Stress and Fatigue Analysis of Bellows
What is a Primary Stress?
Most engineers are familiar with the terms “Normal Stress”, “Shear Stress” and potentially “Equivalent Stress.” However perhaps not so much with the terms “Primary Stress” and “Secondary Stress”. What do these terms mean and why are they important?
“Primary Stress” is a term likely first used by the ASME Boiler and Pressure Vessel (B&PV) Code (1) Section VIII, regarding a particular type of stress to be evaluated in the design of pressure vessels and other pressure-retaining components. Per the 1971 Edition of the Code, a “Primary Stress” is defined as: “A normal stress or a shear stress developed by the imposed loading which is necessary to satisfy simple laws of equilibrium of external and internal forces and moments.”
The basic characteristic of a primary stress is that it is not self-limiting. Primary stresses which considerably exceed the material yield strength will result in failure or at least, in gross distortion. A thermal stress is not classified as a primary stress.
Although not specifically stated as such, the concept of a primary stress applies mostly for the structural design of components. Stresses calculated using basic engineering design formulas are in many cases primary stresses. These stresses are often evaluated against a percentage of the yield stress of the material of construction as part of the design process.
A stress that is not “Primary” may be classified instead as “Secondary.” According to the ASME Code, a Secondary Stress is defined as: “A normal stress or a shear stress developed by the constraint of adjacent parts or by self-constraint of a structure. The basic characteristic of a Secondary Stress is that it is self-limiting. Local yielding and minor distortions can satisfy the conditions which cause the stress to occur and failure from one application of the stress is not to be expected.”
Further sub-categories of each of these types of stresses are discussed in the Code.
The distinction between these types of stresses is important for the design of efficient structures. This is especially important considering the now common use of simulation methods as Finite Element Analysis (FEA).
These design-by-analysis methods provide very detailed information about the distribution of stresses in a component or structure, but can make it more difficult to properly assess whether or not a design is satisfactory (e.g. when comparing stresses against a defined limit) than the use of traditional design-by-formula approaches. Use of stresses directly from a finite element analysis without a Primary vs. Secondary classification may result in overdesign.
Additional information on Primary and Secondary Stress classifications and assessments of the same can be found in the ASME Code. The Code contains a wealth of information for the design of pressure retaining components that may also be useful in the design of general components. There is an extensive database of steel material properties and practical methods for fatigue analysis and efficient component design using limit load analysis methods. See more at www.asme.org.
(1) Per the ASME website, the first ASME B&PV Code was published in 1914-1915 and was the first comprehensive standard for the design, construction, inspection, and testing of boilers and pressure vessels.
Read about the History of the ASME Code.
See a summary of Bill O’Donnell Sr.’s paper “Primary Stress Evaluations for Redundant Structures.”
O’Donnell Consulting Engineers performs (thermal, stress, vibration and fatigue) analysis of equipment to Codes including API, AWS and ASME.
@ O’Donnell Consulting Engineers