# 3.4.2.3 Evaluating Vessel Stresses in CAESAR II

The ASME Section VIII, Division 2 code provides for a fairly elaborate procedure to analyze the local stresses in vessels and nozzles. Only the elastic analysis approach will be discussed in this manual. The user should always refer to the applicable code if any of the limits described in this section are approached, if any unusual material, weld, or stress situation exists, or if there are non-linear concerns such as the material's operation in the creep range.

The first step in the procedure is to determine if the elastic approach is satisfactory. Section AD-160 contains the exact method and basically states that if all of the following conditions are met, then the elastic approach is sufficient and fatigue analysis need not be done:

The expected design number of full-range pressure cycles does not exceed the number of allowed cycles corresponding to an Sa value of 3Sm (4Sm for non-integral attachments) on the material fatigue curve. The Sm is the allowable stress intensity for the material at the operating temperature.

The expected design range of pressure cycles other than startup or shutdown must be less than 1/3 (1/4 for non-integral attachments) the design pressure times (Sa/Sm), where Sa is the value obtained on the material fatigue curve for the specified number of significant pressure fluctuations.

The vessel does not experience localized high stress due to heating.

The full range of stress intensities due to mechanical loads (including piping reactions) does not exceed Sa from the fatigue curve for the expected number of load fluctuations.

Once the user has decided that an elastic analysis will be satisfactory, the comprehensive approach as used in the **CAESAR II** local stress evaluation is appropriate. This method will be described in detail below, after a discussion of the Section VIII Div. 2 Requirements.

**ASME Section VIII Division 2 - Elastic Analysis of Nozzle**

Ideally in order to address the local allowable stress problem, the user should have the endurance curve for the material of construction and complete design pressure / temperature loading information. 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:

Where Pm Pl, Pb, and Q are the general primary membrane stress intensity, the local primary membrane stress intensity, the local primary bending stress intensity, and the total secondary stress intensity (membrane plus bending), respectively; and k, Smh, and Smavg are the occassional stress factor, the hot material allowable stress, and the average material allowable stress intensity (Smh + Smc) / 2

Due to the stress classification defined by Section VIII, Division 2 in the vicinity of nozzles, as given in the 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 intensity (primarily due to internal ); Pl - Local primary membrane stress intensity, which may include: pressure

Membrane stress due to internal pressure;

Local membrane stress due to applied sustained forces and moments.

Q - Secondary stress intensity, which may include:

Bending stress due to internal pressure;

Bending stress due to applied sustained forces and moments;

Membrane stress due to applied expansion forces;

Bending stress due to applied expansion forces and moments

Membrane stress due to applied expansion moments

Each of the stress terms defined in the above classifications contain three parts: two stress components in normal directions and one shear stress component. To combine these stresses, the following rules apply:

1) Compute the normal and shear components for each of the three stress intensities,i.e. Pm, Pl, and Q;

2) Compute the stress intensity due to the Pm and compare it against kSmh;

3) Add the individual normal and shear stress components due to Pm and Pl; compute the resultant stress intensity and compare its value against 1.5 kSmh;

4) 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.

5) 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, P^, 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 + Q + F < Sa

where: F represents fatigue stresses.

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."

**Procedure to Perform Elastic Analyses of Nozzles **

The procedure for checking stresses in vessel shells using WRC 107 can be summarized as follows:

**Step 1**- Check that no geometric limitations invalidate the use of WRC 107;**Step 2**- If WRC 107 is applicable, check to see whether or not the elastic approach as outlined in Section VIII, Division 2, AD-160 is satisfactory;**Step 3**- Compute the sustained, expansion and occasional loads in the vessel shell due to the applied nozzle loads. Consider the local restraint configuration in order to determine whether or not the axial pressure thrust load (P * Ajn) should be added to the sustained (and/or occasional loads). If desired by the user, this thrust load will be automatically calculated and added to the applied loads.**Step 4**- Calculate pressure stresses, Pm, on the vessel shell wall in both longitudinal and circumferential (hoop) directions for both sustained and occasional cases. Notice that two different pressure terms are required in carrying out the pressure stress calculations. P is the design pressure of the system (sustained),while Pvar is the DIFFERENCE between the peak pressure and the design pressure of the system, which will be used to qualify the vessel membrane stress under the occasional load case. Note that the Pm stresses will be calculated automatically if a pressure value is enter by the user.**Step 5**- Run WRC 107 to calculate the Pi, and Q stresses as defined earlier. Note that the local stresses due to sustained, expansion and occasional loads can be computed simultaneously.**Step 6**- Various stress components can be obtained from combining the stress intensities computed from applying the sustained, expansion and occasional loads. These stress intensities can then be used to carry out the stress summations and the results are used to determine acceptability of the local stresses in the vessel shell. Notice now**CAESAR II**can provide the WRC 107 stress summation module in line with the stress calculation routines

Under the above procedure, the equations used in **CAESAR II** to qualify the various stress components can be summarized as follows:

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