As noted previously, piping attached to vessels can bend or otherwise deform the vessel wall, permitting some displacement or rotation of the connection under load. Therefore, totally rigid restraint models may not be accurate representations of piping to vessel connections for example, they will probably be highly conservative when calculating nozzle loads during the expansion loading case. Where possible, a more realistic stiffness for the connection should be estimated when possible. One means of doing this is to use the Welding Research Council Bulletin 297 "Local Stresses in Cylindrical Shells Due to External Loadings on Nozzles — Supplement to WRC Bulletin No. 107", which published in August 1984 as an update to WRC Bulletin 107. This update expanded upon the work done for the evaluation of stresses in two normally intersecting cylindrical shells, but also parameterized finite element analyses done to predict nozzle flexibilities.
As noted, vessel flexibilities usually reduce loads and stresses in the piping system, so use of them is generally less conservative than using completely rigid intersections. However, in some configurations, where the use of flexibilities redistributes loads to rotating equip-ment,their use may be more conservative (and more realistic). An example is shown in Figure 3-80.
With the connection at node point 5 modeled as rigid, the loads from the thermal growth of the rack piping are taken by the nozzle and kept off of the pump battery. However, if the nozzle is truly flexible, it will deform, loading up the pump flanges. It may be necessary to perform a sensitivity study of the model to shed light on the true condition of the system. The results of modeling a system with rigid and flexible nozzles may fall in one of three regions, as shown in Figure 3-81.
In Region 1, stresses are high for both models—the model is insensitive to vessel flexibilities. A redesign of the piping or reinforcement at the intersection is needed. (This is mostly the case with smaller diameter piping and heavy vessels.)
In Region 2, stresses are high in the rigid model and low with the flexible model, indicating that the job is very sensitive to local flexibility. In this case it is necessary to take a closer look at the intersection:
Are the dimensionless parameters well within the limits of the theory? If not, vessel calculations may be way off.
Is the nozzle truly an isolated nozzle? If not, stresses near the nozzle could be much higher.
In most cases of this type the WRC 297 stiffnesses are so much smaller than the rigid stiffness the user can adjust the WRC 297 results toward stiffer junctions, (i.e., greater wall thicknesses, smaller radii) without affecting the piping solutions. Many times even a WRC 297junction 10 to 100 times stiffer than what is normally calculated will still produce similar results. In these cases the analyst can comfortably put more confidence in the WRC 297 solution providing (1) and (2) above are answered in the affirmative.
Is the local vessel model very sensitive to changes (i.e., if the "L" dimensions change, or if the reinforcing pad is left out do the stiffnesses change very much)? If so, then it is necessary to build a range of solutions to study the parameters that effect the model and try to extract the results that are most in line with the assumptions that surround each parameter being varied.
Are other stresses (i.e., those due to pressure) high? If other stresses are high then the room for error is small.
Is the material highly susceptible to cracking or corrosion? In this case, the room for error is also small.
In Region 3, stresses for both models are low. In this case there is probably no problem, need for concern, nor need for extensive time and energy to be devoted to modeling of the nozzles.
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