AutoPIPE Nozzle is based on industry proven empirical methods of Welding Research Council (WRC) Bulletins 107, 297 and 368 provide, for calculating stresses at the vessel /nozzle junction.
In the past many local stress designs have ignored the pressure intensification at Nozzle to vessel junctions and currently only PD5500 uses pressure intensification. The pressure vessel research council (WRC) has published guidelines in their workshop proceedings dated February'98 titled "Nozzle Attachment Design Analysis: ASME code and WRC Bulletins 107, 297 & 368". In particular WRC 368 based on the results of a parametric study using the FAST2 computer program which examines the stress intensity in the nozzle and shell considering internal pressure and the full pressure thrust loading on the nozzle. WRC368 only examines cylinder-cylinder intersections within its geometric limits but includes a comparison with FE results which shows relatively close agreement.
For the design of cylinder intersections subjected to internal pressure, the ASME Boiler and Pressure Vessel Code and most other codes, have basically relied on "area-replacement" rules. These rules, based on replacing the cutout material in the pressure boundary within certain limits, assure that the average membrane stress in the vicinity of the opening is approximately the same as the stress in the unperturbed shell. Such rules do not account for local membrane, bending stresses, and secondary stresses.
The WRC 368 method provides the maximum value of general and local membrane stress intensity ( Pm+PL) and membrane + bending stress intensity (Pm+PL+Q) and will certainly be conservative where only a fraction of the thrust load is acting on the nozzle
Pressure Thrust on Vessel/Nozzle Junctions.
Typical vessel/nozzle configuration showing the pressure thrust acting the nozzle and interconnecting pipework.
P = Internal design or operating pressure of the vessel and piping.
A = Inside pipe area of the nozzle.
The pressure thrust of concern is P*A acting on the “upstream” elbow in a outward radial direction from the vessel nozzle. The balancing force (P*A) acts on the vessel wall opposite to the nozzle as shown in Figure 1. It is assumed this P*A acting on the vessel is resisted by the vessel support and not considered in this load evaluation. The load on the vessel-nozzle junction will be a function of the stiffness between the vessel anchor and load (including any nozzle flexibilities) (i.e. K1(x) , Spring 1), and the stiffness of the system (acting in the X direction) upstream of the thrust load (i.e. K2(x), Spring 2) as shown in figure 2 below.
The force F is in equilibrium with the two spring forces F1 and F2:
F = F1 + F2 (1)
The spring stiffness K and the displacement δ can be related as:
K1 = F1 / δ1
K2 = F2 / δ2
F = δ1 * K1 + δ2 * K2
Since, δ1 = δ2, let’s denote it by δ:
F = δ * ( K1 + K2 )
δ = F / ( K1 + K2 )
Pressure thrust load on the vessel-nozzle junction:
F1 = F * K1 / ( K1 + K2 ) (2)
If the piping system on the other side of the applied load (Spring 2) is stiff, for example due to an anchor, then pressure thrust will be absorbed by the anchor. Thus, the nozzle will experience very little direct axial stress. This can be seen from equation 2. Note that a greater K2 results in a lower thrust force F1. Therefore, in this case including all of the pressure thrust into analysis will be conservative. However if the pipe shown by spring 2 is flexible (maybe an expansion loop or small diameter pipe with bends) then the nozzle will see more of the force due to the pressure thrust. Therefore it is appropriate to analyze the local vessel/nozzle stresses due to most of the pressure thrust load.
See Pressure_Thrust.dat model (segment E) which shows a simplified flexible 8” STD wt piping to the vessel model similar to figure 1 above and the anchor results at E01 show most of the pressure thrust transferred to the anchor.
Note: If the nozzle has a blind or blank flange then it will experience the entire force due to the pressure thrust. Hence, the amount of pressure thrust acting on a nozzle depends on
the structural response of the system due to the pressure load. If the appropriate pressure thrust loads are applied to the piping and are analyzed, the structural load at the nozzle due to pressure can be calculated as shown in model Pressure_Thrust.dat.
Note: AutoPIPE does not automatically include piping loads due to pressure except for the pressure effect on expansion joints. The longitudinal pressure stress is calculated and added to the code compliance piping stresses.
1. Vessel nozzle has a blind or blank flange.
2. Straight run of pipe to an elbow, with no intermediate restraints. The pressure thrust load (PA) load acting on the elbow will be resolved at the nozzle and should be evaluated. See Figure 1
3. Straight run of ‘rigid’ pipe to a pump (or tied bellows unit in this line). The pressure thrust load (PA) load acting on the elbow will be balanced by PA load acting on the ‘rigid’ pump casing. Therefore F1= 0 resolved at the pump base anchor. See Figure 4. Note: If an un-tied axial bellows in the pump discharge line then pump base anchor will see the full PA. Both suction and discharge lines need to be examined.
4. Straight run of pipe to an elbow, with intermediate no-gap axial linestop restraint. The pressure thrust load (PA) load acting on the elbow will be resolved at the linestop. See Figure 5. Therefore, pressure thrust load effect at the nozzle = 0.
5. Straight run of pipe to an elbow, with an intermediate untied axial expansion joint. The expansion joint is too flexible to transmit load, so the pressure thrust load (PA) will be resolved at restraints upstream of the elbow. Therefore, pressure thrust load effect at the nozzle = 0 or small value based on expansion stiffness and movement. If the expansion joint was tied or hinged, you would include the pressure thrust at the nozzle.
If the combined (membrane + bending) stresses exceed the allowable stress with the applied full (pressure thrust option under combinations Load TAB) or partial (applied load with correct sign under LOADS TAB) thrust load then it is suggested to check the membrane and combined (secondary ) stress levels with WRC368 option enabled and thrust load (or option) removed.
WRC368 within its geometric limits provides a good design check of pressure stress levels which includes the full thrust load otherwise use FE analysis to obtain more accurate combined stresses.
If the full pressure thrust is acting on the vessel/nozzle junction e.g. nozzle with a blind flange then FE would generally be the most accurate analysis tool to evaluate.
1. The option "Include Pressure Thrust in Gr, HY Case" in the load Combination - Load Case tab is generally an over-conservative option which pressure thrust in the radial load of the gravity case GR and Hydrotest case HY.
2. FE programs have limitations due to the accuracy of the type of elements used e.g. many programs use thin shell elements which do not capture transverse shear effects of thick shell elements.