In order to address local allowable stresses, the endurance curve for the material of construction and complete design pressure/temperature loading information should be available. If any of the elastic limits are approached, or if there is anything out of the ordinary about the nozzle/vessel connection design, the code should be carefully consulted before performing the local stress analysis. The material Sm table and the endurance curve for carbon steels are given in this section for illustration. Only values taken directly from the code should be used in design.
There are essentially three criteria that must be satisfied before the stresses in the vessel wall due to nozzle loads can be considered within the allowables. These three criteria can be summarized as:
Pm < kSmh
Pm + Pl + Pb< 1.5kSmh
Pm + Pl + Pb + Q < 3Smavg
Where Pm, Pl, Pb, and Q are the general primary membrane stress, the local primary membrane stress, the local primary bending stress, and the total secondary stresses (membrane plus bending), respectively; and K, Smh, and Smavg are the occasional stress factor, the hot material allowable stress intensity, and the average material stress intensity (Smh + Smc)/2.
Due to the stress classification defined by Section VIII, Division 2 in the vicinity of nozzles, as given in Table 4-120.1, the bending stress terms caused by any external load moments or internal pressure in the vessel wall near a nozzle or other opening, should be classified as Q, or the secondary stresses, regardless of whether they were caused by sustained or expansion loads. This causes Pb to disappear, and leads to a much more detailed classification:
Pm - General primary membrane stress (primarily due to internal pressure)
Pl - Local primary membrane stress, which may include:
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Membrane stress due to internal pressure
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Local membrane stress due to applied sustained forces and moments
Q - Secondary stresses, which may include:
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Bending stress due to internal pressure
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Bending stress due to applied sustained forces and moments
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Membrane stress due to applied expansion forces
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Bending stress due to applied expansion forces and moments
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Membrane tress due to applied expansion moments
Each of the stress terms defined in the above classifications contains three parts: two stress components in normal directions and one shear stress component. To combine these stresses, the following rules apply:
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Compute the normal and shear components for each of the three stress types, i.e. Pm, Pl, and Q.
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Compute the stress intensity due to the Pm and compare it against kSmh.
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Add the individual normal and shear stress components due to Pm and Pl; compute the resultant stress intensity and compare its value against 1.5kSmh.
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Add the individual normal and shear stress components due to Pm, Pl, and Q, compute the resultant stress intensity, and compare its value to against 3Smavg.
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If there is an occasional load as well as a sustained load, these types may be repeated using a k value of 1.2.
These criteria can be readily found from Figure 4-130.1 of Appendix 4 of ASME Section VIII, Division 2 and the surrounding text. Note that the primary bending stress term, Pb, is not applicable to the shell stress evaluation, and therefore disappears from the Section VIII, Division 2 requirements. Under the same analogy, the peak stress limit may also be written as:
Pl + Pb + Q + F < Sa
The above equation need not be satisfied, provided the elastic limit criteria of AD-160 is met based on the statement explicitly given in Section 5-100, which is cited below:
"If the specified operation of the vessel meets all of the conditions of AD-160, no analysis for cyclic operation is required and it may be assumed that the peak stress limit discussed in 4-135 has been satisfied by compliance with the applicable requirements for materials, design, fabrication, testing and inspection of this division."
Example: Fatigue Curve (For Values of Sa)
The equations used in CodeCalc to qualify the various stress components can be summarized as follows:
Pm(SUS) < Smh
Pm(SUS + OCC) < 1.2Smh
Pm(SUS) + Pl(SUS) < 1.5Smh
Pm(SUS + OCC) + Pl(SUS + OCC) < 1.5(1.2)Smh
Pm(SUS + OCC) + Pl(SUS + OCC) + Q(SUS + EXP + OCC) < 1.5(Smc + Smh)
If some of the conditions of in ASME VIII Div.2, AD-160 are not satisfied, you probably need to perform the formal fatigue analysis. Peak stresses are required to be calculated or estimated. You may consider using AD-560, Alternative Rules for Nozzle Design instead of Article 4-6, Stresses in Openings for Fatigue Evaluation to calculate the peak pressure stress for the opening. If all conditions of AD-560.1 through AD-560.6 are satisfied, the stress indices given in Table AD-560.7 may be used. If you click the corresponding box, the software uses these pressure stress indices to modify the primary stress due to internal pressure (hoop and longitudinal stresses).
For external loads, the highest peak stress is usually localized in fillets and transitions. If you use WRC107 stress concentration factors (Kn, Kb), the fillet radius between the vessel and nozzle is required. (If a reinforcing pad is used, you can input the pad fillet radius.) The software makes a rough approximation and use WRC 107 Appendix-B equations (3) and (4) to estimate Kn and Kb. The tension and bending stresses are thus modified using Kn and Kb respectively. The software calculates the local stresses for four pairs of points (upper and lower) at the intersection. You should not direct the program to perform the stress summations. Instead, determine which stresses should be added based on locations in order to obtain the peak stress level, and then use Appendix-4 and 5 rules and fatigue curves depending on operation cycles. Based on comparisons with finite element analysis, it is known that the top tip of the fillet weld on the nozzle usually experiences the highest peak stress due to external loads.
It is conservative to add all the peak stresses after including both pressure stress indices and concentration factors. Note that the stress summation may ONLY be used to check stress intensities, not stress levels. You need the peak stress level to perform fatigue analysis. The current stress summation routine does not compare stress level with fatigue allowables according to Appendix 5. However, you may find the stress summation results useful to compare the combined effect due to the stress concentration factor and pressure stress indices.