MODELING NOZZLE FLEXIBILITY The addition of a nozzle flexibility element is meant to model the vessel shell flexibility. Assuming a rigid nozzle would attract too large of reaction forces at the nozzle and would be too conservative for vessel design. AutoPIPE nozzle flexibility element makes it very easy to estimate shell flexibility using several methods. For cylindrical vessels, the WRC297 and Bijlaard are the preferred methods. For cylindrical tanks with large diameters (order of 100 feet), the API 650 method is the preferred method.

For reduced tee branches, the ASME class I piping formula is appropriate. For nozzles on spherical or tori-spherical heads, the Spherical method is the most appropriate and is based on Bijlaard and is also part of the BD5500 British piping code.

The nozzle element is a modified and simplified expansion joint element. While the expansion joint element has 6 stiffnesses, the nozzle element will have only 3 stiffnesses. The three stiffness are, radial, circumferential bending and longitudinal bending stiffnesses. Two shear and torsion stiffnesses are not applied to the nozzle element. Also for the nozzle element, the radial load due to pressure is not added as in the case of the flexible joint. The radial pressure thrust can be added automatically in WinNozl when calculating nozzle stresses.

When modeling the nozzle, the length between the nozzle flange and vessel wall should be modeled as a pipe element. The nozzle element should always be short; and the shorter it is the more accurate the model. It should be centered at the wall of the shell since it is meant to model the bending flexibility of the shell wall. The best way to model the nozzle flexibility element is to start it at outer face of the vessel and end it the inner face. The total length would then be the vessel thickness

AutoPIPE will not calculate stresses in the nozzle or the connected vessel. It is recommended that the anchor reaction forces calculated in AutoPIPE be used in WinNozl for evaluating nozzle as well as vessel or shell stresses per the applicable ASME Div I or II, BD5500, KHK and API 650 codes.

AutoPIPE can transmit these forces directly to WinNozl to minimize errors.

Pressure Thrust on Vessel/Nozzle Junctions Typical vessel/nozzle configuration showing the pressure thrust acting the nozzle and interconnecting pipework.

Anchor or Axial Support

Pressure Thrust

AB

C

Figure 1

Where: 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

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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.

Pressure Thrust (P*A)

Figure 2

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 So: F = δ1 * K1 + δ2 * K2 Since, δ1 = δ2, let’s denote it by δ: So: 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.

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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. Pressure Thrust Guidelines 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. WinNOZL WRC368 within its geometric limits provides a good design check of pressure stress levels which includes the full thrust load otherwise use FEA 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 FEA would generally be the most accurate analysis tool to evaluate. Note: FEA 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.

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