in WRC Bulletin 297, which may be used in a similar way as that explained here.
The convention adopted by WRC 107 to define the applicable orientations of the applied loads and stresses for both spherical and cylindrical vessels are shown in Figure 3-68.
The WRC 107 bulletin is used as follows. Based upon various dimensional ratios of the vessel/nozzle configuration, the engineer selects 12 dimensionless parameters from as many different figures in the bulletin. These 12 parameters are used with local loads in 15 equations to calculate 80 different stresses — circumferential membrane, circumferential bending, longitudinal membrane, longitudinal bending, and shear stresses (in two directions)at each of eight locations in the vessel. These eight locations are the at the inner and outer edges (identified by the subscripts 1 and u respectively) of the vessel, at the 0°, 90°, 180°, and 270° azimuth (identified as Figure 3-68 locations A, D, B, and C respectively) around the nozzle.
It has also been a common practice to use WRC 107 to conservatively estimate vessel shell stress state at the edge of a reinforcing pad, if any. The vessel wall stress at the edge of a nozzle reinforcing pad can be obtained by considering a solid plug (solid inclusion), whose outside diameter is equal to the O.D. of the reinforcing pad, subjected to the same nozzle loading.
Before attempting to use WRC 107 to evaluate the stress state of any nozzle / vessel junction, one shall always make sure that the geometric restrictions limiting the application of WRC 107 are not exceeded. These are dependent on the configuration and curves used (see Appendix A.2 of WRC 107 for details). The CAESAR II WRC 107 module notifies the user when the bounds of the curves are exceeded.
The WRC 107 method should NOT be used when the nozzle is very light or when dimensionless parameters fall outside the limits of their respective figures. The parameters in the WRC 107 figures should not be unreasonably exceeded. Output from the WRC 107 program includes the figure numbers for the curves accessed, the curve abscissa, and the values retrieved. The user is urged to check these outputs against the actual curve in WRC 107 to get a "feel" for the accuracy of the stresses calculated. For example, if parameters for a particular problem are always near or past the end of the figures curve data, then the calculated stresses may not be reliable.
The WRC 107 program can be actived from the Main Menu. The user will be prompted for a job name as shown in the figure below.
After the user selects WRC 107 option, the processor will request an input file name, this entry will also be used for the subsequent output files. The user is then presented with a list of the current units used by CAESAR II. Input for an existing WRC 107 calculation data will always be referred to in its original units setting. If these units are not acceptable, a different unit set must be identified using the DATABASE configuration.
The input data is accumulated by the processor in six spreadsheets. The first sheet is a title block, the second and third sheets collect the vessel and the nozzle (attachment) geometry data, respectively. The nozzle loading is specified on the last three spreadsheets, according to specific load cases, which are sustained, expansion and occasional cases. These loads are found in the CAESAR II output restraint load summary under the corresponding load cases.
The WRC 107 specific input coordinate system has been incorporated into the program. The user only needs to define two vectors specified on the geometry data sheets. The first vector defines the direction of the centerline of the vessel where postitve is from "B" to "A". The second vector defines the direction of the piping/nozzle orientation, with the positive direction of this vector pointing from the nozzle connection towards the vessel centerline. Note, these two vectors must be perpendicular to each other. There is no need to convert the CAESAR II global loads to the local WRC 107 orientation.
Notice that the curves in WRC Bulletin 107 cover essentially all applications of nozzles in vessels or piping; however, should any of the interpolation parameters, i.e. Beta, etc. fall outside the limits of the available curves, some extrapolation of the WRC method must be used. The current default is to use the last value in the particular WRC table. If one wishes to control the extrapolation methodology interactively, you may do so by changing the WRC 107 default from "USE LAST CURVE VALUE" to "INTERACTIVE CONTROL" in the Computation Control option located inside the Configure-Setup module of the MAIN MENU. Once again, data beyond the limits of the bulletin curves should be treated with skepticism.
The following page was reprinted from WRC Bulletin 107 to illustrate how the specified data is used to calculate the stress intensitites at the eight points on the vessel around the nozzle. In the event that a reinforcing pad is defined around the nozzle, the corresponding vessel stresses at the edge of the reinforcing pad will be calculated automatically using the rigid plug assumption discussed earlier.
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