Primary Stress vs. Secondary Stress
What Do These Terms Mean, and Why Are They Important?
A primary stress is a normal or shear stress caused by applied loads, such as pressure or weight, and needed to keep the component in equilibrium. Its fundamental characteristic is that it is not self-limiting: it does not relax as the material yields. A primary stress that exceeds the material’s yield strength by a sufficient margin will cause failure, or at least gross distortion.
A secondary stress is caused by constraint rather than by applied load. The ASME Code defines it as “a normal stress or a shear stress developed by the constraint of adjacent parts or by self-constraint of a structure.” Its fundamental characteristic is that it is self-limiting. Local yielding and minor distortion relieve the conditions that cause it, so a single application of a secondary stress is not expected to cause failure. Thermal stresses are never classified as primary; they are classified as secondary or peak.
Stresses calculated with basic design formulas are in many cases primary stresses, and are compared directly to allowable stress.
Stress Categories and Code Limits
The Code divides primary and secondary stress into subcategories, each with its own limit. The table below summarizes them for the elastic analysis method in Section VIII, Division 2.
| Category | Symbol | Typical source | Limit |
|---|---|---|---|
| General primary membrane | Pm | Pressure or mechanical load averaged through the wall, away from discontinuities | Pm ≤ S |
| Local primary membrane | PL | Membrane stress from applied load near a discontinuity, such as a nozzle-to-shell junction | PL ≤ 1.5S |
| Primary membrane plus bending | PL + Pb | Bending from applied load, such as pressure on a flat head | PL + Pb ≤ 1.5S |
| Primary plus secondary | PL + Pb + Q | Constraint at gross discontinuities, thermal gradients | Range ≤ SPS (generally 3S) |
| Peak | F | Local stress concentrations at notches, fillets, and weld toes | No static limit; evaluated in the fatigue analysis |
S is the allowable stress at design temperature. SPS may be taken as the larger of 3S and 2Sy in some cases. Limits summarized from Section VIII, Division 2, paragraphs 5.2.2 and 5.5.6; see the current edition of the Code for exceptions and complete requirements.
Why Classification Matters in Finite Element Analysis
Finite Element Analysis (FEA) gives a detailed picture of how stress is distributed through a component. FEA calculates the stresses accurately, but it does not categorize them. To compare results against Code limits, the analyst has to separate the stress into the categories above. Linearization can separate membrane, bending, and peak stress through the wall. Whether a stress is primary or secondary, which depends on whether it is caused by applied load or by constraint, is a judgment the analyst must make.
Mistakes in either direction matter. Treating secondary stress as primary produces an overdesigned, more expensive component. Treating primary stress as secondary is unconservative, and can approve a design that will not carry its load. This error is most likely in redundant structures, where load can take more than one path and the correct classification is not obvious. Bill O’Donnell Sr. addressed this problem directly in “Primary Stress Evaluations for Redundant Structures.”
Current editions of Section VIII, Division 2 also allow elastic-plastic analysis, which avoids stress classification entirely, but it demands more of the model and the analyst. The Code also covers material properties, fatigue analysis, and limit load methods, much of which is useful beyond pressure vessel design. See www.asme.org.
O’Donnell Consulting performs finite element analysis of structures to AWS, API, and ASME codes.
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